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Physical Review A

Finite-temperature dynamics of shock waves in an ultracold Fermi gas

Ria Rushin Joseph, L. Rosales-Zárate, P. D. Drummond

Published Jul 31, 2018• 10 citations
Publisher

Abstract

The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.

DOI
10.1103/physreva.98.013638

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The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.
We study the formation and the dynamics of a shock wave originating from the collision between two ultracold clouds of strongly interacting fermions as observed at a lower temperature in an experiment by Joseph et al. [Phys. Rev. Lett. 106, 150401 (2011)]. We use the Boltzmann equation within the test-particle method to describe the evolution of the system in the normal phase. We also show a direct comparison with the hydrodynamic approach and insist on the necessity of including a shear-viscosity and a thermal-conductivity term in the equations to prevent unphysical behavior from taking place.
Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.
We investigate shock waves in the unitary Fermi gas by using the zero-temperature equations of superfluid hydrodynamics. We obtain analytical solutions for the dynamics of a localized perturbation of the uniform gas. These supersonic bright and subsonic dark solutions produce, after a transient time, an extremely large (divergent) density gradient: the shock. We calculate the time of formation of the shock and also simulate the space-time behavior of the waves by solving generalized hydrodynamic equations, which include a reliable dispersive regularization of the shock. We find that the shock spreads into wave ripples whose properties crucially depend on the chosen initial configuration.
Abstract We study the formation and dynamics of shock waves initiated by a repulsive potential in a superfluid unitary Fermi gas by using the order-parameter equation. In the theoretical framework, the regularization process of shock waves mediated by the quantum pressure term is purely dispersive. Our results show good agreement with the experiment of Joseph et al (2011 Phys. Rev. Lett. 106 150401 ). We reveal that the boxlike-shaped density peak observed in the experiment consists of many vortex rings due to the transverse instability of the dispersive shock wave. In addition, we study the transition from a sound wave to subsonic shock waves as the strength of the repulsive potential increases and show a strong qualitative change in the propagation speed of the wavefronts. For a relatively small strength of the repulsive potential, the propagation speed decreases below the sound speed with the increase of the strength as a scaling behavior. For a large strength where the shock waves are formed by colliding two spatially separated clouds, the speed is still smaller than the sound speed, but remains almost unchanged as the strength increases, which can be interpreted as the same expansion speed of the proliferation of the vortex rings originated from the transverse instability.
We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.
The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.