experiments with ultracold atomic gases andrey turlapov institute of applied physics, russian...
TRANSCRIPT
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