A Mixture of Bose and Fermi Superfluids. C. Salomon

Transcription

1 A Mixture of Bose and Fermi Superfluids C. Salomon Enrico Fermi School Quantum Matter at Ultralow Temperatures Varenna, July 8, 2014

2 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner, C.S. Lithium Exp. I. Ferrier-Barbut M. Delehaye S. Laurent M. Pierce A. Grier B. Rem Lithium-Potassium Exp. F. Sievers, D. Fernandes N. Kretschmar M. Rabinovic D. Suchet U. Eismann A. Bergschneider T. Langen N. Navon S. Nascimbène K. Jiang arxiv: To appear in Science, July 17 I. Ferrier-Barbut, M. Delehaye, S. Laurent, A. T. Grier, M. Pierce, B. S. Rem, F. Chevy, and C. Salomon L. Khaykovich

3 103 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 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 Bose-Bose and Bose-Fermi Mixtures Bose-Bose superfluid mixtures first observed long ago: Two hyperfine states in Rb at JILA (Myatt et al. 97) and vortex production Dark-bright soliton production in two Rb BEC, Engels group, PRL 2011 Bose-Fermi mixtures 7 Li - Li at ENS, Rice 23 Na - Li at MIT, Li- 133 Cs in Chicago, Heidelberg, 40 K - 87 Rb at LENS, Hamburg, ETH, JILA, Innsbruck, Singapore,Taiyuan, 23 Na- 40 K at MIT, MPQ Isotopes of Yb, Kyoto and Sr Innsbruck, But no Bose-Fermi superfluids simultaneously! Decades of attempts with 4 He and 3 He Experiment with Li- 7 Li Excitation of center of mass modes: first sounds Simple model Critical velocity and perspectives

6 Fermi Superfluid in the BEC-BCS Crosover 10 year anniversary! Li Fermions with two spin states and attractive interaction 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 /Δ~k F -1 BCS regime: k F a <<1 Cooper pairs k, -k Well localized in Momentum: k~k F Delocalized in position

7 Equation of State in the crossover Pressure equa)on 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)

8 7 Li and Li isotopes

9 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

10 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~ 100 nk Absorption imaging of the in-situ density distributions or Time of Flight

11 In situ Profiles Li Fermi gas at unitarity 7 Li BEC Trap frequencies: v z =15. Hz for bosons, v rad = 440 Hz Lifetime of mixture : 7s in shallowest trap N B = T=90 nk N 0 /N B > 80% T<T c /2 N F = T= 90 nk=0.1t F T F = 50nK Upper bound for T

12 Mixture of Bose and Fermi Superfluids Li SF 7 Li BEC in ToF 1> Li 2> Li Superfluid Core T< T c / 2 for Fermi SF Method used at MIT 0, Rice 0, ENS 09

13 First sounds in mixture of superfluids Superfluids have collective excitations In a mixture of two superfluids, one expects two first sound modes ie density waves excitations 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 waist of the dipole trap shifted from the magnetic trap minimum.

14 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 = 2π 15.3(1) Hz 7 Single Superfluid Ratio = (7/) 1/2 =(m 7 /m ) 1/2

15 Relative displacement of superfluids No damping only when the max relative velocity < 2 cm/s

16 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

17 Mean field model 1.5% down shift in 7 Li BEC frequency BEC osc. amplitude beat at frequency ~ ω ~ ω ) / 2π ( 7 2 Weak interaction regime: k F a 7 <<1 and N 7 <<N 2π h a Boson effective potential 7 Veff = V () r + g7n () r with g7 = m7 m7 = mm7 /( m + m7 ) 0 0 LDA n () r = n ( µ V()) r Where n ( µ ) For the small BEC: Expand is the Eq. of State of the stationary Fermi gas. 0 V ( r) << µ dn µ n () r n ( ) V() r +... d µ

18 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 /3 µ = ξ ( 3π n) / 2m with ξ = 0.38 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:

19 Amplitude modulation Include now back-action on the Fermions Sum-rule approach: mapping onto a coupled oscillator problem z = (1 ερ) cos( % ωt) + ερ cos( % ω7t) z = εcos( % ω t) + (1 + ε)cos( % ω t) 7 7 with ρ = N N 7 and ε =14 2m % ω ω = m7 m ω7 : 0.3 Hence a significant modulation of the amplitude of z 7 at the beat frequency % ω % ω 7 Coherent energy exchange between both gases amplified by quasi-degeneracy of pendulum frequencies

20 Amplitude modulation: theory vs expt BEC alone theory theory Coupled BEC Fermi SF

21 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

22 Undamped oscillations of two BEC s B= 790 Gauss, molecular BEC side 7 Li Reduction of critical velocity by a factor ~2 In contrast to damping observed in Rb condensate mixtures, Myatt, PRL 1997 and dark-bright soliton trains in Engels group, PRL 2011

23 Critical velocity γ = 3.1 s 1 Time(ms) v s = ξ 1/4 v 5 F v c is very close to the speed of sound of unitary gas in elongated trap MIT experiment: v c = 0.32 v F

24 Summary Production of a Bose-Fermi double superfluid Measurement of critical velocity at unitarity first sounds in low temperature limit critical velocity of SF mixture: work in progress. Y. Castin, S. Stringari, Hui Zhai Perspectives Temperature effects and nature of excitations Flat bottom trap for fermions when a bb =a bf Molmer 1997, Trento group, ArXiv FFLO Phase with spin imbalanced gas? Second sound, higher modes, vortices, Bose-Fermi Superfluids in optical lattices and counterflow