Quantum correlations in pumped and damped Bose-Hubbard dimers

Abstract

We propose and analyze two-well Bose-Hubbard models with pumping and losses, finding that these models, with damping and loss able to be added independently to each well, offer a flexibility not found in optical coupled cavity systems. With one well pumped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. Both the systems we analyze remain far from equilibrium, preserving good coherence between the wells in the steady state. We find a degree of quadrature squeezing and mode entanglement in these systems. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.

Pseudo-steady-state non-Gaussian Einstein-Podolsky-Rosen steering of massive particles in pumped and damped Bose-Hubbard dimers

“…Along with the available measurement techniques, recent advances in the technology of optical potentials [13,14] allow for an increased flexibility in the trapping and measurement of ultra-cold gases. Combined with dissipation from a particular well via the use of either an electron beam [15], or by optical means [16], and the possibility of pumping a Bose-Hubbard system from a larger reservoir condensate [17,18], we have new opportunities for the fabrication of nonlinear damped and pumped atom-optical equivalents of optical cavities with varying configurations [19,20]. In this work we investigate two different Bose-Hubbard models [21][22][23] with added pumping and loss, in terms of their utility for the preparation of non-Gaussian EPR states of the two atomic modes, quantifying both the non-Gaussianity of the resulting quantum states and the degree of violation of standard EPR inequalities [24].…”

Quantum behaviour of open pumped and damped Bose–Hubbard trimers

“…Kordas et al have also analysed triangular trimers and inline chains with dissipation at one well [13,14], finding some interesting physical effects. In work closely related to the present article, Olsen et al [15] have analysed a two well Bose-Hubbard dimer with pumping and damping each at only one of the wells, and Olsen has looked at the same system in terms of non-Gaussian properties and Eintein-Podolsky-Rosen correlations [16]. Olsen and Bradley [17] have analysed an open trimer system with pumping at one well and damping at the other two in terms of its performance as a quantum correlated twin atom laser.…”

“…The success of some inequalities in a given situation where others may be unsuccessful in detecting either genuine tripartite entanglement or EPR-steering is always possible in a mixed state non-Gaussian system, and a similar phenomenon for bipartite correlations was found in a two-well pumped and damped Bose-Hubbard model [15,16], where the Reid inequalities were violated in parameter regimes where the Duan-Simon inequalities were not.…”

Quantum-correlated twin-atom laser from a Bose-Hubbard system

“…It is well known in systems with a Kerr-type nonlinearity that the maximum squeezing will occur for θ = 0 [22,33,34], and we find the optimal angle for our correlations by calculating them at all angles and finding the minima. Experimentally this can be done by changing the phase of the local oscillator [35].…”

“…Bose-Hubbard models with pumping and loss have previously been analysed [20][21][22][23], pre-dicting some interesting physical effects, both in the mean fields and the quantum statistical features. Kordas et al have also analysed triangular dimers and inline chains with dissipation at one well [24,25], predicting some interesting phenomena.…”