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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!
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