Quantum breathing dynamics of ultracold bosons in 1D-harmonic traps: Unraveling the pathway from few- to many-body systems

TL;DR

This paper systematically investigates the breathing dynamics of ultracold bosons in a 1D harmonic trap, revealing how few-body behaviors evolve into many-body phenomena using advanced computational methods.

Contribution

It introduces a comprehensive ab initio analysis of bosonic breathing modes across particle numbers, connecting few- and many-body regimes with new computational insights.

Findings

Two-boson breathing behavior explained analytically.

Transition from two-mode to single-frequency breathing with increasing particles.

Dependence of breathing frequency on interaction strength and particle number.

Abstract

Following a `bottom-up approach' in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of bosons ranging from few to many. To this end, we employ the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) which has been developed very recently [S. Kr\"onke, L. Cao, O. Vendrell and P. Schmelcher. {\it New J. Phys.} {\bf 15}, 063018 (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region in which Gross-Pitaevskii theory is well applicable.