Spectral form factor and power spectrum for trapped interacting rotating bosons: Crossover from integrability to quantum chaos

Abstract

The emergence of quantum chaos in a system of trapped interacting bosons with externally impressed rotation is studied through spectral form factor (SFF) and power spectrum using exact diagonalization. Two distinct interaction regimes are considered: the moderate, when the interaction energy is small compared to the trap energy and the strong, when the interaction energy is comparable to the trap energy. In the moderate interaction regime, the SFF for the non-rotating case exhibits a dip-plateau structure with absence of linear ramp, indicating integrable behavior, while for the single-vortex state the SFF exhibits a discernible linear ramp consistent with pseudo-integrable behavior. In the strong interaction regime, the non-rotating case exhibits emergence of a linear ramp with small time span in SFF, indicating that the system has moved further towards chaotic regime but continues to be pseudo-integrable. For the single-vortex and the multi-vortex states in strong interaction regime, the span of the linear ramp in SFF increases progressively with rotation, indicating the system has moved into strong chaotic regime consistent with Gaussian orthogonal ensemble. The power spectrum results with exponent lying in the interval $1 \lesssim α\lesssim 2$ are consistent with the findings of SFF. An understanding of the observed crossover from integrable to quantum chaos is presented in terms of the macroscopic occupation of a single-particle quantum state---the Bose-Einstein condensation---and its depletion driven by interaction and rotation.