Quantum behaviour of open pumped and damped Bose–Hubbard trimers

Abstract

We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-field solutions of our models are noticeably different from the quantum solutions for the mean fields. Due to recent experimental advances, it should be possible to demonstrate the effects we predict and investigate in this article.

Localization control of few-photon states in parity-symmetric ‘photonic molecules’ under balanced pumping

“…Subsequently, two theoretical studies modeled a coherently driven version of this experimental setup using driven-dissipative two-site Bose-Hubbard Hamiltonians [16,17] (note that various quantum effects have previously been explored in dissipative Bose-Hubbard models, e.g. in [18][19][20] and the contained references). These works [16,17] showed that weak signatures of SSB can be traced in the quantum regime with few photons .…”

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: A c-field model

“…However, in recent years it has been realized that by adding controlled sources of dissipation to many-body quantum systems one can engineer novel quantum states of matter [1][2][3][4][5][6]. For example, an appropriate environment coupling can be harnessed to generate robust entangled states [7][8][9], or enable dissipative quantum computation protocols [10]. Further, the addition of driving allows the controlled study of quantum transport processes [11], PTsymmetric quantum mechanics [12,13], and dissipative phase transitions [14].…”

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: a c-field model

“…However, in recent years it has been realized that by adding controlled sources of dissipation to many-body quantum systems one can engineer novel quantum states of matter [1][2][3][4][5][6]. For example, an appropriate environment coupling can be harnessed to generate robust entangled states [7][8][9], or enable dissipative quantum computation protocols [10]. Further, the addition of driving allows the controlled study of quantum transport processes [11], PT -symmetric quantum mechanics [12,13], and dissipative phase transitions [14].…”