One-dimensional Bose gas driven by a slow time-dependent harmonic trap

Abstract

We consider the unitary time evolution of a one-dimensional cloud of hard-core bosons loaded on a harmonic trap potential which is slowly released in time with a general ramp $g(t)$. After the identification of a typical length scale $\ell (t)$, related to the time ramp, we focus our attention on the dynamics of the density profile within a first order time-dependent perturbation scheme. In the special case of a linear ramp, we compare the first order predictions to the exact solution obtained through Ermakov-Lewis dynamical invariants. We also obtain an exact analytical solution for a cloud released from a harmonic trap with an amplitude that varies as the inverse of time. In such situation, the typical size of the cloud grows with a power law governed by an exponent that depends continuously on the initial trap frequency. At high enough initial trap amplitude, the exponent acquires an imaginary part that leads to the emergence of a log-periodic modulation of the cloud expansion.

22 pages, 12 figures

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• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Finite-temperature dynamics of a Tonks-Girardeau gas in a frequency-modulated harmonic trap
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain