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BOSE-EINSTEIN CONDENSATTION-FLIERL(FINAL COPY)
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Transcript of BOSE-EINSTEIN CONDENSATTION-FLIERL(FINAL COPY)
BOSE-EINSTEIN CONDENSATTIONIncluding an introduction to Fermionic Condensates & Ultra-Slow light in a BEC
Aaron Flierl
SUNY BUFFALO
PHY 402
Spring 2016
[6]
1
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
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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
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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 atomsVelocity distribution [16]
Velocity distribution [1]
Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016
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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 = npkλ3dB
Npk is the peak number density of the sample
[5]
Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016
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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
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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
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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
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[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
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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
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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 velocityDr Lene Hau - Harvard [17]
Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016
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References
[1] Bose-Einstein Condensation in a Gas of Sodium AtomsK. 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 condensationof atomic gasesJames R. Anglin & Wolfgang KetterleResearch 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 lightZachary Dutton, Naomi S Ginsberg, Christopher Slower, and Lene HauLyman Laboratory, Harvard University, Cambridge MA 02138
[4] Fermi CondensatesMarkus Greiner, Cindy A. Regal, and Deborah S. JinJILA, 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 : http://massey.dur.ac.uk/resources/mlharris/Chapter2.pdf
[6] Creating new states of matter: Selim Jochim MPI für Kernphysik and UniversitätHeidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich.
[7] “Plugging the hole” : http://cua.mit.edu/ketterle_group/Projects_1995/Plugged_trap/Plugged_trap.htm
[8] “The Strontium Project” : http://www.strontiumbec.com/
[9] “Cooling and Trapping Techniques With Ultra-cold Atoms” : http://large.stanford.edu/courses/2009/ph376/amet1/
[10] Spinor Bose-Einstein condensates Yuki Kawaguchi 1a, Masahito Uedaa,baDepartment 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 : UBLearns.buffalo.edu
[12] https://commons.wikimedia.org/wiki/File:Mplwp_Fermi_Boltzmann_Bose.svg
[13] "Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann Statistics" from the Wolfram
Demonstrations Project
http://demonstrations.wolfram.com/BoseEinsteinFermiDiracAndMaxwellBoltzmannStatist
ics/
[14] Introduction to Quantum Mechanics, 2nd Edition by Griffiths, David J., Pearson Education 2005
[15] “Laser Cooling” : https://en.wikipedia.org/wiki/Laser_cooling
[16] “Bose-Einstein Condensate” : https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate
[17] Q+A with Dr Lene Hau : http://www.physicscentral.com/explore/people/hau.cfm
[18] “Doppler Cooling” : https://en.wikipedia.org/wiki/Doppler_cooling
Aaron Flierl PHY 402 SUNY BUFFALO Spring 2016
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