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We propose and analyse analogs of optical cavities for atoms using three-well Bose-Hubbard models with pumping and losses. We consider triangular configurations. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find quadrature squeezing and mode entanglement for some parameter regimes and demonstrate that the trimer with pumping and damping at the same well is the stronger option for producing non-classical states. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.
We propose and analyse a pumped Bose-Hubbard dimer as a source of continuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian statistics. We use the truncated Wigner representation to calculate third and fourth order cumulants, findi
Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries
We investigate the quantum measurement noise effects on the dynamics of an atomic Bose lattice gas inside an optical resonator. We describe the dynamics by means of a hybrid model consisting of a Bose--Hubbard Hamiltonian for the atoms and a Heisenbe
We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, {
We study the Bose and Fermi Hubbard model in the (formal) limit of large coordination numbers $Zgg1$. Via an expansion into powers of $1/Z$, we establish a hierarchy of correlations which facilitates an approximate analytical derivation of the time-e