condensed matter physics in dilute atomic gases s. k. yip academia sinica
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Condensed matter physics in dilute atomic gases S. K. Yip Academia Sinica. possible to cool and trap dilute atomic gases. Atoms used: 7 Li 23 Na 87 Rb 1 H He* Yb 6 Li 40 K. Some typical numbers: - PowerPoint PPT PresentationTRANSCRIPT
Condensed matter physics in
dilute atomic gases
S. K. YipAcademia Sinica
possible to cool and trap dilute atomic gases
Atoms used:
7Li 23Na 87Rb 1H He* Yb6Li 40K
Some typical numbers:
number of atoms 104 106 108
(final) (mostly)
peak density n < 10 14 cm-3
distance between particles ~ 104 A (dilute gas)
size of cloud ~ m
temperatures: down to nK
nucleus + [ closed electronic shell ] + e _
nucleon N odd atom = boson N even fermion
7Li 23Na 87Rb 1H : Bosons6Li 40K : Fermions
f = I s = I + 1/2hyperfine spin nuclear spin electron spin
mf = - f, - f + 1, …. , f -1, + f (integers for bosons, half-integers for fermions)
_
alkalis
6Li s = 1/2, i = 1; f = 1/2 , 3/2
Magnetic Trap (most experiments):
magnetic moment - . B ( r )
| B ( r ) | increasing from the center
trapped
not trapped
U
r
typically can trap only one species ( else loss due to collisions ) effectively scalar ( spinless ) particles
. .... .. .
.
.. ... .. ...
laser
spin degree of freedom remains
Optical Trap:
U ( r ) = - ( ) E2 ( r , )1
2
( ) > 0 if red detunedex
g ( < res )
atoms attracted to strong field region
(c.f. driven harmonic oscillator)
Identical particles bosons fermions
many particle wavefunctions:
symmetric antisymmetric
can occupy the samesingle particle states
at sufficiently low T
macroscopic occupation
Bose-Einstein Condensation
BOSONS:
Macroscopic wavefunction (common to all condensed particles)
(r, t)
(c.f Schrodinger wavefunction)
Supercurrent:
)(2
** mi
J
ie|| 2||J
Phase gradient supercurrent
Quantized vortices:
)(r
well defined at any position r
If || then unique up to 2n
0 0 2
Rotating superfluid:
if = constant, then not rotating (no current)
rotating constant
but circulation quantized quantized vortices
0 2
[MIT, Science, 292, 476 (2001)]
FERMIONS:
FERMIONS
Exclusion principle:
T=0
Particles filled up to Fermi energy
Normal Fermi gas (liquid)
Generally NOT superfluid
Momentum space: Fermi sphere
Single species (can be done in magnetic traps):
FERMIONS
T=0
Momentum space: Fermi sphere
Two species: need optical trap
still not much interesting unless interacting
6Li s = 1/2, i = 1; f = 1/2 , 3/2
}
(need optical trap)
Can be superfluid if attractive interaction : Cooper pairing
(Bardeen, Cooper, Schrieffer; BCS)
k -k all k’s near Fermi surface
Underlying mechanism for superconductivity (in perhaps all superconductors)
How to get strong enough attractive interaction in dilute Fermi gases
Feshbach Resonances:
B
(1 2)
(others)
Bres
Hydridization level repulsion
Hydridization level repulsion
Lowering of energy attractive interaction
B
Two particles
no coupling:
continuum
closed channel molecule
continuum
with coupling:
effective attractive interaction between fermions
Bound state
eventuallyBEC of molecules
effective attractive interaction between fermions
Bound state
BCS pairing
Smooth crossover from BCS pairing to BEC (Leggett 80)
Experimental evidence:
[MIT, Nature, 435, 1047 (2005)]
(resonance)
New possibilities:
unequal population
[c.f. superconductor in external Zeeman field: pair-breaking ]
Smooth crossover is destroyed ! ( Pao, Wu, Yip; 2006)
uniform superfluid state unstable in shaded region
N
BFhomogenousmixture
Many potential ground states for the shaded region
experiments suggest phase separation near resonance
another likely candidate state: Larkin-Ovchinnikov/ domain-walls (c.f. -junctions in SFS) not yet found
Finite T phase diagram open question
Interesting interacting system even when it is not superfluid (non-Fermi liquid behaviours?)
Many other topics not covered:
atoms in periodic lattice (c.f. solid!)
“random” potential
multicomponent (spin) Bosonic superfluids
low dimensional systems (e.g 1D)
rapidly rotating Bose gas (maximum number of vortices ?)
tunable parameters, often in real time
and many more opportunities!!