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International Conference on Recent Progress in Many-Body Theories

International Conference on Recent Progress in Many-Body Theories Columbus, Ohio, 27-31 July 2009. SECOND SOUND IN STRONGLY INTERACTING FERMI GASES. Sandro Stringari. CNR-INFM. University of Trento. E. Taylor, H. Hu, X.-J. Liu, L. Pitaevskii, A. Griffin, S.S. arXiv:0905.0257.

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International Conference on Recent Progress in Many-Body Theories

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  1. International Conference on Recent Progress in Many-Body Theories Columbus, Ohio, 27-31 July 2009 SECOND SOUND IN STRONGLY INTERACTING FERMI GASES Sandro Stringari CNR-INFM University of Trento E. Taylor, H. Hu, X.-J. Liu, L. Pitaevskii, A. Griffin, S.S. arXiv:0905.0257

  2. The quest for superfluidity in ultracold atomic gases • - Absence of viscosity • Hydrodynamic behavior at T=0 (irrotationality) • Quenching of moment of inertia • quantized vortices • Josephson oscillations • Furthermore, in Fermi gases • Pairing gap • Spin polarization and Chandrasekhar-Clogston limit • This work: SECOND SOUND

  3. COLLECTIVE OSCILLATIONS • Precious tool to investigate the physics of ultracold atomic gases: • Precision testof • - many-body regime(superfluid vs normal, • collisional vs collisionless) • - equation of state(dimensionality, statistics) • - external forces

  4. Test of superfluid T=0 hydrodynamics and of eq. of state in BEC’s ( ): axial compression mode HD Theory (Trento, 1996) Exp (Mit, 1997) :

  5. Oxford exp on BEC’s: (Marago’et al, PRL 84, 2056 (2000)) Superfluid quenching of moment of inertia: Scissors mode: (Guery-Odelin and S.S., PRL 83 4452 (1999)) Above (normal) 2 modes: Below (superfluid) : single mode:

  6. Radial breathing compression mode in two-spin species Fermi gas MC equation of state (Astrakharchick et al., 2005) Innsbruck 2006 BCS mean field (Hu et al., 2004) Universality (S.S. 2004) accurate test of equation of state and of universality at unitarity !!

  7. Equation of state along the BEC-BCS crossover BCS mean field (Leggett, Nozieres, Randeria ideal Fermi gas Nnnn Monte Carlo (Astrakharchick et al., 2004) BEC BCS Energy is always smaller than ideal Fermi gas value. Attractive role of interaction along BCS-BEC crossover relevant dimensionless parameter

  8. First measurement of thermal effect in Casimir-Polder force (JILA-Trento, PRL 2007) center of mass oscillation of trapped BEC gas closed to dielectric substrate Relative frequency shift

  9. SECOND SOUND IN STRONGLY INTERACTING FERMI GASES Why second sound: - dramatic manifestation of superfluidity - sensitive to equation of state at finite T - sensitive to superfluid density Why strongly interacting Fermi gases: - challenging many-body system - hydrodynamic regime easily achieved - non trivial transport coefficients

  10. BEC-BCS crossover in Fermi gases: Interaction tunable thanks to Feshbach resonance BEC regime (molecules) BCS regime (Cooper pairs) unitary limit

  11. Unitary Fermi gas: main features diluteness (interparticle distance >> range of inetraction) strong interactions (scattering length >> interparticle distance) universality (no dependence on interaction parameters) high Tc (of the order of Fermi temperature) robust superfluidity (high critical velocity)

  12. This work: • Second sound in uniform Fermi gas • at unitarity (cfr with He4) • - Effect of harmonic trapping (hybridization) • How to excite and detect second sound

  13. Hydrodynamic equations for superfluids at finite temperature (two-fluid equation, Tisza, Landau) (neglected terms quadratic in v) s is entropy density P is local pressure

  14. At T=0: Eqs. reduce to T=0 superfluid HD eqs equivalent equations

  15. above T: eqs. reduce to collisional HD equations isoentropic condition:

  16. Two fluid HD equations derivable from variational procedure in terms of the velocity fields (Taylor and Griffin PRA 2005) Simple ansatzs in phase (first sound) out of phase (second sound) first sound is pure density mode ( ) follows from second sound is pure temperature mode ( ) follows from

  17. Results for uncoupled first and second sound modes (uniform matter) Unitary Fermi gas (thermodynamics from improved NSR theory) (Taylor et al. arXiv:0905.0257) Liquid He (experiment, Peshkov 1946)

  18. Superfluid density at unitarity (Taylor, Hy. Liu and Griffin PRA 77, 033608 (2008)

  19. Remarkable analogy between unitary Fermi gas • and superfluid Helium follows from • important role played by phonons at low T • single particle gap (unitary Fermi gas) vs • rotons (He4) at higher T Excitation spectrum Unitary Fermi gas (Combescot et al, 2006) Superfluid He4

  20. Coupling bewteen first and second sound Full solution of two-fluid HD equations (uniform matter) Effect of coupling is small even if Landau Placzek ratio is large Second sound is temperature wave

  21. - Situation differs in dilute Bose-Eisntein condensates because of high compressibility. - Strong coupling between first (-----) and second (-----) sound. - Due to weak interactions collisional hydrodynamic regime difficult to achieve in BEC’s. - Thermal vs BEC motion measured at Mit (1998)

  22. What happens in harmonically trapped Fermi gases ? - Elementary excitations are discretized (frequencies of the order of oscillator frequency) - Competing effects in second sound frequencies i) velocity is smaller than first sound and vanishes at Tc ii) discretized values of wave vector are higher (especially close to Tc where Rs is small) superfluid

  23. Previous HD calculations of second sound in harmonic traps • (He et al. (2007), Taylor and Griffin) employed inaccurate • thermodynamics or poor ansatz for velocity field) • - Present work: polynomial ansatz for velocity field with • improved NSR thermodynamics Radial compression mode WITHOUTcoupling (isotropic trap) E. Taylor et al. arXiv:0905.0257

  24. LDA values for second sound frequencies become large near • critical point (consequence of shrinking of superfluid radius) • Crossing of first and second sound frequencies Radial compression mode WITH coupling hybridization Scaling mode unaffected by coupling

  25. How to excite and detect second sound in trapped Fermi gases ? - Density probes - Heat perturbations • Second sound in strongly interacting • superfluids (He4, unitary Fermi gas) • is basically a temperature wave. • It weakly couples to density probes. • At hybridization coupling becomes strong • (effect of trapping)

  26. Density probes • Close to hybridization density • response exhibits typical • bimodal distribution • (direct excitation of dicretized • modes in harmonic trap) • (E. Taylor et al. 0905.0257) • Even if coupling between first • and second sound is small, a • (local) density pulse • can excite second sound mode • (Arahata and Nikuni 0907.2743)

  27. Heat perturbations Can we produce a heat perturbation and excite directly a temperature wave (like in He4) ? New challange for experimentalists !!

  28. Conclusions • Calculated T-dependence of second sound for • Fermi gas at unitarity. Second sound is temperature wave • Analogy with liquid helium • (consequence of strong interactions) • Calculated second sound discretized frequencies in • harmonic trap • Evidence for hybridization between first and • second sound (bimodal effect in density response) • - Need for more accurate calculation of superfluid density

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