C. Salomon

Dual Bose-Fermi Superfluids

Quantum Science SymposiumCity University Hong-Kong, November 9th, 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. JinS. Laurent

M. Rabinovic

C. Enesa

M. PierceM. Delehaye

D. Suchet

F. Chevy T. ReimannC. Salomon

I. Ferrier-Barbut

Theory:

T. Yefsah

• Introduction to quantum gases

• Dual Bose-Fermi superfluid with 7Li-6Li isotopes

• DynamicsCenter of mass modes and link with Equation of StateMeasurement of critical velocity for superfluid counterflow

Outline

1) I. Ferrier-Barbut, M. Delehaye, S. Laurent, A. T. Grier, M. Pierce,B. S. Rem, F. Chevy, and C. Salomon, Science, 345, 1035, 20142) M. Delehaye, S. Laurent, I. Ferrier-Barbut, S. Jin, F. Chevy, C. Salomon, PRL, 115, 265303, 20153) Y. Castin, I. Ferrier-Barbut and C. SalomonComptes-Rendus Acad. Sciences, Paris, 16, 241, 20154) S. Laurent, M. Pierce, M. Delehaye, T. Yefsah, F. Chevy, C. Salomon Phys. Rev. Lett., 118, 103403, 2017

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

+ polaritons and BEC of light

1 K 100 K 104K 106K1 mK1 µK T

thisroom

sun surface

sun centerHigh Tc

SC liquid

4He

cold atomic gases

Dilute, but interacting systems

Typical density:

Interatomic distance range of interatomic potentials

quantum of motion in the trap or box

thermal energy

Equilibrium properties and dynamics are governed by interactions

Neutron stars107 K

Temperature scale of cold gases

Superfluid 3He

Nobel prize 1997S. Chu, C. Cohen-Tannoudji, W. PhillipsLaser cooling and trapping of atoms

Nobel prize 2001E. Cornell, W. Ketterle, C. WiemanBose-Einstein condensation in dilutegases

Bose-Einstein statistics (1924)

Bose-Einstein condensate

Bose enhancement

(0.83 N)1/3= T C kB

hω

Quantum gases in harmonic traps

Dilute gases: 1995, JILA, MIT

Fermi-Dirac statistics (1926)

EF

Fermi sea

Pauli Exclusion

T << T = (6 N)F 1/3

kB

hω

Dilute gases: 1999, JILA

7Li (boson)

6Li (fermion)

~200µm

ENS 2001

T= 0.28 µK = 0.2(1) TC= 0.2 TF

Searching for superfluid Bose-Fermi systems: 4He - 3He mixture

Expected Tc ~ 1 to 20 µK ?Volovik, Mineev, Khalatnikov, JETP, 42, 342 (1975): Fermi liquid theory of mixture

?

4He

The magnitude and sign of a depend sensitively on the detailed shape of longrange potential Importance of position of last bound state

Atom-atom interactions

At low temperature, only s wave collisions, l =0

.

00

( )

tan ( )lim

ik r ikr

k

ar e er

kak

ψ

δ→

= −

= −

a: scattering length|a|~1 to 10 nm

2

1 2 1 24( ) ( )aV r r r r

mπ δ− = −

a > 0 : effective repulsive interactiona < 0 : effective attractive interaction

W(r)

r

66 /C r−

0a ≥

EB=-h2/ma2

0,0 0,5 1,0 1,5 2,0

-200

-100

0

100

200

scat

terin

g len

gth

[nm

]

Magnetic field [kG]

0a ≤

a = ∞

Tuning interactions in quantum gases: Lithium 6

Fermions with two spin states with attractive interaction

BEC of molecules BCS fermionic superfluid

Dilute gases: Feshbach resonance

Interaction strengthBound state No bound state

akFc

FeTT 2/π−≈

80’ Leggett, Nozieres, Schmidt-Rink, Eagles….

N. Navon, S. Nascimbène, F. Chevy, C. Salomon, Science 328, 729-732 (2010)

Pressure equation of state

Equation of State in the BEC-BCS crossover

BCS-BEC crossoverat T~ 0

BECof pairs

BCSregime

P/P0= f(1/kF a)

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~ 50-80 nK

7Li BEC

6Li Fermi gasat unitarity

In situ density profiles

Lifetime of mixture: 7s in shallowest trap

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

First sounds in mixture of superfluids

Superfluids have collective excitationsFor instance low energy excitations of a BEC are phonons, ie density waves

In a mixture of two superfluids, one expectstwo first sound modes Volovik, Mineev, Khalatnikov, JETP, 42, 342,(1975)

In a trap the lowest acoustic mode corresponds to center of mass oscillations of the clouds (dipole mode)

We displace the axial position of the clouds by having the waistof the dipole trap shifted from the magnetic trap minimum.

( )kε

k

( )

: /

k c k

c speed of sound m

ε

µ

=

=

6

7

2 17.06(1)2 15.40(1)

HzHz

ω πω π

= ×= ×

Coupled Superfluids

Long-lived Oscillations of both Superfluids

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

BEC

time

400 ms

Oscillations of both superfluids

Very small damping !Modulation of the 7Li BEC amplitude by ~30% at

Coherent energy exchange between the two oscillators

πωω 2/)~~( 76 −

BEC

Fermi SF

4 s0

Mean field model

πωω 2/)~~( 76 −

2

667

2( ) ( ) bf

eff bf bf

aV 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: kFabf<<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

66 0

(0) ( ) 1eff bf bfdnV g n V r gdµ

= + −

(0)

7 76 0

1 bfdngd

ω ωµ

= −

Thomas Fermi radius of BEC<< TF radius of Fermi Superfluid:

The potential remains harmonic with rescaled frequency

Boson effective potentialand link with Equation of State

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

( )n µ

Example: at unitarity, 1/a=0

A new means to access properties of the EoS !

Equation of State and Bose-Fermi Coupling in BEC-BCS crossover

From EoS in the crossoverN. Navon et al, Science 2010

MIT ’12

6.190 bf

f

aa

≅

Shift in BEC limit7 7/

F bfk aδω ω

1/ kF fa

7 6 7cos( ) (1 )cos( )z t tε ω ε ω= − + +

6 6 7(1 )cos( ) cos( )z t tερ ω ερ ω= − +

with 7

6

NN

ρ = and

Hence a significant modulation of the amplitude of z7at the beat frequency 6 7ω ω−

7 7 7

7 6 7

2 0.21mm m

ω ωεω

−= −

=14

6K67K 7K

Two coupled oscillators

Coherent energy exchange between both gases isamplified by quasi-degeneracy of pendulum frequencies

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 FB k

kF k

εε −+ − ≥

V V

V c c= +c B FSound Modes:

, ', 0EE + =kk FB ' 0+ =k k

,, Bε kk, '', Fε kk

See also Abbad et al. EPJD 69, 126 (2015), F. Chevy, PRA 91, 063606 (2015), W. Zheng and 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

Summary

• Dual Bose-Fermi superfluids have intriguing novel properties

• Surprisingly high critical velocity for superfluid counterflowNature of quasi-particles ? Measure ε(k)

• Role of temperature: phase locking of B-F oscillations

• What happens when abf increases ?• Demixing• Competition between fermionic pairing or Bose-Fermi pairing? • Spin-imbalanced system

FFLO phases, 1D, 2D, 3DIs there a p-wave superfluid in strongly imbalanced Fermi gas?

• 2D Fermi gas and BKT physics

PhD Students and Postdocs are welcome !

Thank you for your attention !