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Experiments with ultracold atomic gases
Andrey Turlapov
Institute of Applied Physics, Russian Academy of Sciences
Nizhniy Novgorod
Fermions: 6Li atoms
670 nm
2s
2p
Electronic ground
state: 1s22s1
Nuclear spin: I=1
1,2
11 up 2
1spin :1 State
0,2
12down 2
1spin :2 State
12
3
45
6
Ground state splitting in high B
710
Optical dipole trap
Trapping potential of a focused laser beam:2EEdU
Laser: P = 100 Wlaser=10.6 m
Trap:U ~ 0 – 1 mK
The dipole potential is nearly conservative: 1 photon absorbed per 30 min
b/c laser=10.6 m >> lithium=0.67 m
2-body strong interactions in a dilute gas (3D)
At low kinetic energy, only s-wave scattering (l=0).
For l=1, the centrifugal barrier ~ 1 mK >> typical energy ~ 1 K
2
2
2
)1()()(
rm
llrVrVeff
L = 10 000 bohr
R=10 bohr ~ 0.5 nm( )V r
s-wave scattering length a is the only interaction parameter (for R<< a)
Physically, only a/L matters
1 2
Feshbach resonance. BCS-to-BEC crossover
200 400 600 800 1000 1200 1400 16000
2500
5000
-5000
-2500
-7500
В, gauss
a, bohr
Singlet 2-body potential:
electron spins ↑↓
Triplet 2-body potential:
electron spins ↓↓
BCS
s/fluid
BEC
of Li2
22 /4,4 :resonanceOn Fka
Fl ikaik
f1
/1
10
b/c s-wave scattering amplitude:
Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas (a → ∞)
[Duke,
Science
(2002)]
M. Gyulassy: “Elliptic flow is everywhere”
Crab nebula
Elliptic, accelerated expansion
Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas (a → ∞)
[Duke,
Science
(2002)]T < 0.1 EF
Superfluidity ?
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
pppppppp
p
aaaaUaap
H,'
''0,
2
2
'''|,',,
''0
2
2121
2121
12212pppp
pppppppppp
p
aaaaUaap
H
High-temperature superfluidity in the unitary limit (a → ∞)
||2exp~
F akET Fc
Bardeen – Cooper – Schrieffer:
Theories appropriate for strong interactions
Levin et al. (Chicago):
Burovsky, Prokofiev, Svistunov, Troyer
(Amherst, Moscow, Zurich):
29.0Fc ET
The Duke group has observed signatures of phase transition in different
experiments at T/EF = 0.21 – 0.27
22.0Fc ET
High-temperature superfluidity in the unitary limit (a → ∞)
Group of John Thomas
[Duke, Science 2002]
Superfluidity ?
vortices
Group of Wolfgang Ketterle
[MIT, Nature 2005]
Superfluidity !!
Breathing mode in a trapped Fermi gas
Trap ON again,
oscillation for variable
offtholdt
Image
1 ms
Releasetime
Trap
ON
Excitation &
observation:
300 m
[Duke, PRL 2004, 2005]
Breathing Mode in a Trapped Fermi Gas
840 G Strongly-interacting Gas ( kF a = 30 )
tAxtx t cose)( /0rms
= frequency = damping timeFit:
Breathing mode frequency
Transverse frequencies of the trap:
107.1yx
z
yx ,
Trap
yx
11.22 x
Prediction for normal collisionless gas:
Prediction of universal isentropic hydrodynamics(either s/fluid or normal gas with many collisions):
1.84 at any T
2.0
1.8
Fre
quen
cy (
)
1.21.00.80.60.40.20.0T/EF
Tc
Frequency vs temperature for strongly-interacting gas (B=840 G)
Hydrodynamic
frequency, 1.84
at all T/EF !!
Collisionless gas
frequency, 2.11
0.10
0.05
0.00Dam
ping
rat
e (1
/
)
1.21.00.80.60.40.20.0
T/EF
Damping rate 1/ vs temperature for strongly-interacting gas (B=840 G)
Hydrodynamic oscillations.Damping vs T/EF
Superfluid
hydrodynamics
Collisional hydrodynamics
of Fermi gas
0/ 2coll FET
:0 As TBigger superfluid
fraction.
In general,
more collisions longer damping.
:0 As TCollisions are Pauli blocked b/c
final states are occupied.
Oscillations damp faster !!
Slower damping
0.10
0.05
0.00Dam
ping
rat
e (1
/
)
1.21.00.80.60.40.20.0
T/EF
Damping rate 1/ vs temperature for strongly-interacting gas (B=840 G)
0.10
0.05
0.00Dam
ping
rat
e (1
/
)
1.21.00.80.60.40.20.0
T/EF
2.0
1.8
Fre
quen
cy (
)
1.21.00.80.60.40.20.0T/EF
))((
1equil. local
fieldmean trap ffE
TfUU
m
f
t
f
Fcoll
vrrv
Black curve – modeling by kinetic equation
0.10
0.05
0.00Dam
ping
rat
e (1
/
)
1.21.00.80.60.40.20.0
T/EF
Damping rate 1/ vs temperature for strongly-interacting gas (B=840 G)
Phase
transitionPhase transition
27.0F
cT
T
Shear viscosity bound
vd
AF
:t coefficienosity Shear visc
d v
Kovtun, Son, Starinets (PRL, 2005):
In a strongly-interacting quantum system
s – entropy density
4
s
Strongly-interacting atomic Fermi gas –
fluid with min shear viscosity ?!!
Quantum Viscosity?
Viscosity: nL
L
2section cross
momentum n(...)
n
PU
m
tm
2
2u
u
Assumption: Universal isentropic hydrodynamics
Calculate viscosity from breathing mode
lki l
lik
k
i
ki x
u
x
u
xn ,,
0
3
22
1 x
One eq.: normal & s/f component flow together
nn
Tn
T
F
3/2
Viscosity / Entropy densityfor a universal isentropic fluid
nT
F
E1
NSsxd
xd
/3
3
particleper entropy - where NS
s
NS
E
/
11
Viscosity / Entropy density
NS
E
s /
11
4
s ?
1.5
1.0
0.5
0.0
/
s
2.52.01.51.00.5
E/EF
s
String theory
limit 1/4
s/f
transition
0T FET 1.1
3He & 4He
near -point
Quark-gluon plasma,
S. Bass, Duke, priv.
Ferromagnetism: An open problems
Itinerant ferromagnetism in 2D
Normal
phase
Ferro-
magnet
Eferro < Enorm at g > 4
22
4 2
2
ferro nm
E
zl
agn
mgn
mE ~,
224 2
2
2
2
norm
2D at T=0:
NEF 2
where N = # of atoms
2D Fermi gas in a harmonic trap
22
)(22222 zmyxm
xV z
z
zFE – condition of 2D in ideal gas at T=0
2
22zm z
z
Open problems
2. Superfluidity in 2D
Berezinskii – Kosterlitz – Thouless transition
BKT transition not yet observed directly in Fermi systems.
Indirect observations in s/c films questioned [Kogan, PRB (2007)]
3. 3-body bound states
2D and quasi-2D analogs of the 3D Efimov states ?
How to parameterizea universal Fermi gas ?
Temperature (T) or Total energy per particle (E) ?
E
S
T
1
Temperature:
Energy measured from the cloud size !!
22tot 3/ zmNEE z
z
UTrap potential
0 UnPForce Balance:
),( TnPpressure ),(3
2Tn
Local energy density (interaction + kinetic)
In a universal Fermi system:
[Ho, PRL (2004)]
totaltotal2 EU Virial Theorem:Thomas, PRL (2005)
Resonant s-wave interactions (a → ± ∞)
Is the mean field ?
Energy balance at a → - ∞: nm
an
m
23/22
2 46
2
nm
aU
2
int
4
Collapse
aikfl /1
10
s-wave scattering amplitude:
In a Fermi gas k≠0. k~kF. Therefore, at a =∞, F
l ikf
10
Fkan
m
aU
1~ where,
4eff
eff2
int
3~ Fkn 3/22222
int 62
)(2
~ nm
nm
kU F
F
?
2 stages of laser cooling
1. Cooling in a magneto-optical trap
Tfinal = 150 K
Phase-space density ~ 10-6
2. Cooling in an optical dipole trap
Tfinal = 10 nK – 10 K
Phase-space density ≈ 1
The apparatus
1st stage of cooling: Magneto-optical trap
laser
|g
|e
photon
atompatompphoton=hk|g
patom-hk|e
1st stage of cooling: Magneto-optical trap
laser
|g
|e mj = –1 mj = +1mj = 0
|g>
Energy
z0
laser +
mj=+1 mj= -1
mj=0
1st stage of cooling: Magneto-optical trap
N ~ 109 T ≥ 150 K n ~ 1011 cm-3
phase space density ~ 10-6
2nd stage of cooling: Optical dipole trap
Trapping potential of a focused laser beam:2EEdU
Laser: P = 100 Wlaser=10.6 m
Trap:U ~ 250 K
The dipole potential is nearly conservative: 1 photon absorbed per 30 min
b/c laser=10.6 m >> lithium=0.67 m
2nd stage of cooling: Optical dipole trapEvaporative cooling
N
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 K, n = 1011 – 1014 cm-3
Absorption imaging
CCD matrix
Imaging over few microseconds
Laser beam
=10.6 m
Trapping atoms in anti-nodes of a standing optical wave
Laser beam
=10.6 m Mir
ror
V(z)
z
Fermions: Atoms of lithium-6 in spin-states |1> and |2>
Absorption imaging
CCD matrix
Imaging over few microseconds
Laser beam
=10.6 m Mir
ror
Photograph of 2D systems
z, m
x,
m
atom
s/m
2 Each cloud ≈ 700 atoms
per spin state
Period = 5.3 m
T = 0.1 EF = 20 nK
Each cloud is
an isolated 2D system
[N.Novgorod, PRL 2010]
Temperature measurementfrom transverse density profileL
inea
r de
nsit
y,
m-1
x, m
Temperature measurementfrom transverse density profile
T
xm
TeTm
xn 22/3
2/3
1
22
Li2
)(
Lin
ear
dens
ity,
m
-1
2D Thomas-Fermi profile:
T=(0.10 ± 0.03) EF
Temperature measurementfrom transverse density profile
Lin
ear
dens
ity,
m
-1
Gaussian fit
T
xm
TeTm
xn 22/3
2/3
1
22
Li2
)(
2D Thomas-Fermi profile:
T=(0.10 ± 0.03) EF
=20 nK
The apparatus (main vacuum chamber)
Maksim Kuplyanin, A.T., Tatyana Barmashova, Kirill Martiyanov, Vasiliy Makhalov