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Journal of Physics Conference Series

Adiabatic evolution of on-site superposition states in a completely-connected optical lattice

Mirta Rodríguez, Stephen R. L. Clark, Dieter Jaksch

Published Feb 1, 2008• 1 citation
Publisher

Abstract

We analyze the dynamical melting of two-component atomic Mott-Insulator states in a completely-connected optical lattice within the adiabatic approximation. We examine in detail the effect of the dynamical phase acquired by the state during the adiabatic melting of the lattice potential. We show how for certain limits an on-site superposition state with two particles per site melts into a macroscopic superposition state, while an on-site superposition state with only one particle per site melts into a coherent state.

DOI
10.1088/1742-6596/99/1/012017

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We analyze the dynamical melting of two-component atomic Mott-Insulator states in a completely-connected optical lattice within the adiabatic approximation. We examine in detail the effect of the dynamical phase acquired by the state during the adiabatic melting of the lattice potential. We show how for certain limits an on-site superposition state with two particles per site melts into a macroscopic superposition state, while an on-site superposition state with only one particle per site melts into a coherent state.
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.
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 propose the dynamical creation of twin Fock states, which exhibit Heisenberg-limited interferometric phase sensitivities, in an optical lattice. In our scheme a two-component Mott insulator with two bosonic atoms per lattice site is melted into a superfluid. This process transforms local correlations between hyperfine states of atom pairs into multiparticle correlations extending over the whole system. The melting time does not scale with the system size which makes our scheme experimentally feasible.
Abstract.: In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles
A large-scale dynamical simulation of the superfluid--Mott-insulator transition in a gas of ultracold atoms placed in an optical lattice is performed using the time-dependent Gutzwiller mean-field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Greiner et al., Nature (London) 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap only.
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