One-dimensional Bose gas driven by a slow time-dependent harmonic trap. (22nd September 2017)

• Record Type: Journal Article
• Authors: Scopa, Stefano; Karevski, Dragi
• Is Part Of: Journal of physics. Volume 50:Number 42(2017)
• Publication Date: 2017-09-22
• Subjects: Tonks–Girardeau -- quantum quench -- quasi-adiabatic evolution; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa890f
• Languages: English
• ISSNs: 1751-8113

Abstract

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 ℓ ( 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 situations, the typical size of the cloud grows with a power law governed by an exponent that depends continuously on the initial trap frequency. At a 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.