Collective many-body bounce in the breathing-mode oscillations of a Tonks-Girardeau gas

Abstract

We analyze the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability-a collective many-body bounce effect. The effect, although being invisible in the evolution of the in situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas wherein the many-body bounce is explained by an increased thermodynamic pressure during the isentropic compression cycle, which acts as a potential barrier for the particles to bounce off. DOI: 10.1103/PhysRevA.96.041605 Collective dynamics in many-body systems emerge as a result of interparticle interactions. Such dynamics can be characterized by a coherent or correlated behavior of the constituents, which cannot be predicted form the single-particle or noninteracting picture. Collective dynamics can therefore serve as an important probe of the underlying interactions and is at the heart of a variety of nonequilibrium phenomena in many-body physics, including the archetypical examples of superfluidity and superconductivity. Among physical systems of current theoretical and experimental interest for understanding nonequilibrium many-body dynamics are ultracold quantum gases [1-10], which offer a versatile platform for realizing minimally complex but highly controllable models of many-body theory.In quantum gases, the simplest manifestations of collective dynamics relate to the frequencies of monopole (breathingmode) and multipole oscillations in harmonic trapping potentials [5,[11][12][13][14][15][16][17][18][19][20][21]. These frequencies, depending on trap configurations, can vary significantly from those of ideal (noninteracting) gases. For example, in a weakly interacting one-dimensional (1D) Bose gas at sufficiently low temperatures, the breathing-mode oscillations of the in situ density occur at a frequency of ω B √ 3ω (where ω is the frequency of the trap) [5,18,19,[22][23][24][25][26][27][28], whereas in an ideal Bose gas the breathing-mode frequency is ω B = 2ω. An even more dramatic qualitative departure from the ideal gas behavior was observed recently in the dynamics of the momentum distribution of a weakly interacting 1D quasicondensate [5,28]: For sufficiently low temperatures, the momentum distribution was oscillating at a frequency of 2ω B , i.e., at twice the rate of the fundamental breathing-mode frequency of the in situ density profile ω B √ 3ω. Furthermore, at intermediate temperatures the oscillations could be decomposed as a weighted superposition of just two harmonics, one oscillating at 2ω B and the other at ω B .In a str...

Finite-temperature dynamics of a Tonks-Girardeau gas in a frequency-modulated harmonic trap

“…Before doing so, however, we momentarily pause to point out that evolution of a harmonically trapped TG gas under the same dynamical protocol can be also analysed using a finite-temperature hydrodynamic approach developed in Ref. [24,26].…”

“…In the hydrodynamic approach, the TG gas evolves according to the following equations for the local 1D density, ρ(x, t), the hydrodynamic velocity, v(x, t), and the entropy per particle, s(x, t) [24,26]:…”

“…Thus, the frequencymodulation of a harmonically trapped Tonks-Girardeau gas represents yet another dynamical scenario, in addition to a simple quench protocol studied in Ref. [24], which can be adequately described by such a theory.…”

“…[23] and provides an exact finitetemperature theory that can in general model the dynamics of a TG gas in arbitrary trapping potentials. So far this treatment has been applied to a harmonically trapped TG gas driven out of equilibrium via a quench of the trap frequency from an initial value to a fixed final value [24]. Such a quench protocol invokes familiar breathing-mode oscillations of the density profile, however, an unexpected many-body effect-dubbed manybody bounce-was also found in the dynamics of the momentum distribution.…”

“…The mapping to Mathieu's equation is facilitated through a scaling solution that exist for the nonequilibrium dynamics of the TG gas in a time-varying harmonic trap. [20,23,24,27]. Such a scaling solution allows the evolution of the density and momentum distributions of the gas to be determined through a single scaling parameter, which itself satisfies an ordinary second-order nonlinear differential equation, the Ermakov-Pinney equation [28,29].…”