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Counterflowing superfluids

Frédéric ChevyLaboratoire Kastler Brossel

ENS FERMI GROUP

Y. Castin (ENS), S. Stringari (Trento), I. Danaila (Rouen), P. Parnaudeau (Poitiers)

S. JinS. Laurent

M. Rabinovic

C. Enessa

M. Pierce M. Delehaye

D. SuchetFC

T. Reimann

C. Salomon

I. Ferrier-Barbut

3He/4He phase diagram

7Li (boson)

6Li (fermion)

~200µm

Achieving double superfluidity withcold atoms

Requirements: •Low abf (no interspecies demixing)•High |aff |(high fermionic Tc)•Positive abb (stable BEC)

6Li – 7Li mixture in the |1>f, |2>f and |2>b

6Li

7Li

I. Ferrier-Barbut, et al., Science 345, 1035 (2014)

T/Tcb,f<0.5

Superfluid mixture @ B=832G

DYNAMICS OF THE MIXTURES

6

7

2 17.06(1)2 15.40(1)

HzHz

ω πω π

= ×= ×

Coupled Superfluids

6

7

2 16.80(2)2 15.00(2)

HzHz

ω πω π

= ×= ×

Single SuperfluidRatio = (7/6)1/2 =(m7/m6)1/2

See also C. Hammer et al Phys. Rev. Lett. 106, 065302 (2011) for boson-boson superfluid counterflow

FREQUENCY SHIFT

Benchmark: Numericalsolution of GPE (P. Parnaudeau/I. Danaila/A. Suzuki)

Sum ruleEffective potential

eff ,7 67 6 6( ) ( ( ))V V g n µ= +r r 06 6 6( ( )) ( )µ n µ V= −r r

0 667 6 6 67

6

( ) ( ) 1 ng n µ V gµ

∂≈ + − ∂

r

(Local Density Approximation)

Harmonic trap: 7 67 6

7 62g n

µωω∆ ∂

≈ −∂

OSCILLATION FREQUENCY OF THE BEC

Weak frequency shift (few percents) of the bosons due to the fermions

67 67 7

6

~ 12

g dnd

ω ωµ

−

Oscillations of 7Li

Large initial displacement:Damped oscillations

Small initial displacement:•Almost no damping (decay time>4s)•Beatnote (coherent coupling between the twooscillators)

Critical velocity

LANDAU’S CRITERION

V

2 2

'/ 2

Momentum Conservation :

Energy Conservation /2+ :

M MMV MV ε

= +

′= k

V V k

The motion of the impurity is damped by the creation of elementary excitations if

min kc kV V

kε ≥ =

V’

,εkk

= sound velocity for a linear excitation spectrum ε=kc

2 2. / 2k k mε= +k V kε≥kV ≥

Critical velocity

cFcb

Landau criterion for a superfluidMixture

(Castin et al. Comptes Rendus Physique 16, 241 (2015) arXiv:1408.1326)

1 Excitation in the bosonic superfluid

1 Excitation in the fermionic superfluid

, , ·B B BE ε= +k k k V

Energy-momentum conservation:

, , ' '·F F FE ε= +k k k V

, ,| | min B k F kB F k k

ε ε −+ − ≥

V V

c B FAcoustic Modes: V c c= +

, , ' 0B FE E+ =k k ' 0+ =k k

,, Bε kk, '', Fε kk

See also Abbad et al. EPJD 69, 126 (2015), F. Chevy PRA 91, 063606 (2015), W. Zheng et H. Zhai, Phys. Rev. Lett. 113, 265304 (2014)

Critical Velocity

experiment

cF

cF+cB

Similar reduction of vc at MIT and Hamburg for fermions.Possible explanations: finite temperature, vortex nucleation…

Validity of Landau’s argument?(see also V.P. Singh et al. arXiv:1509.02168 )

• Argument valid for a constant velocity in an homogeneousmedium.

• But:

Trapping potentialOscillatory motion

vs

Cozzo & Dalfovo, NJP (2003)Crépin, Leyronas & FC under submission

No critical velocity!

THANKS FOR YOURATTENTION!