This experiment aims to demonstrate single-photon interference using a polarization interferometer. It will show that a single photon can interfere with itself by taking two possible paths through the interferometer toward detectors B and B'. This experiment implements Richard Feynman's thought experiment of electrons passing through a double slit. The results are expected to show that the number of photon detections at B and B' cannot be expressed as the simple sum of detections from each path alone, demonstrating wavelike behavior of individual photons.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes a research article that investigates relativistic effects on the linear and nonlinear propagation of electron plasma waves in dense quantum plasma with arbitrary temperature. The key points are:
1) A quantum hydrodynamic model is used to study how relativistic effects from streaming motion impact electron plasma waves in a finite-temperature quantum plasma.
2) Both compressive and rarefactive solitons can form in the plasma depending on factors like electron degeneracy and streaming velocity, when relativistic effects are considered.
3) Relativistic effects are found to significantly influence the linear and nonlinear properties of electron plasma waves in this dense, finite-temperature quantum plasma system.
Quantum jumps of light recording the birth and death of a photon in a cavityGabriel O'Brien
This document summarizes an experiment that observed quantum jumps in the photon number inside a superconducting cavity. Key points:
- Microwave photons were stored in a superconducting cavity for up to half a second and repeatedly probed by non-absorbing atoms passing through.
- An atom interferometer measured the atomic phase shift induced by the non-resonant cavity field, revealing the presence or absence of a single photon.
- Sequences of hundreds of correlated atom measurements were interrupted by sudden changes, recording the creation and destruction of individual photons over time.
- This realized a quantum non-demolition measurement of the photon number in the cavity in real time, allowing observation of its
In search of multipath interference using large moleculesGabriel O'Brien
This document summarizes an experiment that tested the quantum mechanical principle of superposition using large dye molecules. The experiment measured interference patterns when the molecules passed through single, double, and triple slits. It observed less than 1% deviation from the expected interference patterns based on quantum mechanics, providing evidence that the superposition principle applies even to massive particles like these large molecules. The experiment is one of the first to directly observe quantum interference using massive particles rather than light or single particles.
This document summarizes a research project that involves building a toy model of particle collisions using C++ and ROOT. The model simulates collisions by sampling probability distributions measured in real collisions. It generates particles and assigns them properties like momentum and angle. It also models physical processes like jet production and elliptic flow. The goal is to study how properties of particles like jets are affected by a quark-gluon plasma and vice versa. The model allows tuning parameters to learn about collision interactions and switch physics processes on or off.
The document discusses reciprocal lattices and X-ray diffraction from crystal structures. It begins by introducing the concept of a reciprocal lattice as the Fourier transform of a direct lattice, allowing crystal vibrations and electron waves to be expressed as sums of plane waves. Specific examples are given for simple cubic, body-centered cubic, and face-centered cubic crystal structures and their corresponding reciprocal lattices. Bragg's law and the Laue condition for X-ray diffraction are derived from considerations of interference between waves scattered from crystal planes. The structure factor is introduced to account for interference between waves scattered from multiple atoms within a crystal's unit cell.
Quantum teleportation allows the transfer of quantum states between particles at a distance without physically transporting the particles themselves. It relies on the phenomenon of quantum entanglement where the quantum states of particles become linked even when separated spatially. The experiment demonstrated successful quantum teleportation of photons' polarization states between two locations, confirming the non-local effects predicted by quantum mechanics. This technique could enable future applications for quantum communication but does not allow the teleportation of macroscopic objects as depicted in science fiction.
Ultracold atoms in superlattices as quantum simulators for a spin ordering mo...Alexander Decker
This document discusses using ultracold fermionic atoms in optical lattices to simulate spin ordering models. It begins by describing how atoms can be trapped in optical lattices using laser light. It then proposes how a spin ordering Hamiltonian could be used to achieve superexchange interaction in a double well system. Finally, it suggests going beyond double wells to study resonating valence bond states in a kagome lattice, which could provide insights into phenomena like high-temperature superconductivity.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes a research article that investigates relativistic effects on the linear and nonlinear propagation of electron plasma waves in dense quantum plasma with arbitrary temperature. The key points are:
1) A quantum hydrodynamic model is used to study how relativistic effects from streaming motion impact electron plasma waves in a finite-temperature quantum plasma.
2) Both compressive and rarefactive solitons can form in the plasma depending on factors like electron degeneracy and streaming velocity, when relativistic effects are considered.
3) Relativistic effects are found to significantly influence the linear and nonlinear properties of electron plasma waves in this dense, finite-temperature quantum plasma system.
Quantum jumps of light recording the birth and death of a photon in a cavityGabriel O'Brien
This document summarizes an experiment that observed quantum jumps in the photon number inside a superconducting cavity. Key points:
- Microwave photons were stored in a superconducting cavity for up to half a second and repeatedly probed by non-absorbing atoms passing through.
- An atom interferometer measured the atomic phase shift induced by the non-resonant cavity field, revealing the presence or absence of a single photon.
- Sequences of hundreds of correlated atom measurements were interrupted by sudden changes, recording the creation and destruction of individual photons over time.
- This realized a quantum non-demolition measurement of the photon number in the cavity in real time, allowing observation of its
In search of multipath interference using large moleculesGabriel O'Brien
This document summarizes an experiment that tested the quantum mechanical principle of superposition using large dye molecules. The experiment measured interference patterns when the molecules passed through single, double, and triple slits. It observed less than 1% deviation from the expected interference patterns based on quantum mechanics, providing evidence that the superposition principle applies even to massive particles like these large molecules. The experiment is one of the first to directly observe quantum interference using massive particles rather than light or single particles.
This document summarizes a research project that involves building a toy model of particle collisions using C++ and ROOT. The model simulates collisions by sampling probability distributions measured in real collisions. It generates particles and assigns them properties like momentum and angle. It also models physical processes like jet production and elliptic flow. The goal is to study how properties of particles like jets are affected by a quark-gluon plasma and vice versa. The model allows tuning parameters to learn about collision interactions and switch physics processes on or off.
The document discusses reciprocal lattices and X-ray diffraction from crystal structures. It begins by introducing the concept of a reciprocal lattice as the Fourier transform of a direct lattice, allowing crystal vibrations and electron waves to be expressed as sums of plane waves. Specific examples are given for simple cubic, body-centered cubic, and face-centered cubic crystal structures and their corresponding reciprocal lattices. Bragg's law and the Laue condition for X-ray diffraction are derived from considerations of interference between waves scattered from crystal planes. The structure factor is introduced to account for interference between waves scattered from multiple atoms within a crystal's unit cell.
Quantum teleportation allows the transfer of quantum states between particles at a distance without physically transporting the particles themselves. It relies on the phenomenon of quantum entanglement where the quantum states of particles become linked even when separated spatially. The experiment demonstrated successful quantum teleportation of photons' polarization states between two locations, confirming the non-local effects predicted by quantum mechanics. This technique could enable future applications for quantum communication but does not allow the teleportation of macroscopic objects as depicted in science fiction.
Ultracold atoms in superlattices as quantum simulators for a spin ordering mo...Alexander Decker
This document discusses using ultracold fermionic atoms in optical lattices to simulate spin ordering models. It begins by describing how atoms can be trapped in optical lattices using laser light. It then proposes how a spin ordering Hamiltonian could be used to achieve superexchange interaction in a double well system. Finally, it suggests going beyond double wells to study resonating valence bond states in a kagome lattice, which could provide insights into phenomena like high-temperature superconductivity.
1) The document discusses the classical theory of electromagnetic radiation confined within an isothermal enclosure and the discrepancies with experimental observations.
2) It analyzes the temperature dependence of the energy density and pressure of the radiation using thermodynamic considerations.
3) This leads to the derivation of the Stefan-Boltzmann law relating the emissive power of a black body to the fourth power of its temperature.
Basic and fundamental of quantum mechanics (Theory)Halavath Ramesh
Quantum mechanics arose in the early 20th century to explain experimental phenomena that classical mechanics could not, such as black body radiation and the photoelectric effect. The document discusses the origins and fundamental concepts of quantum mechanics, including the dual wave-particle nature of matter and light, the uncertainty principle, and Schrodinger's formulation of quantum mechanics using wave functions and his time-independent equation. It explains that wave functions provide probabilistic information about finding particles in particular regions rather than definite trajectories, replacing Bohr's orbital model.
Fundamentals of modern physics by imran azizDr.imran aziz
The document discusses several key concepts in modern physics including:
1) Classical relativity and reference frames in Newtonian physics.
2) The Michelson-Morley experiment and failures to detect the luminiferous ether.
3) Einstein's theory of special relativity and concepts like simultaneity, time dilation, and length contraction.
4) Wave-particle duality of light and matter like electrons.
A. Morozov - Black Hole Motion in Entropic Reformulation of General RelativitySEENET-MTP
1. The document considers describing the motion of black holes using an entropic action equal to the sum of the areas of black hole horizons.
2. It is shown that this description is consistent with Newton's laws of motion and gravity, up to unknown numerical coefficients.
3. Evaluating these dimensionless coefficients precisely is important for advancing the entropic reformulation of general relativity beyond pure dimensional arguments.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
This document provides an overview of density functional theory and methods for modeling strongly correlated materials. It discusses the limitations of standard DFT approaches like LDA for strongly correlated systems and introduces model Hamiltonians and correction methods like LDA+U, LDA+DMFT, self-interaction correction, and generalized transition state to better account for electron correlation effects. The document outlines the basic theory and approximations of DFT, including Kohn-Sham equations and the local density approximation, and discusses basis set approaches like plane waves, augmented plane waves, and pseudopotentials.
Could humans recognize odor by phonon assisted tunnelingVorname Nachname
This document discusses a proposed physical mechanism for how humans could recognize odors through phonon-assisted tunneling. The mechanism involves inelastic electron tunneling between donor and acceptor sites in olfactory receptors that is mediated by the absorption or emission of odorant molecule phonons. The document evaluates the viability of this proposed mechanism using theoretical models and estimates of parameter values. It finds that the mechanism is physically plausible and consistent with observed features of the sense of smell, provided olfactory receptors have certain general properties that allow electron transfer on appropriate timescales.
This thesis examines the linear response kernel in Conceptual Density Functional Theory. The linear response kernel is defined as the second derivative of the electronic energy with respect to the external potential, and provides insight into a system's inherent reactivity. The author evaluates the linear response kernel for atoms from hydrogen to argon using the Independent Particle Approximation and Coupled Perturbed Kohn-Sham approach. Spin-polarized versions are also investigated. The relationship between linear response and polarizability is explored, allowing definition and evaluation of local polarizability. Finally, static and dynamic linear response are compared using Time-Dependent DFT and the Sternheimer equations.
phonon as carrier of electromagnetic interaction between lattice wave modes a...Qiang LI
The new results reported here mainly include: 1) recognition that phonon is carrier of electromagnetic interaction between its lattice wave mode and electrons; 2) recognition that binding energy of electron pairs of high-temperature superconductivity is due to escape of optical threshold phonons, of electron pairs at or near Fermi level, from crystal by direct radiation; 3) recognition that binding energy of electron pairs of low-temperature superconductivity is possibly due to escape of non-optical threshold phonons by anharmonic crystal interactions; and, 4) recognition of a possible mechanism explaining why some crystals never have a superconducting phase. While electron pairing is phonon-mediated in general, HTS should be associated with electron pairing mediated by optical phonon at or near Fermi level (EF), so the rarity of HTS corresponds to the rarity of such pairing match.
1. The document discusses the derivation of de Broglie's equation relating the wavelength of matter waves to the momentum of particles. It then derives different forms of de Broglie's wavelength equation using kinetic energy and potential energy.
2. It lists properties of matter waves including that lighter particles have greater wavelengths. It derives the Schrodinger time-independent and time-dependent wave equations.
3. It applies the time-independent equation to a particle in an infinite square well, finding the wavefunctions and energy levels based on boundary conditions and normalization.
This document discusses voltammetry, an electroanalytical technique used in qualitative and quantitative analytical chemistry. It introduces the basic concepts and principles of voltammetry, including instrumentation, excitation signals, types of voltammetry, and features of voltammograms. Specifically, it discusses the fundamentals of voltammetric cells, electrodes, hydrodynamic voltammetry, and common shapes of voltammograms including linear scan and peak voltammograms. The overall purpose is to explain the fundamental concepts and applications of voltammetry as an analytical technique.
The document summarizes key aspects of the Standard Model of particle physics. It describes how the Standard Model accounts for fundamental particles like quarks and leptons that interact via four fundamental forces - gravitation, electromagnetism, weak force, and strong force. These interactions are mediated by exchange of spin-1/2 bosons. The Standard Model has been very successful in explaining experimental observations, but questions remain like incorporating gravity and the origin of particle masses.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
1. The document proposes a new experiment involving entanglement and gravitational decoherence using a dual Mach-Zehnder interferometer setup.
2. In the proposed experiment, one interferometer would be placed in a gravitational field, while the other would not. This would result in non-unitary evolution and allow for nonlocal signaling between the two locations.
3. By moving his interferometer in and out of the gravitational field, one experimenter could encode and transmit binary messages to the other, who could decode the messages by observing changes in interference patterns resulting from the non-unitary evolution.
41 Limits on Light-Speed Anisotropies from Compton Scattering of High-Energy ...Cristian Randieri PhD
Limits on Light-Speed Anisotropies from Compton Scattering of High-Energy Electrons -The American Physical Society, Physical Review Letters, June 2010, Vol. 104, N. 24, pp. 241601-1-241601-5, ISSN: 0031-9007, doi: 10.1103/PhysRevLett.104.241601
di J. P. Bocquet, D. Moricciani, V. Bellini, M. Beretta, L. Casano, A. D'Angelo, R. Di Salvo, A. Fantini, D. Franco, G. Gervino, F. Ghio, G. Giardina, B. Girolami, A. Giusa, V. G. Gurzadyan, A. Kashin, S. Knyazyan, A. Lapik, R. Lehnert, P. Levi Sandri, A. Lleres, F. Mammoliti, G. Mandaglio, M. Manganaro, A. Margarian, S. Mehrabyan, R. Messi, V. Nedorezov, C. Perrin, C. Randieri, D. Rebreyend, N. Rudnev, G. Russo, C. Schaerf, M. L. Sperduto, M. C. Sutera, A. Turinge, V. Vegna (2010)
Abstract
The possibility of anisotropies in the speed of light relative to the limiting speed of electrons is considered. The absence of sidereal variations in the energy of Compton-edge photons at the ESRF's GRAAL facility constrains such anisotropies representing the first non-threshold collision-kinematics study of Lorentz violation. When interpreted within the minimal Standard-Model Extension, this result yields the two-sided limit of 1.6 x 10^{-14} at 95% confidence level on a combination of the parity-violating photon and electron coefficients kappa_{o+} and c. This new constraint provides an improvement over previous bounds by one order of magnitude.
This document discusses uncertainty principles and their application to the double slit experiment. It summarizes Heisenberg's uncertainty principle and its limitations in describing position and momentum spreads. It then applies various uncertainty inequalities to analyze Bohr's argument that an interference pattern requires not knowing which slit particles pass through. Local uncertainty principles assert that low momentum uncertainty implies not only large position uncertainty, but low probability of localization. The document analyzes applying these principles to justify Bohr's response to Einstein's proposed resolution of the double slit ambiguity.
This experiment aims to demonstrate particle-like behavior in photons using three detectors (A, B, B'). A laser beam is split into two beams, one detected by A and the other split between B and B' using a polarizing crystal. If photons are waves, detectors B and B' will always both detect photons when A does. But if photons are particles, only B or B' will detect a photon when A does. The experiment measures a value g, which should be ≥1 for waves and ≤1 for particles. A value of g=0.088<1 is found, demonstrating particle-like photon behavior.
1) The document discusses several topics in quantum mechanics including Planck's law, Wien's law, Rayleigh-Jeans law, Compton scattering, the Compton effect, de Broglie's hypothesis of matter waves, and the Davisson-Germer experiment.
2) It explains that Compton scattering results in a shift in wavelength when X-rays interact with electrons. Compton treated this as particle collision between photons and electrons.
3) The Davisson-Germer experiment in 1927 provided the first evidence of matter waves by observing interference patterns when electrons were diffracted by a nickel crystal, supporting de Broglie's hypothesis that particles can behave as waves.
The two slit experiment is described using bullets, waves, and electrons to illustrate the mystery of quantum mechanics. When bullets or waves pass through one slit, they form a distribution behind that slit on the detection screen. When both slits are open, bullets continue to form two distributions while waves interfere to create an interference pattern. Surprisingly, electrons behave like both particles and waves - they arrive on the screen individually like particles but over time form an interference pattern like waves. This illustrates that electrons pass through both slits simultaneously, exhibiting wave-particle duality.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
1) The document discusses the mechanics of neutrino and antineutrino pair emissions according to the 3-spaces model. It provides background on the origins of the neutrino concept and experimental verification of neutrinos.
2) Neutrinos were proposed by Pauli in 1934 to explain missing energy during beta decay of the neutron. Reines and Cowan provided the first detection of neutrinos in 1956 by observing the inverse beta decay of protons to neutrons induced by reactor antineutrinos.
3) The document compares the internal structures of photons and electrons using trispatial equations involving electric and magnetic fields in the 3-spaces model to stabilize the theory of neutrinos.
In class, we talked about all sorts of experiments. I would like to s.pdfAroraRajinder1
In class, we talked about all sorts of experiments. I would like to sum them up here. For each of
the following, name and briefly describe an experiment that... (a)...demonstrates that light
behaves like a wave. (b)...demonstrates that light behaves like particles. (c)...demonstrates that
electrons behave like particles. (d)...demonstrates that electrons behave like a wave.
Solution
a) Young\'s Double-Slit Experiment
A definitive experiment was Young\'s double slit experiment, which demonstrated that light
shined at two slits in a screen show an interference pattern characteristic of waves of light, rather
than particles. The principle behind this phenomenon is diffraction of light due to this any point
source of light spreads and behaves like a light source.
In the early 19th century, English scientist Thomas Young carried out the famous double-slit
experiment (also known as Young\'s experiment), which demonstrated that a beam of light, when
split into two beams and then recombined, will show interference effects that can only be
explained by assuming that light is a wavelike disturbance. If light consisted strictly of ordinary
or classical particles, and these particles were fired in a straight line through a slit and allowed to
strike a screen on the other side, we would expect to see a pattern corresponding to the size and
shape of the slit. However, when this single-slit experiment is actually performed, the pattern on
the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater
the angle of spread.Similarly, if light consisted strictly of classical particles and we illuminated
two parallel slits, the expected pattern on the screen would simply be the sum of the two single-
slit patterns. In actuality, however, the pattern changes to one with a series of alternating light
and dark bands. When Thomas Young first demonstrated this phenomenon, it indicated that light
consists of waves, as the distribution of brightness can be explained by the alternately additive
and subtractive interference of wavefronts.
b) Photoelectric effect Experiment
When light is shined on clean sodium metal in vacuum then ejection of electrons was observed.
Analysis of data from the photoelectric experiment showed that the energy of the ejected
electrons was proportional to the frequency of the illuminating light. This showed that whatever
was knocking the electrons out had an energy proportional to light frequency. The remarkable
fact that the ejection energy was independent of the total energy of illumination showed that the
interaction must be like that of a particle which gave all of its energy to the electron!
c) and d) Feynman\'s double-slit experiment
In Feynman\'s double-slit thought-experiment, a specific material is randomly directed at a wall
which has two small slits that can be opened and closed at will -- some of the material gets
blocked and some passes through the slits, depending on which ones are open.
Ba.
Wave-particle duality postulates that all particles exhibit both wave and particle properties under different experimental conditions. Historically, debates centered around whether light was a wave or particle. Key experiments and theorists helped establish the dual nature of light and matter, including:
- Einstein showing light has particle-like photons; Compton effect confirming this.
- De Broglie proposing electrons and matter have wave properties like wavelength and frequency. Davisson and Germer experimentally verified the wave nature of electrons.
- The double slit experiment demonstrated the wave behavior of electrons through an interference pattern, shocking as electrons were considered particles. This supported matter having wave-particle duality.
1) The document discusses the classical theory of electromagnetic radiation confined within an isothermal enclosure and the discrepancies with experimental observations.
2) It analyzes the temperature dependence of the energy density and pressure of the radiation using thermodynamic considerations.
3) This leads to the derivation of the Stefan-Boltzmann law relating the emissive power of a black body to the fourth power of its temperature.
Basic and fundamental of quantum mechanics (Theory)Halavath Ramesh
Quantum mechanics arose in the early 20th century to explain experimental phenomena that classical mechanics could not, such as black body radiation and the photoelectric effect. The document discusses the origins and fundamental concepts of quantum mechanics, including the dual wave-particle nature of matter and light, the uncertainty principle, and Schrodinger's formulation of quantum mechanics using wave functions and his time-independent equation. It explains that wave functions provide probabilistic information about finding particles in particular regions rather than definite trajectories, replacing Bohr's orbital model.
Fundamentals of modern physics by imran azizDr.imran aziz
The document discusses several key concepts in modern physics including:
1) Classical relativity and reference frames in Newtonian physics.
2) The Michelson-Morley experiment and failures to detect the luminiferous ether.
3) Einstein's theory of special relativity and concepts like simultaneity, time dilation, and length contraction.
4) Wave-particle duality of light and matter like electrons.
A. Morozov - Black Hole Motion in Entropic Reformulation of General RelativitySEENET-MTP
1. The document considers describing the motion of black holes using an entropic action equal to the sum of the areas of black hole horizons.
2. It is shown that this description is consistent with Newton's laws of motion and gravity, up to unknown numerical coefficients.
3. Evaluating these dimensionless coefficients precisely is important for advancing the entropic reformulation of general relativity beyond pure dimensional arguments.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
This document provides an overview of density functional theory and methods for modeling strongly correlated materials. It discusses the limitations of standard DFT approaches like LDA for strongly correlated systems and introduces model Hamiltonians and correction methods like LDA+U, LDA+DMFT, self-interaction correction, and generalized transition state to better account for electron correlation effects. The document outlines the basic theory and approximations of DFT, including Kohn-Sham equations and the local density approximation, and discusses basis set approaches like plane waves, augmented plane waves, and pseudopotentials.
Could humans recognize odor by phonon assisted tunnelingVorname Nachname
This document discusses a proposed physical mechanism for how humans could recognize odors through phonon-assisted tunneling. The mechanism involves inelastic electron tunneling between donor and acceptor sites in olfactory receptors that is mediated by the absorption or emission of odorant molecule phonons. The document evaluates the viability of this proposed mechanism using theoretical models and estimates of parameter values. It finds that the mechanism is physically plausible and consistent with observed features of the sense of smell, provided olfactory receptors have certain general properties that allow electron transfer on appropriate timescales.
This thesis examines the linear response kernel in Conceptual Density Functional Theory. The linear response kernel is defined as the second derivative of the electronic energy with respect to the external potential, and provides insight into a system's inherent reactivity. The author evaluates the linear response kernel for atoms from hydrogen to argon using the Independent Particle Approximation and Coupled Perturbed Kohn-Sham approach. Spin-polarized versions are also investigated. The relationship between linear response and polarizability is explored, allowing definition and evaluation of local polarizability. Finally, static and dynamic linear response are compared using Time-Dependent DFT and the Sternheimer equations.
phonon as carrier of electromagnetic interaction between lattice wave modes a...Qiang LI
The new results reported here mainly include: 1) recognition that phonon is carrier of electromagnetic interaction between its lattice wave mode and electrons; 2) recognition that binding energy of electron pairs of high-temperature superconductivity is due to escape of optical threshold phonons, of electron pairs at or near Fermi level, from crystal by direct radiation; 3) recognition that binding energy of electron pairs of low-temperature superconductivity is possibly due to escape of non-optical threshold phonons by anharmonic crystal interactions; and, 4) recognition of a possible mechanism explaining why some crystals never have a superconducting phase. While electron pairing is phonon-mediated in general, HTS should be associated with electron pairing mediated by optical phonon at or near Fermi level (EF), so the rarity of HTS corresponds to the rarity of such pairing match.
1. The document discusses the derivation of de Broglie's equation relating the wavelength of matter waves to the momentum of particles. It then derives different forms of de Broglie's wavelength equation using kinetic energy and potential energy.
2. It lists properties of matter waves including that lighter particles have greater wavelengths. It derives the Schrodinger time-independent and time-dependent wave equations.
3. It applies the time-independent equation to a particle in an infinite square well, finding the wavefunctions and energy levels based on boundary conditions and normalization.
This document discusses voltammetry, an electroanalytical technique used in qualitative and quantitative analytical chemistry. It introduces the basic concepts and principles of voltammetry, including instrumentation, excitation signals, types of voltammetry, and features of voltammograms. Specifically, it discusses the fundamentals of voltammetric cells, electrodes, hydrodynamic voltammetry, and common shapes of voltammograms including linear scan and peak voltammograms. The overall purpose is to explain the fundamental concepts and applications of voltammetry as an analytical technique.
The document summarizes key aspects of the Standard Model of particle physics. It describes how the Standard Model accounts for fundamental particles like quarks and leptons that interact via four fundamental forces - gravitation, electromagnetism, weak force, and strong force. These interactions are mediated by exchange of spin-1/2 bosons. The Standard Model has been very successful in explaining experimental observations, but questions remain like incorporating gravity and the origin of particle masses.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
1. The document proposes a new experiment involving entanglement and gravitational decoherence using a dual Mach-Zehnder interferometer setup.
2. In the proposed experiment, one interferometer would be placed in a gravitational field, while the other would not. This would result in non-unitary evolution and allow for nonlocal signaling between the two locations.
3. By moving his interferometer in and out of the gravitational field, one experimenter could encode and transmit binary messages to the other, who could decode the messages by observing changes in interference patterns resulting from the non-unitary evolution.
41 Limits on Light-Speed Anisotropies from Compton Scattering of High-Energy ...Cristian Randieri PhD
Limits on Light-Speed Anisotropies from Compton Scattering of High-Energy Electrons -The American Physical Society, Physical Review Letters, June 2010, Vol. 104, N. 24, pp. 241601-1-241601-5, ISSN: 0031-9007, doi: 10.1103/PhysRevLett.104.241601
di J. P. Bocquet, D. Moricciani, V. Bellini, M. Beretta, L. Casano, A. D'Angelo, R. Di Salvo, A. Fantini, D. Franco, G. Gervino, F. Ghio, G. Giardina, B. Girolami, A. Giusa, V. G. Gurzadyan, A. Kashin, S. Knyazyan, A. Lapik, R. Lehnert, P. Levi Sandri, A. Lleres, F. Mammoliti, G. Mandaglio, M. Manganaro, A. Margarian, S. Mehrabyan, R. Messi, V. Nedorezov, C. Perrin, C. Randieri, D. Rebreyend, N. Rudnev, G. Russo, C. Schaerf, M. L. Sperduto, M. C. Sutera, A. Turinge, V. Vegna (2010)
Abstract
The possibility of anisotropies in the speed of light relative to the limiting speed of electrons is considered. The absence of sidereal variations in the energy of Compton-edge photons at the ESRF's GRAAL facility constrains such anisotropies representing the first non-threshold collision-kinematics study of Lorentz violation. When interpreted within the minimal Standard-Model Extension, this result yields the two-sided limit of 1.6 x 10^{-14} at 95% confidence level on a combination of the parity-violating photon and electron coefficients kappa_{o+} and c. This new constraint provides an improvement over previous bounds by one order of magnitude.
This document discusses uncertainty principles and their application to the double slit experiment. It summarizes Heisenberg's uncertainty principle and its limitations in describing position and momentum spreads. It then applies various uncertainty inequalities to analyze Bohr's argument that an interference pattern requires not knowing which slit particles pass through. Local uncertainty principles assert that low momentum uncertainty implies not only large position uncertainty, but low probability of localization. The document analyzes applying these principles to justify Bohr's response to Einstein's proposed resolution of the double slit ambiguity.
This experiment aims to demonstrate particle-like behavior in photons using three detectors (A, B, B'). A laser beam is split into two beams, one detected by A and the other split between B and B' using a polarizing crystal. If photons are waves, detectors B and B' will always both detect photons when A does. But if photons are particles, only B or B' will detect a photon when A does. The experiment measures a value g, which should be ≥1 for waves and ≤1 for particles. A value of g=0.088<1 is found, demonstrating particle-like photon behavior.
1) The document discusses several topics in quantum mechanics including Planck's law, Wien's law, Rayleigh-Jeans law, Compton scattering, the Compton effect, de Broglie's hypothesis of matter waves, and the Davisson-Germer experiment.
2) It explains that Compton scattering results in a shift in wavelength when X-rays interact with electrons. Compton treated this as particle collision between photons and electrons.
3) The Davisson-Germer experiment in 1927 provided the first evidence of matter waves by observing interference patterns when electrons were diffracted by a nickel crystal, supporting de Broglie's hypothesis that particles can behave as waves.
The two slit experiment is described using bullets, waves, and electrons to illustrate the mystery of quantum mechanics. When bullets or waves pass through one slit, they form a distribution behind that slit on the detection screen. When both slits are open, bullets continue to form two distributions while waves interfere to create an interference pattern. Surprisingly, electrons behave like both particles and waves - they arrive on the screen individually like particles but over time form an interference pattern like waves. This illustrates that electrons pass through both slits simultaneously, exhibiting wave-particle duality.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
1) The document discusses the mechanics of neutrino and antineutrino pair emissions according to the 3-spaces model. It provides background on the origins of the neutrino concept and experimental verification of neutrinos.
2) Neutrinos were proposed by Pauli in 1934 to explain missing energy during beta decay of the neutron. Reines and Cowan provided the first detection of neutrinos in 1956 by observing the inverse beta decay of protons to neutrons induced by reactor antineutrinos.
3) The document compares the internal structures of photons and electrons using trispatial equations involving electric and magnetic fields in the 3-spaces model to stabilize the theory of neutrinos.
In class, we talked about all sorts of experiments. I would like to s.pdfAroraRajinder1
In class, we talked about all sorts of experiments. I would like to sum them up here. For each of
the following, name and briefly describe an experiment that... (a)...demonstrates that light
behaves like a wave. (b)...demonstrates that light behaves like particles. (c)...demonstrates that
electrons behave like particles. (d)...demonstrates that electrons behave like a wave.
Solution
a) Young\'s Double-Slit Experiment
A definitive experiment was Young\'s double slit experiment, which demonstrated that light
shined at two slits in a screen show an interference pattern characteristic of waves of light, rather
than particles. The principle behind this phenomenon is diffraction of light due to this any point
source of light spreads and behaves like a light source.
In the early 19th century, English scientist Thomas Young carried out the famous double-slit
experiment (also known as Young\'s experiment), which demonstrated that a beam of light, when
split into two beams and then recombined, will show interference effects that can only be
explained by assuming that light is a wavelike disturbance. If light consisted strictly of ordinary
or classical particles, and these particles were fired in a straight line through a slit and allowed to
strike a screen on the other side, we would expect to see a pattern corresponding to the size and
shape of the slit. However, when this single-slit experiment is actually performed, the pattern on
the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater
the angle of spread.Similarly, if light consisted strictly of classical particles and we illuminated
two parallel slits, the expected pattern on the screen would simply be the sum of the two single-
slit patterns. In actuality, however, the pattern changes to one with a series of alternating light
and dark bands. When Thomas Young first demonstrated this phenomenon, it indicated that light
consists of waves, as the distribution of brightness can be explained by the alternately additive
and subtractive interference of wavefronts.
b) Photoelectric effect Experiment
When light is shined on clean sodium metal in vacuum then ejection of electrons was observed.
Analysis of data from the photoelectric experiment showed that the energy of the ejected
electrons was proportional to the frequency of the illuminating light. This showed that whatever
was knocking the electrons out had an energy proportional to light frequency. The remarkable
fact that the ejection energy was independent of the total energy of illumination showed that the
interaction must be like that of a particle which gave all of its energy to the electron!
c) and d) Feynman\'s double-slit experiment
In Feynman\'s double-slit thought-experiment, a specific material is randomly directed at a wall
which has two small slits that can be opened and closed at will -- some of the material gets
blocked and some passes through the slits, depending on which ones are open.
Ba.
Wave-particle duality postulates that all particles exhibit both wave and particle properties under different experimental conditions. Historically, debates centered around whether light was a wave or particle. Key experiments and theorists helped establish the dual nature of light and matter, including:
- Einstein showing light has particle-like photons; Compton effect confirming this.
- De Broglie proposing electrons and matter have wave properties like wavelength and frequency. Davisson and Germer experimentally verified the wave nature of electrons.
- The double slit experiment demonstrated the wave behavior of electrons through an interference pattern, shocking as electrons were considered particles. This supported matter having wave-particle duality.
On request from a friend - a journey that starts from Young's double split experiment and ends up with fundamental questions about the nature of reality and the essence of science...
Quantum theory provides a framework to understand phenomena at the atomic scale that cannot be explained by classical physics. It proposes that energy is emitted and absorbed in discrete units called quanta. This explains observations like the photoelectric effect where electrons are only ejected above a threshold frequency. Light behaves as both a wave and particle - a photon. Similarly, matter exhibits wave-particle duality as demonstrated by electron diffraction. At the quantum level, only probabilities, not definite values, can be predicted. Quantum mechanics is applied to describe atomic structure and spectra.
This document provides an overview of key topics in early quantum theory that students should understand, including:
- Electrons, J.J. Thompson's experiment determining the electron, and Millikan's experiment measuring the charge of an electron.
- De Broglie's relation connecting the wavelength of a particle to its momentum.
- Wave-particle duality and the principle of complementarity stating that particles can behave as both waves and particles.
- Planck's quantum hypothesis that the energy of atomic oscillations is quantized in integer multiples of Planck's constant.
This document provides an overview of key topics in early quantum theory that students should understand, including:
- Electrons, J.J. Thompson's experiment determining the electron, and Millikan's experiment measuring the charge of an electron.
- De Broglie's relation connecting the wavelength of a particle to its momentum.
- Wave-particle duality and the principle of complementarity established by Bohr.
- That matter can behave as waves according to de Broglie's theory of the dual nature of matter.
- Planck's quantum hypothesis that the energy of atomic oscillations is quantized in integer multiples of Planck's constant.
Quantum theory describes the behavior of matter and energy at the microscopic scale. Some key ideas are:
- Light and matter can behave as both particles and waves (wave-particle duality).
- Planck's constant relates the energy of a system to its frequency or wavelength.
- Einstein's photon model explained the photoelectric effect.
- The Heisenberg uncertainty principle limits the precision with which certain pairs of physical properties can be known.
- Schrödinger's equation describes how quantum systems evolve over time.
This document discusses interference and diffraction of light waves. It begins by introducing Young's double slit experiment and discussing how it demonstrates the wave nature of light through superposition. It then discusses why two slits are used, explaining that single light sources cannot maintain a constant phase difference due to thermal agitation. It also discusses how diffraction occurs when a plane wave passes through a slit and produces an interference pattern on a screen. The document compares interference and diffraction, and discusses how diffraction can be used to prove the uncertainty principle of quantum mechanics. It concludes by discussing how gravity can cause decoherence in double slit experiments and briefly summarizing G.P. Thomson's experiment using electron diffraction through thin metal films.
1. Louis de Broglie hypothesized that all matter exhibits both particle-like and wave-like properties, with the wavelength of the matter wave related to the particle's momentum by the de Broglie equation.
2. Experiments demonstrating the wave-like behavior of electrons and other particles validated de Broglie's hypothesis. Electron diffraction and interference patterns exhibited wave-like characteristics.
3. The wave function describes a particle's quantum mechanical state and contains all observable properties of the particle. It represents the matter wave associated with the particle.
Quantum theory describes the behavior of small particles like electrons and photons. It seems counterintuitive because particles can act like waves and exist in multiple states at once until observed. The theory was developed between 1900-1930 and helped establish modern physics. It includes ideas like wave-particle duality, Heisenberg's uncertainty principle, and quantum fluctuations that allow particles to briefly exist from nothing. While still incomplete, quantum theory is well-supported by evidence and critical to technologies like computers.
Alexander G Foigel - An interpretation of relativistic mechanics - 2005.pdfIliaStambler1
An Interpretation of Relativistic Mechanics
By Alexander G Foigel
Annales de la Fondation Louis de Broglie, Volume 30, no 3-4, 289-307, 2005
[Originally in open access: https://fondationlouisdebroglie.org/AFLB-303/aflb303m339.pdf
Translated from Russian into English by Ilia Stambler]
ABSTRACT. The present article reports on the finding of the principal basis behind relativistic mechanics. From the independence of the speed of light upon the velocity of the light source it is concluded that the vacuum consists of the light carrying ether. The second crucial conclusion is that the elementary particles represent specific excitations of some parts of rigid ether. The motion of the electron in the atom undergoes multiple reflections, and the electron trajectory represents a broken line. The forces of inertia are conditioned by the properties of the ether excitation that is identified with the physical body. The constancy of the transverse dimensions of freely moving particles and bodies is determined by de Broglie waves. The invariants in the theory of relativity are the transverse dimensions of moving objects and the speed of light.
Einstein, in his famous photoelectric effect experiment demonstr.pdfarri2009av
Einstein, in his famous \"photoelectric effect experiment\" demonstrated that light can behave as
a waves. In 1924, Louis de Broglie suggested that just as light exhibits wave properties. All
microscopic material particles such as electrons, protons, atoms, molecules etc. have also dual
character. They behave as a particle as well as wave. This means that an electron which has been
regarded as a particle also behaves like a wave. The particle nature of an electron is explained by
classical mechanics. For example, electron has a mass ~ 9.1 X10*-31 kg. But the classical
mechanics fails to explain the wave nature of electron. The wave nature of electron is explained
by quantum mechanics. Can you give more examples of wave behavior of electron in order to
illustrate dual character of electron?
Solution
the wave nature of electron was explained by the experiments like Thompsons Experiment, in
which G.P.Thompson allowed electron beam pass through a thin foil of gold and got caught on
the photographic plate on whic he found the Diffraction pattern of electron beam just like x-ray,
thus this experiment allows wave nature of electron..
The document discusses wave-particle duality and Louis de Broglie's hypothesis that all matter has both wave-like and particle-like properties. It summarizes key experiments that supported this idea, including Davisson and Germer's 1927 experiment in which electron beams were diffracted by crystal lattices, demonstrating their wave-like behavior. The document also explains how de Broglie's hypothesis resolved issues with early atomic models by introducing the concept of electron standing waves within atoms.
Light has both wave-like and particle-like properties. Historically, there were two theories on the nature of light - Newton's corpuscular theory proposed that light consisted of particles, while Huygens' wave theory proposed that light consisted of waves. Experiments in the 19th century supported the wave theory, but phenomena like the photoelectric effect could only be explained by treating light as particles. Now it is understood that light behaves as waves under conditions like interference and diffraction, but as particles under conditions involving interactions with matter. Maxwell's theory showed that light is an electromagnetic wave.
1. The document discusses key concepts in quantum physics including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's time-independent wave equation.
2. It provides details on experiments that verified the wave-like properties of matter including electron diffraction experiments by Davisson and Germer.
3. The document derives expressions for the energy levels of particles confined in one-dimensional potential wells and boxes in terms of Planck's constant and other variables.
1. Single Photon Interference
Parker Henry
May 5, 2015
Abstract
This experiment will demonstrate the ability of a single photon to
interfere with itself in a wavelike manner. This will be demonstrated
using three detectors to conditionally detect photons reaching either of
two detectors B or B’ through either of two possible paths within a small
time after detector A detects a photon. This single-photon interference
will be argued to arise due to no knowledge of which of the two paths it
took to reach either detector B or B’. This experiment is an extension
of the original experiment by Grangier et al. [2], which showed that
photons arrive at detectors B and B’ as lumps. The same result from the
experiment by Grangier et al. will be shown to continue to hold in this
experiment, thus demonstrating wave-particle duality in photons.
1 Introduction
The previous experiment ([1]) demonstrated that “photons exist.” That is to
say, it was demonstrated that photons can be demonstrated to possess particle-
like behavior, in that they can be demonstrated to have a definite position.
It is the goal of the following experiment to demonstrate wavelike behavior in
photons as well, in that a single photon, when passed through an interferometer,
can interfere with itself in a wavelike manner.
To review the previous experiment, a reproduction and slight refinement
of the original experiment done by Grangier et al. [2], it was demonstrated
that photons can possess definite position by means of three light detectors —
A, B, and B’ — and a laser of 405nm wavelength, along a path which was
subdivided via a down-converting crystal into a path toward A and a path
toward the B and the B’ detectors. The path toward the latter two detectors
was further subdivided with a polarizing crystal which would partially transmit
and partially reflect the laser toward B and B’, respectively. When detector A
was triggered by a photon, detectors B and B’ would seek photons within a
window of 4.74 nanoseconds of the detection event at A. It was argued that if
light behaved as a classical wave in this context, then both detectors B and B’
would be simultaneously triggered with every detection event at A, whereas if
light were behaving as a collection of particles called photons, then one or the
other would be triggered.
1
2. Figure 1: Diagram of the experiment. Note the polarizing interferometer (la-
beled as PI) in the dashed box. λ/2 denotes a half-wave plate, DC is the down-
conversion crystal, FFC is the fiber-to-fiber coupler, SPCMs are the single-
photon counting modules, and A, B, and B’ denote detectors A, B, and B’,
respectively [3, Fig L3.2, p.464].
To quantify the preceding discussion, let NB is the number of instances
within a time T in which detector B is triggered, let NB be the number of
instances in which detector B’ is triggered, and let NBB be the number of
instances in which both detectors are triggered within the 4.74 nanosecond win-
dow of detector A being triggered. A ratio g, which satisfies the proportionality
relation
g ∝
NBB
NBNB
was experimentally determined with computer software which counted the num-
ber of counts on the detectors. It was argued that if light was behaving as a
classical wave, then g ≥ 1, but if light consisted of photons which behaved as
particles, then g < 1. Indeed, g was experimentally measured in ([1]) to be
0.088(10), in support of the hypothesis that photons behave as particles.
This experiment will show that individual photons can interfere with each
other when passed through a polarization interferometer. The new experimental
setup is depicted in Figure (1). It will also be shown that it remains the case
that g < 1, as in the previous experiment. Thus, the following experiment will
not only be demonstrating wavelike behavior in photons via self-interference,
but it will simultaneously be demonstrating wavelike and particle-like behavior
in photons, in the truest sense of wave-particle duality.
2
3. Figure 2: Young’s Double-Slit Experiment. Feynman’s own thought experi-
ments are based on this actual experiment.
2 Feynman’s Thought Experiment on Single-Electron
Interference
In Volume III of the Feynman Lecture Series [4, Vol. III, Lecture I], Richard
Feynman proposes a series of gedankenexperiments, or thought experiments, of
three different objects – bullets, water waves, and electrons – going through
two holes, and detecting the output of the objects on a wall behind the holes.
Thomas Young did this very experiment with light, and Feynman’s gedankenex-
periments are geometrically identical in their setup, which is shown in Figure 2.
Feynman’s thought experiments, particularly the one with electrons, elucidate
the behavior in photons which we seek to experimentally demonstrate with the
following experiment.
Feynman first argues that if a machine gun of bullets is fired at the double
slits, and a detector is rapidly sliding up and down the backstop in Figure 3, then
the density P of all bullets hitting the wall, which is a function of the position
z along the wall, is simply the sum of the density functions P1 of bullets from
hole 1 on wall 2 and P2 of bullets from hole 2. This can be written succinctly
as
P = P1 + P2 (1)
Thus, the bullets exhibit particle-like behavior.
Feynman’s second thought experiment is similar to his first, though now
water waves are traversing through the two holes onto the backstop. This ex-
periment is depicted in Figure (4). The detector is detecting the intensities of
the waves striking the absorber wall. In this thought experiment, the waves will
show interference. If
ϕ1 = h1eiωt
is the wavefunction for the water waves passing through hole 1, for a complex
3
4. Figure 3: Feynman’s thought experiment with bullets. Note that the density
of the bullets striking the backstop (c) due to the contributions of both holes is
the sum of the individual densities (b). [4, Vol. III, Lecture I].
amplitude h1, and if
ϕ2 = h2eiωt
is the wavefunction for the water waves passing through hole 2, for a complex
amplitude h2, then the total wave function is given by
ϕ = (h1 + h2)eiωt
If hole 1 is blocked off, then the intensity I1 detected is proportional to |h1|2
.
If hole 1 is blocked off, then the intensity I2 detected is proportional to |h2|2
.
If both holes are open, then
|h1 + h2|2
= |h1|2
+ |h2|2
+ 2|h1||h2| cos δ
where δ is the phase difference between h1 and h2. Then the intensity I is given
by
I = I1 + I2 + I1I2 cos(δ) (2)
Thus, I is not simply I1 + I2. This is what Feynman means if the waves show
interference. The interference is constructive if δ = 0, and destructive if δ = π.
Feynman denotes the last term in equation (2) as the interference term.
If the intensity in the second thought experiment is regarded as a density
function of the detection of water waves, then we may take the density to exhibit
particle-like behavior if there is no interference, and to exhibit wavelike behavior
if there is interference.
In Feynman’s third gedankenexperiment, electrons are fired by an electron
gun, as in Figure 5. A mobile Geiger counter goes along the back wall to measure
the rate of electrons striking the backstop. If detectors were to be placed at each
hole, then a single electron would trigger one or the other, never both at the
same time; “each electron either goes through hole 1 or it goes through hole
2 (not both)” [4, Vol. III, Lecture I]. Thus, one concludes that the electrons
arrive in lumps on the backstop.
4
5. Figure 4: Feynman’s thought experiment with water waves. Note that the water
waves are exhibiting interference [4, Vol. III, Lecture I].
Figure 5: Feynman’s thought experiment with electrons. Though electrons can
be measured to have definite position, they interfere with each other. [4, Vol.
III, Lecture I].
5
6. However, if P1 is the clicking rate along the back wall of the electrons when
hole 2 is closed off, and P2 is the clicking rate when hole 1 is closed off, and if
P is the clicking rate when both are open, then
P = P1 + P2
Indeed, if ϕ1 is the probability density amplitude for hole 2 being closed, which
is in general a complex number, then
P1 = |ϕ1|2
and if ϕ2 is the probability density amplitude for hole 1 being closed, then
P2 = |ϕ2|2
The total probability density P is then
P = |ϕ1 + ϕ2|2
= |ϕ1|2
+ |ϕ2|2
+ 2|ϕ1||ϕ2| cos(δ)
where δ is the phase difference between ϕ1 and ϕ2. Hence,
P = P1 + P2 + 2 P1P2 cos(δ)
This is mathematically identical to the water-wave intensities from the second
thought experiment, yet the electrons arrive in discrete lumps, unlike the water
waves. This is an instance of wave-particle duality.
Feynman argues that the electrons’ nonclassical behavior is connected to
knowledge of which path the electrons took. Indeed, he argues that if any sort
of detectors are placed at hole 1 or hole 2, then the interference effect would
disappear, and the electron probability densities would add as if they were simple
bullets from the first thought experiment! Furthermore, if hole 1 is blocked off,
then the experimenter knows that the electrons went through hole 2, and vice
versa. The electrons still collect as lumps, and so this result is identical to the
bullet result. It seems from this gedankenexperiment that any sort of knowledge
of which path the electrons take destroys the interference effect of the double-slit
phenomenon. Feynman goes so far as to posit that all of the other mysteries of
quantum mechanics could be reduced to this particular quantum phenomenon
[4, Vol. III, Lecture I].
Feynman’s first two gedankenexperiments are relatively easy to implement.
His third experiment, he cautions, would require slits on an experimentally un-
feasible scale to carry out that exact experiment. However, versions of this
thought experiment have been implemented in spirit by various actual exper-
iments. The following single-photon interference experiment with lasers, pho-
tons, and photon detectors is one implementation of Feynman’s thought exper-
iment. This experiment will seek to demonstrate the same behavior in photons
as that of the electrons in Feynman’s third thought experiment.
6
7. 3 Connection of Feynman’s Thought Experiment
to Single-Photon Interference
As will be seen, the single-photon-interference experiment is a version of Feyn-
man’s thought experiment which uses photons rather than electrons. This ex-
periment will demonstrate single-photon interference using a polarization inter-
ferometer to vary the lengths of two paths along which a photon may travel.
The description and experimental setup are from Beck, Quantum Mechanics:
Theory and Experiment [3, Lab 3, p.463-474].
In this experiment, the photons in the beam, which has been shown to consist
of single photons under the conditional detection mechanism with detector A,
will be shown to interfere with themselves. In this experiment, what that means
is that a photon will be able to travel down either of two paths toward detectors
B and B’. These paths will be created with a pair of birefringent crystals, as will
be discussed in the experimental setup. The idea is that if it is not known which
path the photon took to get to the detectors, then the photon will interfere with
itself in the sense that if N1 is the number of detection events at one detector
due solely to hole number 1 being open to the photon, and N2 is the number of
detection events at that same detector due solely to hole number 2 being open,
then N, the number of detection events when both holes are open, will not be
N1 + N2:
N = N1 + N2
This assertion is consistent with Feynman’s third thought experiment involving
electrons. The following experiment will demonstrate this assertion.
4 Classical Theory of Polarization
To describe the effect of the polarization interferometer on the photon, we first
describe the classical theory of wave polarization. Suppose a wave is propagating
in vacuum in the z-direction, with wave vector k = kuz, where uz is the unit
normal vector in the z-direction, and k is related to the wavelength λ, frequency
f, and angular frequency ω by
k =
2π
λ
=
2πf
c
=
ω
c
One can write the electric field E as
E = Exux + Eyuy
If φ is the phase difference between Ex and Ey, E0x is the amplitude of the wave
in the x direction, and E0y is the amplitude of the wave in the y direction, we
can rewrite E as
Ex = E0x cos(kz − ωt)
Ey = E0y cos(kz − ωt + φ)
7
8. Figure 6: Diagram of birefringence in a crystal. Note the transmitted ordinary
ray, which is perpendicular to the optic axis, and the transmitted extraordinary
ray, which is parallel [5].
E can be written in terms of complex exponentials, where it is agreed that the
real part of the complex exponential is taken whenever the physical value of the
field is desired:
E = E0xei(kz−ωt)
ux + E0yei(kz−ωt+φ)
uy
If we let
E0 = E2
0x + E2
0y
be the amplitude of E and
ε =
E0x
E0
ux +
E0y
E0
eiφ
uy
be the normalized polarization vector, then E can be written succinctly as
E = E0ei(kz−ωt) E0x
E0
ux +
E0y
E0
eiφ
uy = E0ei(kz−ωt)
ε
Optical detectors respond to the power incident on the detector from the electric
field. This power is proportional to the intensity I, given by
I = |E|2
= E∗
E = E2
0
5 Theory of Birefringence
The above theory of classical polarization was derived in vacuum. If a wave
propagates in a linear medium, however, then it has an index of refraction n
which determines the speed v = c/n of the wave through the medium. The
value k becomes
k =
ω
v
=
n2π
λ
A birefringent material has two indices of refraction, which are distinguished
by its internal axis of polarization. Light which is solely along this axis, which is
called the axis of rotation, is refracted by an index n1, and light which is normal
to this axis is refracted by an index n2. This can be seen diagrammatically in
8
9. Figure 7: Birefringence in calcite. Note that the calcite makes two images of
the same × appear from the black paper [5].
Figure 6, and an example of this phenomenon occurring with calcite can be seen
in Figure 7.
The discussion of the theory of polarization shows that any light wave can be
decomposed into two orthogonal components: a component with polarization
orthogonal to the optic axis, and another component with polarization parallel
to the optic axis. In the birefringent medium, the component of the beam
orthogonal to the optic axis becomes the ordinary ray, and the component
parallel becomes the extraordinary ray (see Figure 6).
6 The Polarization Interferometer
Other optical apparatuses in this experiment include the linear polarizer and
the half-wave plate. The action of the linear polarizer is to project the incident
wave along its optic axis and transmit that projection, i.e. if the optic axis
makes an angle θ with the x-axis, and the incident wave is
Ei = E0ei(kz−ωt)
ε
then the transmitted wave is given by
Et = E0ei(kz−ωt
(ε · uθ)uθ
The action of the half-wave plate is that if its axis of polarization is at an angle
θ to the polarization of the incident wave, then it rotates the polarization by an
angle 2θ.
These actions can be represented in terms of linear algebra, using basis
components ux and uy, as follows: if a linear polarizer is at an angle θ to the x-
axis, and a light beam E is incident on it, then the action of the linear polarizer
on the beam is described by JθE, where
Jθ =
cos2
θ cos θ sin θ
cos θ sin θ sin2
θ
9
10. Figure 8: A simple polarization interferometer, which induces a phase difference
φ between the ordinary and the extraordinary rays [3, p.36].
Figure 9: A polarization interferometer, which induces a phase shift proportional
to φ, and which will be able to show coherence length [3, p.37].
projects the beam along the axis of θ. Similarly, if a light beam is incident on
a half-wave plate with axis of polarization at an angle θ to the x-axis, then the
action is given by Jλ/2,θE, where
Jλ/2,θ =
cos(2θ) sin(2θ)
sin(2θ) − cos(2θ)
A simple polarization interferometer, with parallel axes of polarization, such
as the one shown in Figure 8, induces a phase shift
Jp,φ =
eiφ
0
0 1
between the ordinary and the extraordinary rays. It also projects the top ray
along the x-axis, projects the bottom ray along the y-axis, and then recombines
them, so its total effect on the incident beam is
J = Jπ/2 + Jp,φJ0 =
eiφ
0
0 1
However, we use a modified version of the polarization interferometer shown
in Figure 8, because the coherence length is so short that to see any interference,
the lengths of the top and bottom paths must be nearly equal. We thus use a
polarization interferometer as in Figure 9. The axes of polarization of the two
birefringent materials are again parallel. The action of this device is given by
J = Jp,φJλ/2,45J0 + Jλ/2,45Jπ/2 =
0 eiφ
1 0
10
11. Figure 10: Diagram of the polarizing interferometer. λ/2 denotes the half-wave
plates, BDP denotes a beam-displacing polarizer, and PBS denotes a polarizing
beam splitter. Note the angles θ1, θ2 (which is fixed at 45 degrees throughout
the experiment), and θ3. B and B’ refer to the detectors B and B’ [3, Fig L3.1,
p.464].
If φ is set to 0, then this apparatus is simply a half-wave plate. If φ is not zero,
then the path length of the two branches differs, then this apparatus acts as a
half-wave plate, with an additional phase shift. This phase shift, however, will
alter the path length of one path, making single-photon interference observable.
7 Experimental Setup
Much of the setup of the experiment is identical to Lab 2 of Beck, which the
experimenter carries out in [1]. Therefore, the theory of photon detection by the
detectors remains the same as in Lab 2, so we do not repeat the full discussion
here. As in Lab 2, there are two detectors B and B’ at the outputs of a polarizing
beam splitter, and a detector A for an idler beam. Detector A is triggered by
a photon, which triggers the detection event in which detectors B and B’ seek
photons within a 4.7 nanosecond interval of detector A having detected a photon.
The polarizing crystal will transmit the light if its polarization is normal to its
optic axis, and reflect it if the light’s polarization is parallel to the optic axis.
It was shown in Lab 2 of Beck that this beam consists of single photons.
The new feature of this experiment is the addition of the polarization inter-
ferometer (the PI in Figure 1) A calcite crystal is used to create birefringence.
As discussed in Section 5, If the incident light is decomposed into two orthogonal
components: one parallel to the axis of polarization of the calcite, and the other
orthogonal to it, then the orthogonal component of the incident beam becomes
the ordinary ray, and the parallel component becomes the extraordinary ray.
The polarization interferometer in Figure 10 is a modification of the one
described in Section 6. First, we add a linear polarizing plate to polarize the
light incoming from the down-converting crystal to 0 degrees. We add two
half-wave plates at varying angles of polarization (θ1 and θ3 in Figure 10) to
polarize the light beam at varying angles before and after being acted on by
the polarization interferometer from Figure 9. A half-wave plate fixed at a 45
degree polarization angle corresponds to θ2.
The optical equipment in Figure 1 is aligned by placing an 810 nm laser
11
12. into the optical equipment, to verify that the light beams indeed travel on the
correct paths for the light from the 405 nm laser source to be detected by the
detectors. The position of the polarization interferometer such that the path
lengths are equal, and hence there is no phase shift between the two paths, is
found. We do not go into detail about either of these parts because they were
laborious and they were carried out by the lab instructor prior to entering the
laboratory.
8 Experimental Procedure
First, the room must be completely dark so as not to damage the photodetection
equipment.
A 405 nm laser is turned on while θ1 and θ3 from Figure (1) are varied at 0
degrees and at 22.5 degrees. At these varying angles, the counts AB and AB’
are determined.
Having obtained these counts, the procedure in the preceding paragraph
is carried out again, though this time one of the beams in the polarization
interferometer (the PI in Figure (1) is blocked. The AB and AB’ counts are
again determined, with θ1 and θ3 being either at 0 degrees or at 22.5 degrees.
Finally, the coherence length of the photon is determined by varying the
vertical orientation of the first birefringent crystal. This is done by altering the
number of divisions on a dial, which allows the crystal to point at a different
angle, and thus create a different path length in the extraordinary branch of
the polarization interferometer in Figure 10. The ordinary branch length is
kept constant, however, leading to a difference in the path lengths between the
ordinary and extraordinary branches. The dial is started at 40 divisions, and
incremented by 0.5 divisions, until it reaches 130 divisions. If φ is the number
of divisions, then we seek the number
δ(φ) = NAB −
2
3
NAB
NAB is multiplied by 2/3 because the B detector is only 2/3 as efficient as
the B’ detector. If δ(φ) is high in magnitude, then this means that a photon
traveling along this path has high self-interference, whereas if it is low, then it
is not exhibiting self-interference.
9 Results
The results of detecting the beam at varying angles θ1, θ3 are summarized in
Table 1.
These results may be explained in terms of the polarization axes of the
polarization interferometer, the half-wave plates, and the polarizing crystal.
The polarization interferometer and the polarizing crystal were both set up
with optical axes at 0 degrees, and were fixed on these axes throughout the
experiment.
12
13. Table 1: Table of counts obtained at angles θ1, θ3
θ1 (degrees) θ3 (degrees) Is one beam blocked? NAB NAB NAB/NAB g
0 0 No 195 53119 0.00367 0.58(21)
22.5 0 No 21952 25626 1.01 0.121(5)
0 22.5 No 20838 27653 0.754 0.093(9)
22.5 22.5 No 1589 50983 0.0312 0.163(40)
22.5 22.5 Yes 11543 13960 0.827 0.056(63)
When θ1 = θ3 = 0 degrees, then the entering light wave at a polarization of 0
degrees remains at 0 degrees polarization after leaving the first half-wave plate,
and then it is almost only transmitted as an extraordinary beam in the first
birefringent crystal. The fixed half-wave plate then rotates the polarization by
45 degrees, so that it becomes the ordinary component of the second birefringent
crystal. Since this component dominates the extraordinary component, and it
is parallel to the polarizing crystal’s own optic axis, the polarizing crystal will
almost entirely reflect the light beam to the B’ detector, and so we see in the
table that NAB is much less than NAB .
When θ1 = 22.5 degrees, and θ3 = 0 degrees, then the entering light, starting
at a polarization of 0 degrees because of the linear polarizer, is rotated to a
polarization of 45 degrees. Then the ordinary and the extraordinary components
at the first birefringent crystal are approximately equal in magnitude. The beam
is projected onto either the ordinary or extraordinary axis with equal probability.
The second half-wave plate makes the ordinary component extraordinary, and
the extraordinary component ordinary. With θ3 = 0, the incident beam to the
third half-wave plate is not rotated at all, so the polarization of the entire beam
remains 45 degrees. The polarizing crystal then, in approximately equal parts,
transmits and reflects the light wave into detectors B and B’. Thus, the ratio
NAB/NAB is measured as 1.01.
The case θ1 = 0 degrees, θ3 = 22.5 degrees has a similar result, though this
time it is because at θ1 = 0, one path of the polarizing interferometer — the
path which is initially extraordinary, which becomes ordinary when leaving —
dominates the other component. However, θ3 = 22.5 degrees rotates this beam
by 45 degrees, so that the polarizing crystal will, in roughly equal parts, transmit
and reflect the beam toward detectors B and B’. Thus, NAB/NAB = 0.754
With θ1 = θ3 = 22.5 degrees, there are two different trials based on whether
one path was blocked, or both paths were left open. As in the θ1 = 22.5
degrees, θ3 = 0 degree case, the photons are projected with equal probability
onto the ordinary or the extraordinary axes. However, with θ3 = 22.5 degrees,
these photons are rotated in polarization by 45 degrees. What is observed is that
NAB/NAB = 0.0312. However, when one beam is blocked in the θ1 = θ3 = 22.5
degree case, the ratio changes entirely: NAB = NAB = 0.827.
As we see from the table, all of the g values are less than 1. As it was argued
13
14. Figure 11: The difference between the AB and two thirds of the AB’ counts as
a function of the difference between path lengths.
Figure 12: The difference between the AB and two thirds of the AB’ counts
as a function of the number of divisions passed. Note that 1 wavelength is
approximately 2.5 divisions.
in the previous experiment [1], this implies that the photons have a definite
position when they are detected by the detectors B and B’. The result from
that experiment, that light consists of individual photons which can behave as
particles, then carries to this experiment.
Finally, the coherence length of the photons is determined by altering the
path length of the extraordinary path of the polarizing interferometer. The
results of altering the number of divisions is shown in Figure 11.
We use the conversion factor of 2.5 divisions to one wavelength, after look-
ing at the original graph in Figure 12 and finding approximately when the wave
repeats itself. The wavelength is 810 nanometers (the down-converting crystal
halves the wavelength of the incoming photon, in order to preserve energy con-
servation), and then we convert nanometers to millimeters with 1000 nanometers
to 1 millimeter. Having converted divisions to millimeters, we arrive at Figure
14
15. 11.
Because δ = NAB − (2/3)NAB oscillates rapidly, yet the overall amplitude
seems to decrease as a function of the distance, one can conjecture that the data
may fit a damped sine curve. However, an attempt to fit this data to a damped
sine curve was unsuccessful, due to the wild oscillations of the data, so this is a
very crude approximation. Still, one can see from Figure 11 that the distance at
which the “amplitude” reaches 1/e of the initial value is 16 millimeters. Thus,
the coherence length of the photon is approximately 16 millimeters.
10 Conclusion
What could cause the difference between the runs in which θ1 = 22.5 degrees,
θ3 = 0 degrees, and in which θ1 = θ3 = 22.5 degrees, with one path blocked or
no path blocked? One possible explanation comes from quantum theory, and it
lies in knowing which path a photon took. In the θ1 = 22.5 degree, θ3 = 0 degree
case, the photons which trigger detector B were initially of the extraordinary
component of the polarization interferometer, and the photons which trigger
detector B’ were initially of the ordinary component. With θ1 = θ3 = 22.5
degrees, and one path blocked, it is again known which path a photon took,
simply because one of the paths was not blocked. With one path blocked,
the photons that come through the other path will have, before reaching the
polarizing crystal, a polarization of 45 degrees, plus a multiple of 90 degrees,
because they have been projected onto either the ordinary or extraordinary axis.
Thus, the photons trigger detectors B and B’ in equal measure.
However, when neither path is blocked in the θ1 = θ3 = 22.5 case, then
no knowledge is available of which path a photon reaching the detectors took
to get there. One would assume, if the photons were behaving in a particle-
like manner `a la Feynman’s first thought experiment, that the counts on the
detectors would simply add if both paths were opened. Both paths are open, yet
this does not happen; the detection counts of the photons are adding as waves
do, in the manner of Feynman’s second thought experiment. However, the value
of g is less than 1 throughout the experiment, which implies that the photons
are collecting in lumps at the detectors. In conclusion, this experiment shows
that photons follow the paradigm of Feynman’s third thought experiment in
which electrons experience wave-particle duality: not only are photons neither
waves nor particles, but they are both.
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