Mesoscopic entanglement via a three-well Bose–Hubbard system and comparison with an optical beamsplitter

Abstract

Abstract.We compare and contrast the entangling properties of a three-well Bose-Hubbard model and an optical beamsplitter. The coupling between the different modes is linear in both cases, and we may identify two output modes. Obvious differences are that our Bose-Hubbard model, with only the middle well initially occupied, does not have a vacuum input port, there is no equivalent of a collisional, χ (3) nonlinearity with the beamsplitter, and the results of the Bose-Hubbard model show a timedependence. In the non-interacting case, we obtain analytic solutions and show that, like a beamsplitter, the Bose-Hubbard system will not produce entanglement for classical initial states. We also show that whether inseparability or entanglement are detected depends sensitively on the criteria measured, with different criteria giving contradictory predictions.

Negative differential conductivity and quantum statistical effects in a three-site Bose-Hubbard model

“…Assuming a tight-binding approximation [16,17], we model the optical lattice system by a three-site Bose-Hubbard chain [9,10,[18][19][20], with one orbital per site. This model is justified when the interaction energy is much smaller than the singleparticle ground-state energy of the local trapping potential (see Ref.…”

Quantum correlations in pumped and damped Bose-Hubbard dimers

“…In general, we were not able to find exact analytical solutions for the mode amplitudes, except in the case of χ = 0. In this particular case, everything remains completely classical, with no interesting quantum statistical features, as shown for Bose-Hubbard models without loss and pumping [36][37][38].…”

“…The violation of this inequality is thus an indication of the inseparability of, and entanglement between, the two modes. As shown by Olsen [36][37][38], this is useful for systems where number conservation holds, in which case the Duan-Simon criterion may not detect inseparability. Although this is not the case here, it is still of interest to compare the predictions with the quadrature inequalities defined above.…”

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

“…[16,17], in which situation the population initially in the middle well does not transfer completely to the two outer wells when χ = 10 compared to that for 10 −3 because the positive-P equations ran into divergence problems after Jt = 25.…”

“…Our model uses an inline Bose-Hubbard trimer, with coherent pumping into the middle well and outcoupling from the two end wells, and is a pumped and damped development of the atomic mode splitter described by Chianca and Olsen [16] and compared to an optical beamsplitter [17]. As we will show in what follows, both the modes in the end wells and the modes outcoupled from them possess non-classical correlations such as entanglement and Einstein-Podolsky-Rosen steering.…”