A Mixture of Bose and Fermi Superfluids. C. Salomon

Transcription

1 A Mixture of Bose and Fermi Superfluids C. Salomon INT workshop Frontiers in quantum simulation with cold atoms University of Washington, April 2, 2015

2 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner, C.S. Lithium Exp. M. Delehaye S. Laurent M. Pierce I. Ferrier-Barbut A. Grier B. Rem U. Eismann A. Bergschneider T. Langen N. Navon Lithium-Potassium Exp. F. Sievers, D. Fernandes N. Kretschmar M. Rabinovic T. Reimann D. Suchet L. Khaykovich I. Ferrier-Barbut, M. Delehaye, S. Laurent, A. T. Grier, M. Pierce, B. S. Rem, F. Chevy, and C. Salomon Science, 345, 1035, 2014

3 104 years of quantum fluids Bose Einstein condensate Superconductivity High T c 77 K 4 He T~ 2.2 K 3 He 2.5 mk 100 nk dilute gas BEC Also BEC of photons and cavity polaritons Fermi gas superfluid

4 Superfluid mixtures Bose-Bose superfluid mixtures first observed long ago: Two hyperfine states in Rb at JILA (Myatt et al. 97) and vortex production Spinor condensates at MIT, Hamburg, Berkeley, ENS,. Dark-bright soliton production in two Rb BEC, Engels group, PRL 2011 Rb

5 Boson-fermion interactions Cooper pairing of electrons in superconductors (phonon exchange) High-energy physics / Meissner effect P. W. Anderson, P.R. 130, 439 (193) 4 He - 3 He mixtures Ultracold atom mixtures Strong boson - fermion repulsion prevented double SF so far Bose-Fermi Systems Li - 7 Li (2001) ENS, Rice Schreck et al., PRL 87, (2001) Truscott et al., Science 291, 2570 (2001) T (K) 23 Na - Li (2002) 40 K - 87 Rb (2002) Li - 87 Rb (2005) 3 He - 4 He (200) Li - 40 K - 87 Rb (2008) Li - 85,87 Rb (2008) 84,8,88 Sr - 87 Sr (2010) Li Yb (2011) 170,174 Yb Yb (2011) 40 K - 41 K - Li (2011) 11 Dy - 12 Dy (2012) 23 Na - 40 K (2012) Li Cs (2013) 52 Cr - 53 Cr (2014) 3 He concentration None doubly superfluid!! Tc ~ 50 µk? Rysti et al., PRB 85, (2012) A novel system: a double superfluid mixture of Li and 7 Li

6 Outline Experiment with Li- 7 Li isotopes Excitation of center of mass modes: first sounds Simple model Critical velocity for two-superfluid counterflow Perspectives

7 7 Li and Li isotopes

8 Fermi Superfluid in the BEC-BCS Crosover Li Fermions with two spin states and tunable attractive interaction The hydrogen atom of many-body physics! Molecular condensate Strongly bound Size: a << n -1/3 n -1/3 : average distance between particles On resonance na 3 >> 1 k F a 1 Pairs stabilized by Fermi sea Size of pairs hv F / ~k F -1 BCS regime: k F a <<1 Cooper pairs k, -k Well localized in Momentum: k~k F Delocalized in position

9 Equation of State in the crossover Pressure equation of state P/P 0 = f(1/k F a) BEC of pairs BCS regime BCS-BEC crossover at T~ 0 N. Navon, S. Nascimbène, F. Chevy, C. Salomon, Science 328, (2010) S. Nascimbène, N. Navon, K. Jiang, F. Chevy, C. Salomon, Nature 43 (2010)

10 Tuning interactions in 7 Li and Li Li in states 1> and 2> X 1/100 7 Li in state 2> Li- 7 Li 40.8 a 0

11 Experimental Setup Magneto-optical trap of bosonic 7 Li and fermionic Li After evaporation in a magnetic trap we load the atoms in a single beam optical trap (OT) with magnetic axial confinement. T~ 40 µk Evaporative cooling of mixture in OT ~ 4 second ramp, T~ 80 nk Absorption imaging of the in-situ density distributions or Time of Flight

12 In situ Profiles Li Fermi gas at unitarity N B = T=80 nk N 0 /N B > 80% T<T c /2 7 Li BEC N F = T= 80 nk ~ T c /2 T F = 800 nk Trap frequencies: v z =15. Hz for bosons, v rad = 440 Hz Expected SF fractions: N 0 /N B > 0.8 N 0 /N F ~0.8 Lifetime of mixture : 7s in shallowest trap

13 Long-lived Oscillations of both Superfluids Fermi Superfluid ω = 2π 17.0(1) Hz ω = 2π 15.40(1) Hz 7 Coupled Superfluids BEC ω = 2π 17.14(3) Hz ω 7 = 2π 15.3(1) Hz Single Superfluid Ratio = (7/) 1/2 =(m 7 /m ) 1/2

14 Oscillations of both superfluids BEC Fermi SF 0 Very small damping! Modulation of the 7 Li BEC amplitude by ~30% at ~ ω ~ ω ) / 2π ( 7 4 s

15 Mean field model 1.5% down shift in 7 Li BEC frequency BEC osc. amplitude beat at frequency ~ ω ~ ω ) / 2π ( 7 Weak interaction regime: k F a 7 <<1 and N 7 <<N 2 2π a7 Boson effective potential Veff = V () r + g7n () r with g7 = m7 m7 = mm 7 /( m + m7) 0 0 LDA n () r = n ( µ V()) r Where n ( µ ) is the Eq. of State of the stationary Fermi gas. For the small BEC: Expand 0 V ( r) << µ dn µ n ( r) n ( ) V( r) +... d µ

16 Effective potential With TF radius of BEC<< TF radius of Fermi SF, we get: (0) dn Veff = g7n (0) + V( r) 1 g7 dµ 0 The potential remains harmonic with rescaled frequency (0) dn ω7 = ω7 1 g7 dµ 0 n ( µ ) The equation of state is known in the BEC-BCS crossover N. Navon et al., Science, 2010

17 Effective potential With TF radius of BEC<< TF radius of Fermi SF, we get: (0) dn Veff = g7n (0) + V( r) 1 g7 dµ 0 The potential remains harmonic with rescaled frequency (0) dn ω7 = ω7 1 g7 dµ At unitarity 0 µ = ξ (3 π n ) / 2m with ξ = /3 Bertsch param. We simply get 3 g7n (0) 13kF a 7 ω7 = ω7 1 ω (0) = 7 1 5/4 4µ 7πξ ~ ω7 = 2π Hz ω7 = 2π 15.40(1) Hz From Thomas Fermi radius of Li superfluid, we find very close to the measured value:

18 Bose-Fermi Coupling in BEC-BCS crossover From EoS in the crossover N. Navon et al, Science 2010 MIT 12 Shift in BEC limit.190 a a 7

19 What is the critical velocity for superfluid counterflow?

20 Landau critical velocity Impurity of mass M moving with velocity v inside a superfluid Emission of an elementary excitation of momentum p and energy (p) Energy and momentum conservation: ε Sound excitations phonons

21 critical velocity Bose gas MIT: 3D geometry, moving laser beam v c /c s between 0.1 and 0.2 2D geometry: ENS 2012 Seoul Univ. + Many theory papers! Fermi gas in BEC-BCS crossover MIT: 3D geometry, moving standing wave method C. Raman et al. PRL 1999 R. Onofrio et al. PRL 2000 Miller, PRL 2007 v c /c s ~ 0. v c /v F ~ 0.3 LASER Hamburg: 3D geometry v c /c s ~ 0.8 v c /v F ~ 0.3 Weimer et al. PRL 2015

22 BEC: a new probe of Fermi superfluid Fermi SF BEC The BEC is a mesoscopic probe of the Fermi SF near its center finite mass impurity! No damping only when the max relative velocity < 2 cm/s

23 Critical velocity for superfluid counterflow Initial damping γ = 3.1 s 1 Time(ms) v s = ξ 1/4 v 5 F v c appears higher than the speed of sound of unitary gas in elongated trap!

24 Critical velocity for two T=0 Bose gas quasi-particles: Bogoliubov dispersion: ω = ck + ( k /2 m) s 7 ε ( k ) 2 µ m7cs = n = ng = µ n ε ( k Fermi gas quasi-particles: F ) Two contributions: phonons, ε ( k and pair breaking ph ) ε f ( k ) Bose gas moving with velocity v ε B ( k ) + kv. Energy and momentum conservation ε ( k) kv. = ε ( k) B B F Combescot Kagan Stringari 1 k ε ε Landau critical velocity: v = min ( ( k) + ( k) ) c k B F Y. Castin, I. Ferrier-Barbut and C. Salomon Comptes-Rendus Acad. Sciences, Paris, 1, 241 (2015)

25 Counter-flow critical velocity Several excitation branches in the Fermi gas At unitarity, we expect the phonon modes to dominate: v = c + c c B F The critical velocity is the sum Combescot, Kagan and Stringari PRA 74, (200) of the speed of sound in Bose gas c B and speed of sound in Fermi gas c F theory Theory c c B F = 0.10(2) v = 0.3(4) v F F v c = 0.4() v F Experiment vc = 0.42(4) vf v / c = 1.1(20) c F

26 Counter-flow critical velocity in BEC-BCS crossover BEC side BCS side

27 Critical velocity in the BEC-BCS crossover

28 Critical velocity in the BEC-BCS crossover Speed of sound c B Speed of sound c F? Astrahkarchik J. Thomas BCS BEC Compatible with v c =c B +c F around unitarity

29 Comparison with other measurements in pure Fermi gases Laser excitation: moving standing wave potential (MIT) or laser stirrer (Hamburg) LASER Weimer et a PRL 15 MIT Miller, PRL 2007

30 Summary Production of a Bose-Fermi double superfluid First sounds in low temperature limit Measurement of critical velocity in BEC BCS crossover Theory: - role of Bose-Fermi interaction: M. Habad, Recati, Stringari, Chevy arxiv: v1 - Lifetime of excitations: W. Zheng, Hui Zhai, PRL 113, Influence of harmonic trap Perspectives Temperature effects and nature of excitations Flat bottom trap for fermions when a bb =a bf Ozawa et al Search for FFLO Phase with spin imbalanced gas Rotations, vortices, second sound, higher modes Bose-Fermi Superfluids in optical lattices and phase diagram