Second sound and the superfluid fraction in a resonantly interacting Fermi gas

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1 Second sound and the superfluid fraction in a resonantly interacting Fermi gas Meng Khoon Tey Tsinghua University China Workshop on Probing and Understanding Exotic Superconductors and Superfluids Trieste, Oct 2014

2 Meng Khoon Tey Leonid Sidorenkov Rudi Grimm Leonid Sidorenkov 1,2, Meng Khoon Tey 1,2, Rudolf Grimm 1,2 Yan-Hua Lev Sandro Yan-Hua Hou Hou 3, Lev Pitaevskii Pitaevskii 3,4, Sandro Stringari Stringari 3

3 Outline Second sound Experimental results Obtaining temperature dependence of the superfluid fraction

4 Two-fluid model of superfluid helium T 0 v s v n a superfluid at finite temperature Lev D. Landau = a superfluid component + a normal component zero viscosity + zero entropy finite viscosity + carries entropy

5 Two-fluid model of superfluid helium normal part superfluid part TWO sound modes are possible: FIRST SOUND isentropic oscillation SECOND SOUND isobaric oscillation

6 second sound in superfluid helium Picture from Russell Donnelly, Phys. Today 62(10), 34 (2009)

7 First and second sound in superfluid helium First sound Second sound microphone thermal sensor ~

8 Significance of second sound Landau s model vs Tisza s BEC model Superfluid fraction in Helium II Actual speed of second sound Landau Tisza

9 Observing second sound in cold atoms? Second sound in BEC Stamper-Kurn et al, Phys. Rev. Lett. 81, (1998), Mappelink et al., Phys. Rev. Lett. 103, (2009), Mappelink et al., Phys. Rev. A 80, (2009). Differences from second sound in Helium II: Second sound in a BEC reduces to the motion of a condensate over a stationary thermal gas. hydrodynamic conditions not well satisfied.

10 Observing second sound in cold atoms? Temperatures ~ 100 nk Average distance ~ 1 µm de Broglie wavelength ~ 5 µm 1 µm

11 Observing second sound in cold atoms? Temperatures ~ 100 nk Average distance ~ 1 µm de Broglie wavelength ~ 5 µm 1 µm

12 Observing second sound in cold atoms? Temperatures ~ 100 nk Average distance ~ 1 µm de Broglie wavelength ~ 5 µm 1 µm

13 Observing second sound in cold atoms? Temperatures ~ 100 nk Average distance ~ 1 µm de Broglie wavelength ~ 5 µm 1 µm

14 Observing second sound in cold atoms? scattering n a 3 <<1 n a 3 >1 length a n a 3 <<1 Magnetic Field B

15 Resonantly-interacting Fermi gases Equation of State P= P(n, T) Ku et al., Science 335, pg (2012) (MIT) Nascimbène et al., Nature 463, (2010) (ENS) Horikoshi et al., Science 327, (2010) (Tokyo) Kinast et al., Science 307, (2005) (Duke)

16 Coupling between temperature and density variations in second sound for a resonantly interacting Fermi gas (δp/p) (δt/t) ρ (δn/n) (δt/t)

17 Experiment trapping beam excitation beam normal component only normal + superfluid components 6 Li atoms, 50/50 spin mixture B = 834 G atoms per spin state T = 0.135(10) T F trap excitation beam imaging beam

18 Second sound excitation Sidorenkov et al., Nature 498, 78 (2013)

19 1D Landau two-fluid model Strongly-interacting Fermi gas in an elongated trap Assumptions: 1. Thermal equilibrium along transverse direction, 2. flow fields independent of radial position. Making use of local density approximation, Landau s two-fluid hydrodynamic equations become: 1D thermodynamic quantities Bertaina, Pitaevskii & Stringari, Phys. Rev. Lett. 105, (2010).

20 Higher order collective oscillations Excitation beam Imaging beam k=1 k=2 k=3

21 Higher order collective oscillations S anchez Guajardo et al., PRA 87, (2013)

22 Higher order collective oscillations MKT et al., PRL 110, (2013) Yan-hua Hou et al., PRA 88, (2014)

23 Advantages of trap inhomogeneity Temperature dependence for free!

24 Normalized speeds of the first and second sound Calculation based on 1D hydrodynamics model for the first sound first sound second sound Uncertainty in T c from EoS

25 Normalized speeds of the first and second sound Calculation based on 1D hydrodynamics model for the first sound first sound second sound Uncertainty in T c from EoS

26 1D superfluid fraction

27 Superfluid fraction in the UNIFORM system Superfluid helium Weakly-interacting BEC

28 Conclusions S anchez Guajardo et al., PRA 87, (2013) Yan-hua Hou et al., Phys. Rev. A 88, (2014) M.K. Tey et al., PRL 110, (2013) Sidorenkov et al., Nature 498, 78 (2013)

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