Variational theory of two-fluid hydrodynamic modes at unitarity

Taylor, Edward; Hu, Hui; Liu, Xia-Ji; Griffin, Allan

doi:10.1103/physreva.77.033608

Cited by 27 publications

(68 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using a variational approach [30], one can obtain their eigenfrequencies at finite temperatures as 129Í2-25 2 "â nd 2 _ 440Í3 -252 2 '^*=^ " 5(25í3-21)'"' • In these equations ¡2 = M0M4/M2 and Í3 = where we have introduced tbe dimensionless moments…”

Section: Theoretical Predictionsmentioning

confidence: 99%

Higher-nodal collective modes in a resonantly interacting Fermi gas

et al. 2013

View full text Add to dashboard Cite

We report oti experimental investigations of longitudinal collective oscillations in a highly elongated, harmonically trapped two-component Fermi gas with resonantly tuned 5-wave interactions ("unitary Fermi gas"). We focus on higher-nodal axial modes, which in contrast to the elementary modes have received little attention so far. We show how these modes can be efficiently excited using a resonant local excitation scheme and sensitively analyzed by a Fourier transformation of the detected time evolution of the axial density profile. We study the temperature dependence of the mode frequencies across the superfluid phase transition. The behavior is qualitatively different from the elementary modes, where the mode frequencies are independent ofthe temperature as long as the gas stays in the hydrodynamic regime. Our results are compared to theoretical predictions based on Landau's two-fluid theory and available experimental knowledge of the equation of state. The comparison shows excellent agreement and thus both represents a sensitive test for the validity of the theoretical approach and provides an independent test of the equation of state. The present results obtained on modes of first-sound character represent benchmarks for the observation of second-sound propagation and corresponding oscillation modes.

show abstract

Section: Theoretical Predictionsmentioning

confidence: 99%

Higher-nodal collective modes in a resonantly interacting Fermi gas

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Thus, the solutions of the two-fluid hydrodynamic equations for superfluid helium are perfectly described by decoupled first and second sound modes. For resonantly interacting atomic Fermi gases, the universality relations give rise to ρ 0 (∂T /∂ρ)s = 2T /3 = 0 [9]. Close to the superfluid transition temperature T c ≃ 0.167T F , where T F is the Fermi temperature, we estimate from the MIT data that the LP parameter is about ǫ LP ≃ 0.4.…”

Section: Two-fluid Hydrodynamicsmentioning

confidence: 84%

“…The present work is dedicated to in memory of Professor Allan Griffin, who was always enthusiastic on observing the second sound in resonantly interacting atomic Fermi gases and was the driving force of our recent works [9,14,18]. We thank Edward Taylor …”

Section: Acknowledgmentsmentioning

confidence: 99%

See 1 more Smart Citation

Probing the critical exponent of the superfluid fraction in a strongly interacting Fermi gas

Liu

2013

Phys. Rev. A

View full text Add to dashboard Cite

We theoretically investigate the critical behavior of second sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature Tc, the frequency or the sound velocity of second sound mode depends crucially on the critical exponent β of superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like (1 − T /Tc) β−1/2 when β < 1/2. In a highly elongated trap, the speed of second sound reduces by a factor 1/ √ 2β + 1 from that in a homogeneous three-dimensional superfluid. Our prediction could be readily tested by measurements of second sound wave propagation in a setup such as that exploited by Sidorenkov et al. [Nature 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.

show abstract

“…First and second sound of the system are described by Landau's two-fluid hydrodynamic equations which involve only local thermodynamic variables and superfluid density. As discussed in the previous works [20][21][22], using Hamilton's variational principle [23], first and second sound modes of these equations with frequency ω can be obtained by minimizing a variational action, which, in terms of displacement fields u s (r) and u n (r) for superfluid and normal fluid components, takes the following form [20],…”

mentioning

confidence: 99%

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

Liu¹,

Hu²

2014

Annals of Physics

View full text Add to dashboard Cite

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau's two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii-Kosterlitz-Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. Our predictions can be readily examined in current experimental setups for 2D dilute Bose gases. Low-energy excitations of a quantum liquid in its superfluid state -in which inter-particle collisions are sufficiently frequent to ensure local thermodynamic equilibrium -can be well described by Landau's two-fluid hydrodynamic theory [1,2]. It is now widely known that there are two types of excitations, namely first and second sound, which describe respectively the coupled in-phase (density) and out-of-phase (temperature) oscillations of the superfluid and normal fluid components [3]. Historically, Landau's two-fluid hydrodynamic theory was invented to understand the quantum liquid of superfluid helium [2]. The study of first and second sound in such a system has greatly enriched our knowledge of the fascinating but challenging many-body physics. For any new kind quantum fluids, it is therefore natural to anticipate that first and second sound may also provide a powerful tool to characterize their underlying physics.

show abstract

Variational theory of two-fluid hydrodynamic modes at unitarity

Cited by 27 publications

References 40 publications

Higher-nodal collective modes in a resonantly interacting Fermi gas

Higher-nodal collective modes in a resonantly interacting Fermi gas

Probing the critical exponent of the superfluid fraction in a strongly interacting Fermi gas

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

Contact Info

Product

Resources

About