Signatures of Self-Trapping in the Driven-Dissipative Bose-Hubbard Dimer

TL;DR

This paper explores the self-trapping transition in a driven-dissipative Bose-Hubbard dimer, revealing how quantum dynamics and spectral properties indicate a localization-delocalization crossover influenced by system parameters and asymmetries.

Contribution

It introduces a detailed analysis of quantum dynamics and spectral signatures of self-trapping in a driven-dissipative Bose-Hubbard dimer, highlighting effects of asymmetry and parameter variations.

Findings

Signatures of a localization-delocalization crossover identified.

Steady-state imbalance affected by pump-loss asymmetry.

Spectral properties reveal transition characteristics.

Abstract

We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is independent of any Hamiltonian parameter, and cannot therefore capture the competition between hopping-induced delocalization and the interaction-dominated self-trapping regime. We focus instead on the exact quantum dynamics of the particle imbalance after the system is prepared in a variety of initial states, and on the frequency-resolved spectral properties of the steady state, as encoded in the single-particle Green's functions. We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio. We further show that a finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.