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Physical Review A

Quantum correlations in pumped and damped Bose-Hubbard dimers

M. K. Olsen, C. V. Chianca, K. Dechoum

Published Oct 3, 2016• 10 citations
Publisher

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.

DOI
10.1103/physreva.94.043604

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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.
We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott-insulator states, we find statistical mixtures with the same second-order coherence g(2)(0){g}^{(2)}(0)g(2)(0) as a Fock state with nnn photons, but a mean photon number of n/2.n/2.n/2. These mixed states occur when nnn pump photons have the same energy as nnn interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to a classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevskii approach.
We propose and evaluate a method to construct a quantum-correlated twin-atom laser using a pumped and damped Bose-Hubbard in-line trimer which can operate in a stationary regime. With pumping via a source condensate filling the middle well and damping using either an electron beam or optical means at the two end wells, we show that bipartite quantum correlations build up between the ends of the chain and that these can be measured either in situ or in the outcoupled beams. While nothing similar to our system has yet been achieved experimentally, recent advances mean that it should be practically realizable in the near future.
The dynamical evolution of an ultracold Bose gas distributed across the sites of an optical lattice is investigated theoretically in the framework of the Bose-Hubbard model. First, the focus is set on the evolution of squeezing correlations in the two mode system. It is shown that the eigenstates of the Hamiltonian do not exploit the full region of possible squeezing allowed by Heisenbergs uncertainty relation for number and phase fl uctuations. The development of nonclassical correlations and relative number squeezing is studied at the transition from the Josephson to the Fock regime. Comparing the full quantum evolution with classical statistical simulations allows us to identify quantum aspects of the squeezing formation. In the quantum regime, the measurement of squeezing allows us to distinguish even and odd total particle number states. Then, a far from equilibrium quantum field theory method, the so-called two-particle-irreducible effective action approach, is presented for the description of the dynamics in larger lattices. The resulting dynamics is compared to the classical statistical time evolution. The validity of the quantum field evolution is probed for various initial conditions in the classical regime.
We propose and analyze a pumped and damped Bose-Hubbard dimer as a source of continuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian statistics. We use and compare the results of the approximate truncated Wigner and the exact positive-PPP representation to calculate and compare the predictions for intensities, second-order quantum correlations, and third- and fourth-order cumulants. We find agreement for intensities and the products of inferred quadrature variances, which indicate that states demonstrating the EPR paradox are present. We find clear signals of non-Gaussianity in the quantum states of the modes from both the approximate and exact techniques, with quantitative differences in their predictions. Our proposed experimental configuration is extrapolated from current experimental techniques and adds another apparatus to the current toolbox of quantum atom optics.