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arXiv:cond-mat/0209621 · Physical Review A

Controlling two-species Mott-insulator phases in an optical lattice to form an array of dipolar molecules

M. G. Moore, H. R. Sadeghpour

Published Apr 17, 2003• 27 citations

Abstract

We consider the transfer of a two-species Bose-Einstein condensate (BEC) into an optical lattice with a density such that a Mott-insulator state with one atom per species per lattice site is obtained in a deep lattice regime. Depending on collisional and transition parameters, the result could be either a ``mixed'' or a ``separated'' Mott-insulator phase. Such a mixed two-species insulator would be well suited for the formation of dipolar molecules via photoassociation. The resulting array of dipolar molecules could then be used for the formation of a dipolar molecular condensate or for computation. For the case of a ${}^{87}\mathrm{Rb}{\ensuremath{-}}^{41}\mathrm{K}$ two-species BEC, however, the large interspecies scattering length makes it difficult to obtain the desired mixed Mott-insulator phase. To overcome this difficulty, we investigate the effect of varying the lattice frequency on the mean-field interaction and propose a favorable parameter regime, under which a lattice of dipolar molecules could be generated.

DOI: 10.1103/physreva.67.041603

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We consider the transfer of a two-species Bose-Einstein condensate (BEC) into an optical lattice with a density such that a Mott-insulator state with one atom per species per lattice site is obtained in a deep lattice regime. Depending on collisional and transition parameters, the result could be either a mixed'' or a separated'' Mott-insulator phase. Such a mixed two-species insulator would be well suited for the formation of dipolar molecules via photoassociation. The resulting array of dipolar molecules could then be used for the formation of a dipolar molecular condensate or for computation. For the case of a

{}^{87}\mathrm{Rb}{\ensuremath{-}}^{41}\mathrm{K}

two-species BEC, however, the large interspecies scattering length makes it difficult to obtain the desired mixed Mott-insulator phase. To overcome this difficulty, we investigate the effect of varying the lattice frequency on the mean-field interaction and propose a favorable parameter regime, under which a lattice of dipolar molecules could be generated.

We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.

We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold ^{87}Rb^{133}Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions.

We present a general lattice model for a multicomponent atomic Bose-Einstein system in an optical lattice. Using the model, we analytically study the quantum phase transition between the Mott insulator and a superfluid. A mean-field theory is developed from the Mott-insulator ground state. When the interspecies interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak interspecies interactions, the multispecies system is miscible. Finally, the phase diagram is discussed with emphasis on the role of interspecies interactions. The tip and the shape of the Mott insulator lobes do not depend on the interspecies interactions, but the latter indeed modify the position of the phase boundaries.

We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of

^{87}

Rb-

^{41}

K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of

^{87}

Rb and varied the number of

^{41}

K, and used the parameters estimated by experiments. We show that the phase separated

^{87}

Rb-

^{41}

K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.

We investigate the quantum phases of a dipolar Bose-Einstein condensate (BEC) in an optical lattice based on the extended Bose-Hubbard model taking into account the three-body scattering. Accordingly, the phase diagrams from the superfluid state to the Mott-insulator state for such BEC systems are obtained and analyzed, employing both the mean-field approach and the functional-integral method. In particular, we explore the combined effects of three-body interaction and dipole-dipole interaction on the insulating lobes in detail. The experimental scenario is also discussed.