Experiments with ultracold atomic gases

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Experiments with ultracold atomic gases
Andrey Turlapov Institute of Applied Physics,
Russian Academy of Sciences Nizhniy Novgorod
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How ultracold Fermi atoms are related to nuclear
physics ?
The atoms are fermions With the atoms, one may
see major Fermi phenomena (as in other Fermi
systems) Fermi statistics Cooper pairing and
superfluidity strong interactions, i.e. Uint
EF
One may see even more with the atoms (the
phenomena unobserved in the other Fermi
systems) BEC-to-BCS crossover, i.e. crossover
between a gas of Fermi atoms and a gas of
diatomic Bose molecules stability of a
resonantly interacting matter resonant
superfluidity viscosity at the lowest quantum
bound (???) itinerant ferromagnetism (???).
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Good about atoms
Fundamentally no impurities Control over
interactions tunable s-wave collisions somewhat
tunable p-wave collisions dipole-dipole
collisions (perspective) Tunable spin
composition, more than 2 spins Tunable energy,
temperature, density Tunable dimensionality (2D
at Nizhniy Novgorod) Direct imaging
Bad about atoms
Small particle number (N 102 106 ltlt
NAvogadro) Non-uniform matter (in parabolic
potential) Coarse temperature tuning (dT gt EF/20
as opposed to dT EF/105 in solid-state-physics
experiments) No p-wave (and higher) collisions in
thermal equilibrium
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Fermions 6Li atoms
2p
670 nm
2s
Electronic ground state 1s22s1
Nuclear spin I1
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Optical dipole trap
Trapping potential of a focused laser beam
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Fermi degeneracy
Fermi energy
At T0
Phase space density r Natoms / Nstates 1
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2-body strong interactions in a dilute gas (3D)
L 10 000 bohr
R10 bohr 0.5 nm
s-wave scattering length a is the only
interaction parameter (for Rltlt a)
Physically, only a/L matters
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Scattering in 1-channel model
a gt 0 (a gt gtR) Repulsive mean field
The mean field (for weak interactions)
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Fano Feshbach resonance
Singlet 2-body potential electron spins ??
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Fano Feshbach resonance Zero-energy scattering
length a vs magnetic field B
5000
2500
a, bohr
200
400
600
800
1000
1200
1400
1600
0
-2500
-5000
-7500
?, gauss
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Instability of the agt0 region towards molecular
formation
Singlet 2-body potential electron spins ??
a, bohr
Triplet 2-body potential electron spins ??
?, gauss
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BCS-to-BEC crossover
Singlet 2-body potential electron spins ??
a, bohr
?, gauss
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Resonant s-wave interactions (a ? 8)
Is the mean field
?
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Universality
L
Strong interactions agtLgtgtR
At a?8, the system is universal, i.e., L is
the only length scale - No dependence on
microscopic details of binary interactions - All
local properties depend only on n and T
Experiment (sound propagation, Duke, 2007) b -
0.565(.015) Theory Carlson (2003) b - 0.560,
Strinati (2004) b - 0.545
Compare with neutron matter a 18 fm, R 2
fm
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2 stages of laser cooling

1. Cooling in a magneto-optical trap Tfinal
150 mK Phase-space density 10-6
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The apparatus
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1st stage of cooling Magneto-optical trap
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1st stage of cooling Magneto-optical trap
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1st stage of cooling Magneto-optical trap

N 109 T 150 mK n 1011 cm-3 phase
space density 10-6
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2nd stage of cooling Optical dipole trap
Trapping potential of a focused laser beam
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2nd stage of cooling Optical dipole
trapEvaporative cooling
Evaporative cooling - Turn on collisions by
tuning to the Feshbach resonance -
Evaporate The Fermi degeneracy is achieved at
the cost of loosing 2/3 of atoms. Nfinal 103
105 atoms, Tfinal 0.05 EF, T 10 nK 1 mK,
n 1011 1014 cm-3
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Absorption imaging
Laser beam l10.6 mm
Imaging over few microseconds
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Trapping atoms in anti-nodes of a standing
optical wave
Laser beam l10.6 mm
Mirror
V(z)
z
Fermions Atoms of lithium-6 in spin-states 1gt
and 2gt
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Absorption imaging
Laser beam l10.6 mm
Mirror
Imaging over few microseconds
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Photograph of 2D systems
Each cloud is an isolated 2D system
Each cloud 700 atoms per spin state Period
5.3 mm
atoms/mm2
x, mm
T 0.1 EF 20 nK
z, mm
N.Novgorod, PRL 2010
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Temperature measurementfrom transverse density
profile
Linear density, mm-1
x, mm
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Temperature measurementfrom transverse density
profile
T(0.10 0.03) EF
Linear density, mm-1
2D Thomas-Fermi profile
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Temperature measurementfrom transverse density
profile
Gaussian fit
T(0.10 0.03) EF 20 nK
Linear density, mm-1
2D Thomas-Fermi profile
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The apparatus (main vacuum chamber)
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Superfluid and normal hydrodynamics of a
strongly-interacting Fermi gas
T lt 0.1 EF Superfluidity ?
Duke, Science (2002)
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Superfluidity

1. Bardeen Cooper Schreifer hamiltonian
on the far Fermi side of the Feshbach resonance
2. Bogolyubov hamiltonian on the far Bose
side of the Feshbach resonance
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High-temperature superfluidity in the unitary
limit (a ? 8)
Bardeen Cooper Schrieffer
Theories appropriate for strong
interactions Levin et al. (Chicago) Burovsky,
Prokofiev, Svistunov, Troyer (Amherst, Moscow,
Zurich)
The Duke group has observed signatures of phase
transition in different experiments at T/EF
0.21 0.27
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High-temperature superfluidity in the unitary
limit (a ? 8)
Group of John Thomas Duke, Science
2002 Superfluidity ?
vortices
Group of Wolfgang Ketterle MIT, Nature
2005 Superfluidity !!
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Breathing mode in a trapped Fermi gas
Excitation observation
Trap ON again, oscillation for variable

1 ms
time
300 mm
Duke, PRL 2004, 2005
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Breathing Mode in a Trapped Fermi Gas
840 G Strongly-interacting Gas ( kF a -30 )
Fit
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Breathing mode frequency w
Transverse frequencies of the trap
Trap
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Frequency w vs temperature for
strongly-interacting gas (B840 G)
Collisionless gas frequency, 2.11
Hydrodynamic frequency, 1.84 at all T/EF !!
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Damping rate 1/t vs temperature for
strongly-interacting gas (B840 G)
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Hydrodynamic oscillations.Damping vs T/EF
Collisional hydrodynamics of Fermi gas
Superfluid hydrodynamics
In general, more collisions longer
damping.
Bigger superfluid fraction.
Collisions are Pauli blocked b/c final states are
occupied.
Slower damping
Oscillations damp faster !!
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Damping rate 1/t vs temperature for
strongly-interacting gas (B840 G)
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Black curve modeling by kinetic equation
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Damping rate 1/t vs temperature for
strongly-interacting gas (B840 G)
Phase transition
Phase transition
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Maksim Kuplyanin, A.T., Tatyana Barmashova,
Kirill Martiyanov, Vasiliy Makhalov