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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Ultracold atoms in optical lattices

Immanuel Bloch

Published Jun 1, 2007• 0 citations
Publisher

Abstract

This report results from a contract tasking Ludwig-Maximilian University of Munich as follows: The grantee will investigate controlled collisions between atoms in optical lattices production of strongly correlated quantum system with tunable internctions low dimensional degenerate quantum systems and rotating Bose-Einstein condensates in optical lattices -- observing the fractional Quantum Hall effect with bosons.

DOI
10.1109/cleoe-iqec.2007.4386729

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This report results from a contract tasking Ludwig-Maximilian University of Munich as follows: The grantee will investigate controlled collisions between atoms in optical lattices production of strongly correlated quantum system with tunable internctions low dimensional degenerate quantum systems and rotating Bose-Einstein condensates in optical lattices -- observing the fractional Quantum Hall effect with bosons.
Abstract : This report results from a contract tasking Ludwig-Maximilian University of Munich as follows: In this new grant proposal, we specifically try to address important questions that have emerged out of our previous work and that should provide major advances for the field of quantum state engineering and quantum simulations, as well as quantum information processing. Possible applications also include non-classical matter wave field states that are especially useful for improving the performance of matter wave based atom interferometers. The grant proposal will be focused on research to be carried out on an existing and a completely novel experimental apparatus, focusing on two fundamental topics: (1) Generation of robust multi-particle entanglement in optical lattices, with low decoherence rates as a resource for quantum information processing and improved atom interferometers; and (2) The construction of a novel experimental apparatus with the possibility to address, observe and manipulate single atoms on single sites of an optical lattice. Based on our experience with previous experiments, we find these two topics to be of fundamental importance for future advances in this field.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
Ultracold atoms in optical lattices represent a valuable resource for atom interferometry and for the quantum simulation of condensed matter systems, taking advantage of the possibility to tune interactions, adding disorder and changing quantum statistics. I will present a review of the work recently conducted at LENS in this fascinating field, discussing experiments with ultracold bosons, fermions and atomic mixtures in both periodic and disordered optical potentials, as well as the applications of a novel noninteracting 39K Bose-Einstein condensate.
We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S\o{}rensen et al., Phys. Rev. Lett. 94, 086803 (2005)]. Extending the previous work, we investigate conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field and finite on-site interaction. Furthermore, we characterize the ground state in such systems by calculating Chern numbers which can provide direct signatures of topological order and explore regimes where the characterization in terms of wave-function overlap fails. We also discuss various issues which are relevant for the practical realization of such FQH states with ultracold atoms in an optical lattice, including the presence of a long-range dipole interaction which can improve the energy gap and stabilize the ground state. We also investigate a detection technique based on Bragg spectroscopy to probe these systems in an experimental realization.
The emergence of macroscopic quantum coherence appears through Bose–Einstein condensation (BEC), which was first seen in superfluid helium and later achieved in ultracold atomic gases as a weakly interacting quantum fluid. This article aims to provide a study of the rotational properties of a two-component ultracold bosonic mixture with homogeneous and inhomogeneous interactions in the fractional quantum Hall (FQH) regime, where strong effective magnetic fields or rapid rotation drive the system into a strongly correlated quantum fluid state. Ultracold atomic gases offer a versatile experimental platform to realize and test the predictions of the composite fermion approach, bridging condensed matter physics with atomic physics through the unifying concept of weakly interacting quantum fluids emerging from strong correlations. A quantum interference-based atom laser in a two-component BEC is scientifically original and technologically promising, following recent advances in multi-species condensates. In this article, we explore the possibility of realizing an atom laser from ultracold binary atomic gases via their rotational properties in the FQH regime, where the controlled emission of quasiholes or coherent matter waves from the correlated state may provide a route toward an atom-laser scheme based on strongly correlated FQH states.