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