Quantum manifestation of the classical bifurcation in the driven dissipative Bose-Hubbard dimer

TL;DR

This paper investigates how classical bifurcations in a driven dissipative Bose-Hubbard dimer manifest in quantum dynamics, revealing a quantum signature of classical limit cycle bifurcations through stationary density matrix features.

Contribution

It demonstrates the quantum manifestation of classical bifurcations in a driven dissipative Bose-Hubbard dimer, linking classical limit cycles to quantum stationary states.

Findings

Classical bifurcation leads to a limit cycle with unique frequency characteristics.

Quantum stationary density matrix exhibits features reflecting classical bifurcation.

Brief discussion on chaotic attractors in the Bose-Hubbard trimer.

Abstract

We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose-Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.