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International Conference on Quantum Information

Towards Quantum Simulation with Neutral Atoms in Optical Lattices

Carl J. Williams, Kaushik Mitra, Carlos A. R. Sá de Melo

Published Jan 1, 2007• 0 citations
Publisher

Abstract

A key approach to initializing a neutral atom quantum computer is the superfluid to Mott-insulating quantum phase transition. This paper elucidates the wedding cake structure when Bosonic atoms are in a harmonically confined optical lattice.
DOI
10.1364/icqi.2007.iwc4

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One of the essential features of a quantum computer is a quantum 'register' of well-characterized qubits. Neutral atoms in optical lattices are a natural candidate for such a register. We have demonstrated a patterned-loading technique that can be used to load atoms into large arrays of tightly confined but optically resolvable lattice sites. We have also seen preliminary indications of the Mott-insulator transition, which provides a route for single-atom initialization of the individual sites. Combining the two experiments should allow for large arrays of individually addressable single atoms, a system which provides a starting point for further quantum computation studies.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
We review novel methods for the investigation, control and manipulation of neutral atoms in optical lattices. These setups allow unprecedented quantum control over large numbers of atoms and thus are very promising for applications in quantum information processing. After introducing optical lattices we discuss the superfluid (SF) and Mott insulating (MI) states of neutral atoms trapped in such lattices and investigate the SF-MI transition as observed experimentally recently. In the second part of the paper we give an overview of proposals for quantum information processing and show different ways to entangle the trapped atoms, in particular the usage of cold collisions and Rydberg atoms. Finally, we discuss briefly the implementation of quantum simulators, entanglement enhanced atom interferometers, and ideas for robust quantum memory in optical lattices.
We describe weakly interacting atomic or molecular bosons trapped in harmonically confined optical lattices, which exhibit a wedding cake structure consisting of insulating (Mott) shells. We show that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping and find that the order parameter equation in the superfluid regions is not of the standard Gross-Pitaevskii type except near the insulator-to-superfluid boundaries. We obtain the excitation spectra in the Mott and superfluid regions, and we show that the superfluid shells possess low-energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Furthermore, we discuss the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs in thin (wide) superfluid shells (rings) limited by three- (two-) dimensional Mott regions. Last, we propose an experiment to detect superfluid shells using Laguerre-Gaussian beams and Bragg spectroscopy.
Atomic or molecular bosons in harmonically confined optical lattices exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping. It is found that the order parameter equation in the superfluid region is not of the Gross-Pitaeviskii type except near the insulator to superfluid boundaries. The excitation spectra in the Mott and superfluid regions are obtained, and it is shown that the superfluid shells posses low energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Lastly, the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs are discussed in thin (wide) superfluid shells (rings) limited by three (two) dimensional Mott regions.