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Ldb Convergenze Parallele_12

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  • 1. What is a Quantumbit? PD Dr. Kilian Singer Universität Mainz www.quantenbit.de/#/teach/Public%20Outreach/ start
  • 2. Overview • Classical information processing • Quantum information processing • Scalable quantum information processing
  • 3. Overview Classical information processing • Quantum information processing • Scalable quantum information processing
  • 4. What is a Bit ? • Bit is smallest classical information carrier: 0 or 1 – e.g.: TTL 0Volt, 5 Volt Combination of Bits with Gattes => Computer NOT NAND 74LS00 With this you can build an universal computer! Try it:http://www.nand2tetris.org/
  • 5. How do you build a gate? NAND 74LS00 With this you can build an universal computer! Try it:http://www.nand2tetris.org/
  • 6. Relais in Z1 Zuse (1938) Through miniaturization from the Bit to the computer 601.08.2013 Vaccum tube computer Collosus (1944) Transistor Computer IBM 7090(1959) First micro chip byJack Kilby (1958)
  • 7. Overview Classical information processing Quantum information processing • Scalable quantum information processing
  • 8. What is a quantumbit ? What is quantummechanics? What is classical mechanics?
  • 9. Newton mechanics Bdescribes the movement of one particle Newton’s law Trampoline?
  • 10. Newton mechanics describes movement of plantsn
  • 11. Quantum mechanics describes the movement of a small particle Questions: • Where do the spectral lines come from? • Why are they at these wavelength? • Why does the electron not fall into the atom core? (as moved charge transmits electromagnetical radiation)
  • 12. Bohr’s atom modell Niels Bohr (1913) Centrifugal force=Coloumb force Coulomb potential => Coloumb force Questions:  Where do the spectral lines come from? • Why are they at these wavelength? • Why does the electron not fall into the atom core? (as moved charge transmits electromagnetical radiation)
  • 13. Interference with lightwaves
  • 14. Interference with lightwaves
  • 15. Complex numbers (for first semesters) • Application – Electronics – Quantum mechanic – Fractals: e.g. Mandelbrot: fractals.bat
  • 16. Complex numbers • Solution of equation • Imaginary number i: • General complex number:
  • 17. Complex numbers • Solution of equation • Imaginary number i: • General complex number:
  • 18. Euler’s formula
  • 19. What is the relation between ex and sin(x) & cos(z) ? Taylor series: Taylor series also work for complex numbers: Maxima-File http://maxima.sourceforge.net/
  • 20. What is light? Photo effect (1905 Albert Einstein) Existency of photons with energy Short wavelength UV light Alcali metal electrode Monochromatic light Quarz window
  • 21. Do single photons interfere?
  • 22. DeBroglie (1929) Wave character of particles
  • 23. Bohr’s atom model Multiples of the DeBroglie-wave length have to fit on circumference Questions:  Where do the spectral lines come from?  Why are they at these wavelength? • Why does the electron not fall into the atom core? (as moved charge transmits electromagnetical radiation)
  • 24. Why does the electron not fall into the atom core? Schrödinger equation (1926) Erwin Schrödinger http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 25. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 26. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 27. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 28. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 29. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 30. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 31. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 32. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 33. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 34. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 35. Schrödinger’s equation http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html
  • 36. Interpretation Probability density in analogy to the light intensity:
  • 37. Quantized Energy levels as a consequence of boundary conditions
  • 38. 1d 2dbox 2dcirc 2dharmonic coulomb 1dbox http://www.falstad.com/mathphysics.html Quantized Energy levels as a consequence of boundary conditions
  • 39. What is a quantumbit ? • QBit is smallest quantunmechanical information carrier:
  • 40. What is a quantumbit ? • QBit is smallest quantunmechanical information carrier: • Mathematical representation with vectors: Measurement 50% 50%
  • 41. Through lower temperatures from quantum bits to quantum computers Nuclear spins in silicon Molecular NMR photons nanomechanical oscillators superconducting qubits Rydberg atoms Atoms in optical dipol traps Trapped ions Atoms in cavities Quantum dotsNV color centers Quantum bits
  • 42. Temperature scales Anders Celsius (1701- 1744) Daniel Fahrenheit (1686 – 1736) William Thomson Baron Kelvin (1824 – 1907) Absolute temperature scale: Atoms and molecules at rest: 0 °K = - 273,15 °C Melting point of ice: 0 °C = 273,15 °K Evaporation point of water: 100 °C = = 373,15 °K
  • 43. Gas thermometer pressure p and volume V increase with increasing temperature T N : Amount of gas molecules in mol kB : Boltzmann‘s constant 1,38 · 10−23 J/K Boyle-Mariotte‘s law p . V = N . kB . T What happens at T=0 ???
  • 44. Interessante Effekte bei Tiefen Temperaturen • Supraconductivity • Suprafluidity • Nuclear magnetic resonance tomography • Quantumcomputing …
  • 45. Movie to supraconductivity
  • 46. Movie to suprafluidity
  • 47. What is the lowest temperature reached? Inner core of sun: 15 000 000 K Human: 300 K Cold atoms: 0.000 000 001 K
  • 48. Doppler cooling
  • 49. Optical molasses
  • 50. Magnetic trap
  • 51. Magneto-optical trap
  • 52. Magneto-optical trap
  • 53. Sisyphus cooling Nobelprice1997 (Chu, Cohen-Tannoudji, Phillips)
  • 54. Bose Einstein condensate
  • 55. Bose Einstein condensate Nobelprice 2001 (Wieman, Ketterle, Cornell)
  • 56. Bose Einstein condensate: Matter-wave interference with macroscopic wavefunction
  • 57. Atom-Laser Thermal cloud ….. Bose-condensate
  • 58. Linear Paul trap Wolfgang Paul (Nobel price1989) RF RF DC DC
  • 59. Harmonic Oscillator Linear Paul Trap: Axial Confinement (DC potential) In the ground state:
  • 60. Lineare Paul-Trap: radial confinement by Wolfgang Lange
  • 61. P1/2 S1/2 t = 7 ns 397 nm Doppler cooling D5/2 t = 1 s Energy Level scheme of Calcium+ 866 nm Repumping
  • 62. Doppler Cooling Atom at Rest nLaser frequency as seen by atom
  • 63. Doppler Cooling Moving atom nLaser frequency as seen by atom
  • 64. Doppler Cooling nLaser frequency as seen by atom
  • 65. Laser cooled ion crystall Mainz, 40Ca+