Abstract
We examine spinor Bose-Einstein condensates in optical superlattices theoretically using a Bose-Hubbard Hamiltonian that takes spin effects into account. Assuming that a small number of spin-1 bosons is loaded in an optical potential, we study single-particle tunneling that occurs when one lattice site is ramped up relative to a neighboring site. Spin-dependent effects modify the tunneling events in a qualitative and quantitative way. Depending on the asymmetry of the double well different types of magnetic order occur, making the system of spin-1 bosons in an optical superlattice a model for mesoscopic magnetism. We use a double-well potential as a unit cell for a one-dimensional superlattice. Homogeneous and inhomogeneous magnetic fields are applied and the effects of the linear and the quadratic Zeeman shifts are examined. We also investigate the bipartite entanglement between the sites and construct states of maximal entanglement. The entanglement in our system is due to both orbital and spin degrees of freedom. We calculate the contribution of orbital and spin entanglement and show that the sum of these two terms gives a lower bound for the total entanglement.
Highlights
We examine spinor Bose-Einstein condensates in optical superlattices theoretically using a Bose-Hubbard Hamiltonian which takes spin effects into account
We obtain a lower bound of the total entanglement, which is given by the sum of the orbital entanglement and the spin entanglement
We have studied the effect of magnetic fields
Summary
The atoms we have in mind are alkali-metal atoms like 23Na and 87Rb. Degenerate gases of alkali-metal atoms are weakly interacting systems, but due to the confining lattice of counter-propagating laser beams some of the atoms are forced to be very close to each other and become strongly interacting. The term proportional to U2 describes spin-dependent interactions: it penalizes nonzero spin configurations on individual lattice sites in the case of antiferromagnetic interactions (e.g. 23Na) and favors high-spin configurations in the case of ferromagnetic interactions (e.g. 87Rb). The parameters can be controlled by adjusting the intensity of the laser beams; it is possible to move from regimes of strong tunneling (U0 ≪ t) to regimes of very weak tunneling (t ≪ U0) For bulk lattices it has been shown theoretically [18] and experimentally [19] that the system can be in an Mott-insulating regime (for t ≪ U0) and in a superfluid phase, where the kinetic energy dominates (for U0 ≪ t), and that it is possible to switch from one regime to the other by tuning the laser strength.
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