Experiments with ultracold atomic gases Andrey Turlapov Institute of Applied Physics, Russian...

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


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


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


laser

|g

|e mj = –1 mj = +1mj = 0

|g>

Energy

z0

laser +

mj=+1 mj= -1

mj=0


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

Experiments with ultracold atomic gases Andrey Turlapov Institute of Applied Physics, Russian...

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