skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries

Abstract

We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t{sub c{sub 1}}. For tunneling well below t{sub c{sub 1}} one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids.

Authors:
; ; ;  [1];  [2];  [3]
  1. T.C.M. Group, Department of Physics, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
  2. (United Kingdom)
  3. (Netherlands)
Publication Date:
OSTI Identifier:
20786359
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063622; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; DENSITY; DENSITY FUNCTIONAL METHOD; DISTRIBUTION; ELECTRON GAS; EXPANSION; GEOMETRY; HALL EFFECT; LAYERS; LIQUIDS; MAGNETIC FIELDS; MELTING; ROTATION; THREE-DIMENSIONAL CALCULATIONS; TUNNEL EFFECT; TWO-DIMENSIONAL CALCULATIONS; VORTICES

Citation Formats

Cooper, N. R., Lankvelt, F. J. M. van, Reijnders, J. W., Schoutens, K., Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, and Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam. Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Cooper, N. R., Lankvelt, F. J. M. van, Reijnders, J. W., Schoutens, K., Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, & Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam. Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries. United States. doi:10.1103/PHYSREVA.72.0.
Cooper, N. R., Lankvelt, F. J. M. van, Reijnders, J. W., Schoutens, K., Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, and Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam. Thu . "Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786359,
title = {Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries},
author = {Cooper, N. R. and Lankvelt, F. J. M. van and Reijnders, J. W. and Schoutens, K. and Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP and Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam},
abstractNote = {We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t{sub c{sub 1}}. For tunneling well below t{sub c{sub 1}} one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • Through exact numerical diagonalization for small numbers of atoms, we show that it is possible to access quantum Hall states in harmonically confined Bose gases at rotation frequencies well below the centrifugal limit by applying a repulsive Gaussian potential at the trap center. The main idea is to reduce or eliminate the effective trapping frequency in regions where the particle density is appreciable. The critical rotation frequency required to obtain the bosonic Laughlin state can be fixed at an experimentally accessible value by choosing an applied Gaussian whose amplitude increases linearly with the number of atoms while its width increasesmore » as the square root.« less
  • We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole position.
  • We propose fractional spin Hall effect (FSHE) by coupling pseudospin states of cold bosonic atoms to optical fields. The present scheme is an extension to interacting bosonic system of the recent work [X.-J. Liu, X. Liu, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. 98, 026602 (2007) and S.-L. Zhu, H. Fu, C.-J. Wu, S.-C. Zhang, and L.-M. Duan, Phys. Rev. Lett. 97, 240401 (2006)] on optically induced spin Hall effect in noninteracting atomic system. The system has two different types of ground states. The first type of ground state is a 1/3-factor Laughlin function and has themore » property of chiral-antichiral interchange antisymmetry, while the second type is shown to be a 1/4-factor wave function with chiral-antichiral symmetry. The fractional statistics corresponding to the fractional spin Hall states are studied in detail and are discovered to be different from that corresponding to the fractional quantum Hall (FQH) states. Therefore the present FSHE can be distinguished from FQH regime in the measurement.« less
  • We present and characterize an experimental system in which we achieve the integration of an ultrahigh finesse optical cavity with a Bose-Einstein condensate (BEC). The conceptually novel design of the apparatus for the production of BECs features nested vacuum chambers and an in vacuo magnetic transport configuration. It grants large scale spatial access to the BEC for samples and probes via a modular and exchangeable ''science platform.'' We are able to produce {sup 87}Rb condensates of 5x10{sup 6} atoms and to output couple continuous atom lasers. The cavity is mounted on the science platform on top of a vibration isolationmore » system. The optical cavity works in the strong coupling regime of cavity quantum electrodynamics and serves as a quantum optical detector for single atoms. This system enables us to study atom optics on a single particle level and to further develop the field of quantum atom optics. We describe the technological modules and the operation of the combined BEC cavity apparatus. Its performance is characterized by single atom detection measurements for thermal and quantum degenerate atomic beams. The atom laser provides a fast and controllable supply of atoms coupling with the cavity mode and allows for an efficient study of atom field interactions in the strong coupling regime. Moreover, the high detection efficiency for quantum degenerate atoms distinguishes the cavity as a sensitive and weakly invasive probe for cold atomic clouds.« less
  • We consider the effective spin Hamiltonian describing a mixture of two species of pseudo-spin-(1/2) Bose gases with interspecies spin exchange. First we analyze the stability of the fixed points of the corresponding classical dynamics, of which the signature is found in quantum dynamics with a disentangled initial state. Focusing on the case without an external potential, we find all the ground states by taking into account quantum fluctuations around the classical ground state in each parameter regime. The nature of entanglement and its relation with classical bifurcation is investigated. When the total spins of the two species are unequal, themore » maximal entanglement at the parameter point of classical bifurcation is possessed by the excited state corresponding to the classical fixed point which bifurcates, rather than by the ground state.« less