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arXiv:1703.02634 · Journal of Statistical Mechanics Theory and Experiment

Tunable zero and first sounds in ultracold Fermi gases with Rabi coupling

Luca Lepori, Luca Salasnich

Published Apr 1, 2017• 1 citation
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Abstract

Abstract We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. By using a Born approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions ( D = 1, 2, 3). Then, adopting the Landau–Vlasov equation and hydrodynamic equtions, we investigate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profles of the fermionic system.

DOI
10.1088/1742-5468/aa6580

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Abstract We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. By using a Born approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions ( D = 1, 2, 3). Then, adopting the Landau–Vlasov equation and hydrodynamic equtions, we investigate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profles of the fermionic system.
We study the zero sound and the first sound in a dilute and ultracold disk-shaped normal Fermi gas with a strong harmonic confinement along the axial direction and uniform in the two planar directions. Working at zero temperature we calculate the chemical potential $\ensuremath{\mu}$ of the fermionic fluid as a function of the uniform planar density $\ensuremath{\rho}$ and find that $\ensuremath{\mu}$ changes its slope in correspondence to the filling of harmonic axial modes (shell effects). Within the linear response theory, and under the random phase approximation, we calculate the velocity cs0{c}_{s}^{0}cs0​ of the zero sound. We find that also cs0{c}_{s}^{0}cs0​ changes its slope in correspondence of the filling of the harmonic axial modes and that this effect depends on the Fermi-Fermi scattering length aF{a}_{F}aF​. In the collisional regime, we calculate the velocity cs{c}_{s}cs​ of first sound showing that cs{c}_{s}cs​ displays jumps at critical densities fixed by the scattering length aF{a}_{F}aF​. Finally, we discuss the experimental achievability of these zero sound and first sound waves with ultracold alkali-metal atoms.
We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.
We evaluate the transition from zero-sound to first-sound behaviour with increasing collisionality in the propagation of density waves through an ultracold gaseous mixture of fermionic atoms in the normal state confined inside a cigar-shaped harmonic trap. We study for this purpose the evolution of the one-body distribution functions associated with a density perturbation generated in the central region of the cloud, as obtained by numerical solution of the Vlasov–Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture. The speed of propagation of the density disturbance is found to decrease in both cases as the magnitude of the coupling strength is increased. The results are compared with the values of the speed of zero sound and of first sound, as obtained analytically from the limit of vanishing collisionality and from linearized hydrodynamics. The main effects of the quasi-one-dimensional confinement are the stabilization of zero-sound excitations in the attractive regime before collapse and the lowering of the hydrodynamic sound velocity by a factor relative to three-dimensional behaviour.
Landau’s Fermi-liquid (FL) theory has been successful at the phenomenological description of the normal phase of many different Fermi systems. Using a dilute atomic Fermi fluid with tunable interactions, we investigate the microscopic basis of Landau’s theory with a system describable from first principles. We study transport properties of an interacting Fermi gas by measuring its density response to a periodic external perturbation. In an ideal Fermi gas, we measure for the first time the celebrated Lindhard function. As the system is brought from the collisionless to the hydrodynamic regime, we observe the emergence of sound and find that the experimental observations are quantitatively understood with a first-principle transport equation for the FL. When the system is more strongly interacting, we find deviations from such predictions. Finally, we measure the momentum-space shape of the quasiparticle excitations and see how it evolves from the collisionless to the collisional regime. Our study establishes this system as a clean platform for studying Landau’s theory of the FL and paves the way for extending the theory to more exotic conditions, such as nonlinear dynamics and FLs with strong correlations in versatile settings.
Abstract At low temperature, a normal gas of unpaired spin‐1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length , the sole parameter of the short‐range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, as the uncontrolled error made by the relaxation time approximations increases when the temperature drops below the Fermi temperature. Here, sound waves in the hydrodynamic regime are studied up to second order in the Chapman‐Enskog's expansion. It is found that the frequency of the sound wave is shifted above its linear departure as where and are the speed and wavenumber of the sound wave and the typical collision time scales as . Besides the shear viscosity, the coefficient is described by a single second‐order collision time, which is computed exactly from an analytical solution of the transport equation, resulting in a positive dispersion . The results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second‐order hydrodynamics.
Abstract We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in D dimensions. Using the Landau’s two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D ⩾ 2. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.