dual bose-fermi superfluids · 1 excitation in the bosonic superfluid. 1 excitation in the...
TRANSCRIPT
C. Salomon
Dual Bose-Fermi Superfluids
OIST, September 27, 2017
ENS FERMI GAS GROUP
Y. Castin, F. Werner, X. Leyronas (ENS), S. Stringari (Trento), A. Recati, T. Ozawa,O. Goulko (Amherst), C. Lobo, J. Lau (Southampton), I. Danaila (Rouen)
S. Jin
S. Laurent
M. Rabinovic
C. Enesa
M. PierceM. Delehaye
D. Suchet
F. Chevy T. ReimannC. Salomon
I. Ferrier-Barbut
Theory:
Bose Einstein condensate Superconductivity
106 years of quantum fluids
4He
dilute gas BECFermi gas superfluid
T~ 2.2 K
High Tc77 K
100 nK
2.5 mK3He
20 years of BEC !
• Bose-Fermi double superfluid mixture with 6Li-7Li isotopes
• Measurement of critical velocity for superfluid counterflow
• Temperature effect: phase locking of the B-F oscillations
• Perspectives
Outline
I. Ferrier-Barbut, M. Delehaye, S. Laurent, A. T. Grier, M. Pierce,B. S. Rem, F. Chevy, and C. Salomon, Science, 345, 1035, 2014M. Delehaye, S. Laurent, I. Ferrier-Barbut, S. Jin, F. Chevy, C. Salomon, PRL, 115, 265303, 2015Y. Castin, I. Ferrier-Barbut and C. SalomonComptes-Rendus Acad. Sciences, Paris, 16, 241, 2015
Superfluid mixturesBose-Bose superfluid mixtures first observed long ago:
Two hyperfine states in Rb at JILA (Myatt et al. ’97) and vortex productionMixtures of BEC at LENSSpinor condensates at MIT, Hamburg, Berkeley, ENS, ….
Dark-bright soliton production in two Rb BEC, Engels group, PRL 2011
Rb
Bose-Fermi mixtures studied in many labsbut none with double superfluidity !
Searching for superfluid Bose-Fermi systems: 4He - 3He mixture
Expected Tc ~ 50 µK ?Volovik, Mineev, Khalatnikov, JETP, 42, 342 (1975): Fermi liquid theory of mixture
?
7Li (boson)
6Li (fermion)
~200µm
ENS 2001
7Li and 6Li isotopes
Requirements: • Low abf (no interspecies demixing)• High |aff |(high fermionic superfluid Tc)• Positive abb (stable BEC)
Double superfluidity with cold atoms
abf = 40.8 a0
6Li – 7Li mixture in the |1>f, |2>f and |2>b
Experimental Setup
Absorption imaging of the in-situdensity distributions or Time of Flight
Magneto-optical trap of bosonic7Li and fermionic 6LiAfter evaporation in a magnetic trapwe load the atoms in a single beamoptical trap (OT) with magnetic axial confinement. T~ 40 µK
Evaporative cooling of mixture in OT
~ 4 second ramp, T~ 80 nK
7Li BEC
6Li Fermi gasat unitarity
In situ density profiles
Trap frequencies: vz=15.6 Hzfor bosons, vrad= 440 Hz
NB= 2 104
T=80 nKN0/NB> 80%T<Tc/2
NF= 2 105
T= 80 nK ~ Tc/2TF= 800 nK
Unitary 6Li Fermi gas can cool any species fulfilling the requirements to BEC See also 6Li-41K, USTC, China, PRL ’16, and 6Li-173Yb, UWash, PRL’17
Cool molecules to quantum regime ?
6
7
2 17.06(1)2 15.40(1)
HzHz
ω πω π
= ×
= ×
Coupled Superfluids
Long-lived Oscillations of Superfluid counterflow
6
7
2 17.14(3)2 15.63(1)
HzHz
ω πω π
= ×
= ×
Single SuperfluidRatio = (7/6)1/2 =(m7/m6)1/2
Fermi Superfluid
BECtime 400 ms
Oscillations of both superfluids
Very small damping !Modulation of the 7Li BEC amplitude by ~30% at πωω 2/)~~( 76 −
BEC
Fermi SF
4 s0
Mean field model
πωω 2/)~~( 76 −
267
67 6 6767
2( ) ( )effaV V r g n r with g
mπ
= + =
67 6 7 6 7/ ( )m m m m m= +
1.5% down shift in 7Li BEC frequency
Weak interaction regime: kFa67<<1 and N7<<N6
Boson effective potential
LDA 0 06 6 6( ) ( ( ))n r n V rµ= −
is the Eq. of State of the stationary Fermi gas. )(6 µnWhere
BEC osc. amplitude beat at frequency
For the small BEC: 06)( µ<<rV 0
0 0 66 6 6
6
( ) ( ) ( ) ....dnn r n V rd
µµ
≈ − +Expand
(0)6
67 6 676 0
(0) ( ) 1effdnV g n V r gdµ
= + −
(0)
7 7 676 0
1 dngd
ω ωµ
= −
With TF radius of BEC<< TF radius of Fermi SF, we get:
The potential remains harmonic with rescaled frequency
Effective potential
From Thomas Fermi radius of 6Li superfluid, we find:very close to the measured value:
Hz43.152~7 ×= πω
7 2 15.40(1) Hzω π= ×
The equation of state at low T is known in the BEC-BCS crossoverN. Navon et al., Science, 2010, Ku et al., MIT, 2012
( )n µ
Example: at unitarity, 1/a=0
Bose-Fermi Coupling in BEC-BCS crossover
From EoS in the crossoverN. Navon et al, Science 2010
MIT ’12
67
6
6.190 aa
≅
Shift in BEC limit
What is the critical velocityfor superfluid counterflow ?
Increase relative velocity
Increase initial displacement
Critical velocity for superfluid counterflow
Time(ms)
13.1 sγ −=
Initial damping
Vc = 2 cm/sis quite high !
V
2 2
'/ 2
Momentum Conservation :
Energy Conservation /2+ :
M MMV MV ε
= +
′= k
V V k
Motion of impurity is damped by the creation of elementary excitations if:
min kc kV V
kε ≥ =
V’
,εkk
For a linear excitation spectrum εk=kc, Vc= c, the sound velocity
2 2. / 2k k Mε= +k V kε≥kV ≥
Landau criterion
cFcb
Critical velocities
1 Excitation in the bosonic superfluid
1 Excitation in the fermionic superfluid
, , ·B B BE ε= +k k k V
Energy-momentum conservation: , ' , ' '·E ε= +k k k VF F F
, ,| | min B k F kB F k k
ε ε −+ − ≥
V V
V c c= +c B FSound Modes:
, , ' 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)
Revisiting Landau criterionfor a Bose-Fermi mixture @ T=0Y. Castin, I. Ferrier-Barbut and C. SalomonComptes-Rendus Acad. Sciences, Paris, 16, 241 (2015)
cFcB
Counter-flow critical velocity
cB+cF
Counter-flow critical velocityin BEC-BCS crossover
BCS sideBEC side
Critical velocity in the BEC-BCS crossover
Speed of sound cF
J. Thomas ’07Navon’10
Astrakharchik
Speed of sound cB
cF+cB
Near unitarity, data are consistent with both vc= cF and vc= cF+cB
• Landau and Castin criteria are valid for a constantvelocity in an homogeneous medium.
• But:Trapping potential Oscillatory motion
Cozzo & Dalfovo, NJP (2003)
Accelerated motion:Cerenkov radiationNo true critical velocity!
Discussion: a word of caution !
See also: V. P. Singh et al., arXiv:1509.02168, Weimer et al, PRL’15 (Hamburg)Miller et al., PRL 2007 (MIT)
Dissipation in Bose-Fermi mixtureInfluence of Temperature
So far, all experiments performed at T/TF = 0.03-0.05
Stopping evaporation at higher temperature: 0.03 < T/TF < 0.5
Small initial displacement of the Bose and Fermi clouds
Measure oscillation frequencies and damping rate
Next
Frequency analysisat finite temperature
Low temperature:
Blue: two SuperfluidsOrange: Fermi gas non SF and BECGreen diamond: no SF
6 / 7 0.925B F Fω ω ω=
B Fω ω=
Tc,B
For T > Tc,B= 0.34 TFThe Bose gas is dragged by the Fermi gas!
Dissipation at finite temperature
T/TF=0.4. The two clouds appear to oscillatein phase with equal and moderate damping !
bosons
fermions
Summary
• Measurement of critical velocity in in a Bose –Fermi superfluid
Influence of harmonic trap and finite size: work in progress
• Phase locking of oscillations induced by dissipation
• Perspectives
Flat bottom trap for fermions when abb=abf Ozawa et al. 2014
Search for FFLO Phase with spin-imbalanced gas
Rotations and vortices, second sound, higher modes
Bose-Fermi Superfluids in optical lattices and phase diagram