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arXiv:1810.03507 · Physical Review A

Shock waves in colliding Fermi gases at finite temperature

Silvia Chiacchiera, D. Davesne, Mi­chael Urban

Published Nov 21, 2018• 3 citations
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Abstract

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.

DOI
10.1103/physreva.98.053622

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•Jan 10, 2012•2 citations
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.
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 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.
Motivated by a recent experiment [Phys. Rev. Lett. 106, 150401 (2011)], we simulate the collision between two clouds of cold Fermi gas at unitarity conditions by using an extended Thomas-Fermi density functional. At variance with the current interpretation of the experiments, where the role of viscosity is emphasized, we find that a quantitative agreement with the experimental observation of the dynamics of the cloud collisions is obtained within our superfluid effective hydrodynamics approach, where density variations during the collision are controlled by a purely dispersive quantum gradient term. We also suggest different initial conditions where dispersive density ripples can be detected with the available experimental spatial resolution.
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.
In this paper, we develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond sss-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.
Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.