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arXiv:0809.0288 · Optics Express

Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms

R. A. Williams, Jean-Damien Pillet, S. Al-Assam, B. Fletcher, M. Shotter, Christopher J. Foot

Published Oct 9, 2008• 45 citations
arXivHTMLPDF

Abstract

We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.

DOI
10.1364/oe.16.016977

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We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.
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 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.
Vortex nucleation in a rotating optical lattice of ultracold atoms Ross Williams, Brasenose College, Oxford D.Phil thesis, Michaelmas 2009 This thesis describes the design and implementation of a two-dimensional rotating optical lattice for ultracold atoms. Rotating optical lattices for ultracold atoms have generated a great deal of theoretical interest due to the close analogy between electrons under a magnetic field and rotating neutral atoms. However, such is the difficulty associated with creating rotating lattice potentials which do not cause significant heating of the atoms there has been only one previous experimental realisation of a practical device, [Phys. Rev. Lett. 97, 240402 (2006)]. There S. Tung et al. reported that heating due to rotation limited the optical lattice to depths of less than 30% of the condensate’s chemical potential. We describe a new method for generating a rotating optical lattice, based on acousto-optic deflection and forming the lattice in the focal plane of a high numerical aperture lens. The intrinsically smooth rotation and excellent degree of control over the rotation frequency enabled a new breed of experiments to be performed, allowing the weak-lattice regime to be surpassed for the first time. In particular we report on the first experiments with a rotating optical lattice where lattice depths were reached such that a two-dimensional array of weakly-linked condensates was created, realising a bosonic Josephson-junction array under an effective magnetic field. We observe a new method of vortex nucleation, whereby rotation-induced phase differences between neighbouring condensates are converted to vortices upon ramping down the lattice. The arrangement for generating a rotating optical lattice also allowed the first realisation of a two-dimensional optical lattice with variable periodicity, known as an accordion lattice. Calibration of the accordion lattice is described, together with a discussion on the crossover from quantum to classical dynamics in large periodicity optical lattices.
The use of a dynamic ``accordion'' lattice with ultracold atoms is demonstrated. Ultracold atoms of 87Rb^{87}\mathrm{Rb}87Rb are trapped in a two-dimensional optical lattice, and the spacing of the lattice is then increased in both directions from 2.2 to 5.5 $\ensuremath{\mu}$m. Atoms remain bound for expansion times as short as a few milliseconds, and the experimentally measured minimum ramp time is found to agree well with numerical calculations. 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.
A collection of ultracold atoms subject to a spatially periodic potential energy can exhibit behavior analogous to strongly-correlated electrons in a crystal lattice. This was shown recently by the experimental demonstration of the superfluid to Mott-insulator quantum phase transition for a three-dimensional optical lattice. An optical lattice consists of atoms subject to a periodic potential produced by interfering laser beams. The analogy between ultracold atoms in optical lattices and electrons in crystal lattices is manifestly a rich one. One interesting area in particular is the correspondence between the fractional quantum Hall effect for electrons in strong magnetic fields and rotating quantum gases. Here strongly-correlated effects can potentially be enhanced utilizing rotating optical lattices. Recently, we have also made a a proposal to extend the analogy to doped semiconductor materials. Lattice “defects” achieve behaviors similar to P-type and N-type semiconductor materials. Naturally the interest is to adjoin P-type and N-type atoms lattices to produce an atom diode, and then an NPN or PNP lattice “sandwich” to achieve bipolar transistor-like behavior for ultracold atoms. Such heterogeneous structures can indeed be made to mimic their electronic counterparts.
The experimental realization of two-dimensional (2D) Bose gases with a tunable interaction strength is an important challenge for the study of ultracold quantum matter. Here we report on the realization of an optical accordion creating a lattice potential with a spacing that can be dynamically tuned between 11 and 2 $\ensuremath{\mu}\mathrm{m}$. We show that we can load ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms into a single node of this optical lattice in the large spacing configuration and then decrease nearly adiabatically the spacing to reach a strong harmonic confinement with frequencies larger than ${\ensuremath{\omega}}_{z}/2\ensuremath{\pi}=10$ kHz. Atoms are trapped in an additional flat-bottom in-plane potential that is shaped with a high resolution. By combining these tools we create custom-shaped uniform 2D Bose gases with tunable confinement along the transverse direction and hence with a tunable interaction strength.