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arXiv:cond-mat/0208375 · Physical Review Letters

Creation of a Dipolar Superfluid in Optical Lattices

Bogdan Damski, Luis Santos, E. Tiemann, Maciej Lewenstein, Svetlana Kotochigova, Paul S. Julienne, P. Zoller

Published Mar 17, 2003• 162 citations
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Abstract

We show that, by loading a Bose-Einstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mott-insulator phase with exactly one atom of each species per lattice site. A subsequent photoassociation leads to the formation of one heteronuclear molecule with a large electric dipole moment, at each lattice site. The melting of such a dipolar Mott insulator creates a dipolar superfluid, and eventually a dipolar molecular condensate.

DOI
10.1103/physrevlett.90.110401

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We show that, by loading a Bose-Einstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mott-insulator phase with exactly one atom of each species per lattice site. A subsequent photoassociation leads to the formation of one heteronuclear molecule with a large electric dipole moment, at each lattice site. The melting of such a dipolar Mott insulator creates a dipolar superfluid, and eventually a dipolar molecular condensate.
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 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 consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/R(3) interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with an ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.
The superfluid--Mott-insulator phase transition of dipolar bosons in optical lattice is analyzed. By using the Bogoliubov approach and decoupling approximation, the energy spectrum and zero-temperature phase diagram of dipolar bosonic atoms in an optical lattice are obtained analytically. The results show that in these systems the superfluid--Mott-insulator phase transition can be induced by tuning the dipole-dipole interaction and the position of the phase boundary can be moved when the on-site interaction is varied. Corresponding to a large on-site interaction, the dipole-dipole interaction is attractive near the critical point of the superfluid--Mott-insulator phase transition.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
Ultracold ground-state dipolar 40K^{40}\mathrm{K}40K87Rb^{87}\mathrm{Rb}87Rb molecules recently have been produced in a loose harmonic trap by employing a magnetic field sweep across a Feshbach resonance followed by stimulated Raman adiabatic passage [K.-K. Ni et al., Science 322, 231 (2008)]. The overall experimental efficiency for molecule formation was around 2020%20. We show that the efficiency can be increased to nearly 100100%100 if one first loads the atomic gases into an optical lattice of the appropriate depth and tunes the interspecies attraction to have exactly one atom of each species at an occupied lattice site. Our proposed scheme provides a large enhancement to the dipolar molecule density, even at relatively high temperatures, and avoids three-body recombination loss by preventing lattice sites from being triply occupied.