Dynamical properties of quantum gases following a sudden change of confining potential

Abstract

The response of a quantum system to a sudden change of its parameters entering in the hamiltonian, such as the confining potential or two-body particle-particle interactions, is an interesting issue in physics. This issue is experimentally realized in the field of ultra-cold quantum gases, where the advances in such field allow a full control of the parameters of the confined gas. The subsequent time evolution of the system following a sudden change of a specific parameter, called quench, is interesting and allows the study of dynamical non-equilibrium properties of the system. In this thesis we considered the case of quench of trapping potential for different one-dimensional systems. The dynamical quantities we were interested are the one-body density matrix and the resulting mass current density distribution. Using the time evolution propagator, we derived the time dependent one-body density matrix and the current density of an initially harmonically trapped noninteracting system following a quench of the potential. For a one-dimensional system of bosons with large atom number interacting through a repulsive delta potential initially confined by a potential well, we derived the so-called long-time asymptotic one-body density matrix during free expansion. The third system we examined is a quantum impenetrable gas of bosons (a Tonks–Girardeau gas) with a given atom number. We derived an explicit exact analytical expression for the mass current distribution (mass transport) after quench from one harmonic trap to another harmonic trap. We showed that, the current distribution is a suitable collective observable and under the weak quench regime, it exhibits oscillations at the same frequencies as those predicted for the peak momentum distribution in the breathing mode. The analysis is extended to other possible quenched systems.