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arXiv:cond-mat/0204137 · Physical Review Letters

Creation of a Molecular Condensate by Dynamically Melting a Mott Insulator

Dieter Jaksch, V. Venturi, J. I. Cirac, Carl J. Williams, P. Zoller

Published Jul 2, 2002• 207 citations
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Abstract

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.

DOI
10.1103/physrevlett.89.040402

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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.
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.
We analyze the outcome of a Mott insulator to superfluid transition for a two-component Bose gas with two atoms per site in an optical lattice in the limit of slow ramping down the lattice potential. This manipulation of the initial Mott-insulating state transforms local correlations between hyperfine states of atom pairs into multiparticle correlations extending over the whole system. We show how to create macroscopic twin Fock states in this way, and that, in general, the obtained superfluid states are highly depleted even for initial ground Mott-insulator states.
The phase transition from a superfluid to a Mott insulator has been observed in a 23Na^{23}\mathrm{Na}23Na Bose-Einstein condensate. A dye laser detuned $\ensuremath{\approx}5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ red of the Na $3^{2}S\ensuremath{\rightarrow}3^{2}P_{1∕2}$ transition was used to form the three-dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the time scale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the ${\mathrm{Na}}_{2}\phantom{\rule{0.3em}{0ex}}(1)^{3}\ensuremath{\Sigma}_{g}^{+}$ state.
We produce 84 Sr 2 molecules using Bose-enhanced Raman photoassociation. We apply the stimulated Raman adiabatic passage (STIRAP) technique on a Bose-Einstein condensate (BEC) to produce more than 8 × 10 3 ultracold molecules. This chemical reaction is only made possible because of the Bose enhancement of the optical transition dipole moment between the initial atomic state and an intermediate molecular state. We study the effect of Bose enhancement by measuring the transition Rabi frequency in a BEC and by comparing it with measurements for two atoms in sites of a Mott insulator. By breaking the dimers' bond and directly observing the separated atoms, we measure the molecular inelastic collision rate parameters. We discuss the possibility of applying Bose-enhanced STIRAP to convert a BEC of atoms into a BEC of molecules, and argue that the required efficiency for STIRAP is within experimental reach.