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  1. 1. BOSE-EINSTEIN CONDENSATTIONIncluding an introduction to Fermionic Condensates & Ultra-Slow light in a BEC Aaron Flierl SUNY BUFFALO PHY 402 Spring 2016 [6] 1
  2. 2. Statistical Distributions • µ ≈ EF up to temperatures of 2000K • F-D and B-E are limiting case where particle has wave function with a λ comparable to interatomic spacing • At high T B-E and F-D statistics converge to classical regime and agree with M-B • F-D always guarantees a 50% chance of finding a Fermion at EF • With increasing T F-D statistics shows increased chance of exciting electrons into the conduction band • At T ≈ 0K F-D statistics yields 0% chance of finding a Fermion with E > EF “Fermi-Sea” • Increase in T yields an increased chance of finding a particle at a higher energy • For Bosons, chemical potential must always be less than the minimum allowed energy [Griffiths problem 5.30] [14] [12] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 2
  3. 3. Statistical Distributions • Plots of all 3 distributions with increasing T • Note different behavior at low T, similar behavior at high T [13] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 3
  4. 4. What is a Bose-Einstein Condensate? • State of matter • First predicted theoretically by Bose and Einstein in 1925 • First BEC created in 1995 using a gas of Rb cooled to 170nK • Cool VERY dilute gas of non-interacting Bosons to near absolute zero using combination of laser and evaporative cooling • In a BEC Bosons macroscopically occupy the lowest energy state • This “quantum degeneracy” occurs when de Broglie wavelength becomes comparable to spacing between atoms • BEC’s can have superfluid properties; behave as a fluid with zero viscosity. Defy gravity and surface tension. • BEC’s can have EXTREME optical properties • In 1998 light was slowed to 17m/s in a BEC of Na atoms Velocity distribution [16] Velocity distribution [1] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 4
  5. 5. What is a Bose-Einstein Condensate? • At low T the de Broglie wavelength is large enough that wave functions of individual atoms begin to overlap • These particles can now be described by a single wave function • BEC forms when phase space density = 1 and at a Temperature called the “critical temperature” Tc λdB = ( 2πћ2/ mkBT )1/2 PSD = npkλ3 dB Npk is the peak number density of the sample [5] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 5
  6. 6. Critical Temperature • Must occur when all of particles can barely be accounted for in excited states g(ϵ) is confining potential • This means any further loss in KE will lead to larger occupation of ground state • At this temperature, chemical potential must be zero (Griffiths problem 5.30)** • Potential of trap approximated as 3d HO with cylindrical symmetry ρ2 = x2 + y2 + λ2z2 and λ = ωz/ωr (ratio of axial and radial trap frequencies) [8] BEC of 84Sr : T > Tc T ≈ Tc T < Tc [5] [5] [5] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 6
  7. 7. Laser Cooling Laser Cooling [15, 18] • Lasers are “detuned” to a frequency which corresponds to an energy BELOW a desired energy level transition • Due to Doppler effect, photon scattering occurs for atoms moving towards light • Loss of momentum is in direction of motion • After emission of photon, gained momentum is in random direction • Repeat process many times, net loss of momentum • Thermal energy related to KE, therefore a net loss in thermal energy • Temperature limit due to mean squared velocity of random process. • γ term is inverse of lifetime for excited state of the atom Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 7
  8. 8. Evaporative Cooling“atom trap” [1] • Combined with laser cooling the high phase space densities required for BEC can be achieved • Atoms trapped in “potential well” • “hot” atoms with enough KE escape • Slowly decrease well depth to achieve further cooling • rf-induced “spin-flips” remove higher energy atoms • Magnetic field vanishes at center of spherical quadrupole potential where it changes direction rapidly. A hole in the trap! [9] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 8
  9. 9. [7] • Magnetic moment of trapped atoms required to be in opposite direction of magnetic field • “Majorana flip” magnetic moment of some atoms will flip without a field present • Slightly “detuned” laser ultra-focused on this “hole” creates a repulsive optical dipole force which acts as a “plug” • Optical dipole force arises due to coherent interaction of inhomogenous EM field with induced dipole moment of the atom • These magneto-optic traps only permit study of weak-field seeking states, whose spin degree of freedom is frozen. • Single spin state BEC “scalar” BEC • Optical traps allow for study of states with non-zero quantum number m • Spinor BEC, spin-f BEC has 2f + 1 space/time varying compoonents U = -µ·B Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 9
  10. 10. Fermionic Condensates BEC “Fermi Sea” • Pairs of Fermions have integer spin and can form condensates • Major breakthrough was the ability to control interactions • Favor pairing such as cooper pairs of electrons • Current experiments aim to study connection between BEC’s, superfluidity, and superconductivity • BSC-BEC Crossover theory [4] [6] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 10
  11. 11. Ultra-Slow Light in a BEC! • BEC is illuminated with a coupling laser • Optical properties of atoms can be dramatically altered • Becomes a coupled atomic-light medium • Coupling laser couples state |2 › and |3 › • lower level unoccupied, coupling laser splits higher level into two symmetric energy levels • Energy gap proportional to E of coupling laser • Probe laser tuned to the |1 › |3 › transition is “injected” into the BEC • It is this laser pulse which travels at extremely low group velocity Dr Lene Hau - Harvard [17] Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 11
  12. 12. References [1] Bose-Einstein Condensation in a Gas of Sodium Atoms K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 [2] Bose–Einstein condensation of atomic gases James R. Anglin & Wolfgang Ketterle Research Laboratory for Electronics, MIT-Harvard Center for Ultracold Atoms, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA [3] The art of taming light: ultra-slow and stopped light Zachary Dutton, Naomi S Ginsberg, Christopher Slower, and Lene Hau Lyman Laboratory, Harvard University, Cambridge MA 02138 [4] Fermi Condensates Markus Greiner, Cindy A. Regal, and Deborah S. Jin JILA, National Institute of Standards and Technology and University of Colorado, and Department of Physics, University of Colorado, Boulder, CO 80309-0440 [5] Bose-Einstein Condensate : [6] Creating new states of matter: Selim Jochim MPI für Kernphysik and Universität Heidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich. [7] “Plugging the hole” : [8] “The Strontium Project” : [9] “Cooling and Trapping Techniques With Ultra-cold Atoms” : [10] Spinor Bose-Einstein condensates Yuki Kawaguchi 1a, Masahito Uedaa,b aDepartment of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113- 0033, Japan bERATO Macroscopic Quantum Control Project, JST, Tokyo 113-8656, Japan [11] Chapter 5 lecture slides Dr. Hao Zeng : [12] [13] "Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann Statistics" from the Wolfram Demonstrations Project ics/ [14] Introduction to Quantum Mechanics, 2nd Edition by Griffiths, David J., Pearson Education 2005 [15] “Laser Cooling” : [16] “Bose-Einstein Condensate” : [17] Q+A with Dr Lene Hau : [18] “Doppler Cooling” : Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016 12