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

References in corpus (11)

• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Interaction quench in a trapped one-dimensional Bose gas
• Gradient critical phenomena in the Ising quantum chain
• Hydrodynamic description of Hard-core Bosons on a Galileo ramp
• Quench from Mott Insulator to Superfluid
• Gradient critical phenomena in the Ising quantum chain: surface behaviour
• Quantum quench dynamics of the Bose-Hubbard model at finite temperatures