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arXiv:cond-mat/0310702 · Physical Review A

Transverse laser modes in Bose-Einstein condensates

Graeme Whyte, Patrik Öhberg, Johannes Courtial

Published May 13, 2004• 11 citations
arXivHTMLPDF

Abstract

Bose-Einstein condensates (BECs) are in many ways similar to laser light. In Fox-Li-type simulations, which involve free evolution of a two-dimensional BEC in combination with periodic focusing and localized loss, we model here numerically the BEC equivalent of transverse aspects of laser resonators. We discuss possible experimental realizations in the form of periodic series of light pulses interacting with the BEC. We show that such experiments can result in trapped, structurally stable, modes analogous to Hermite-Gaussian laser modes. This outlines a new way of trapping BECs and illustrates further the analogy between BECs and laser light.

DOI
10.1103/physreva.69.053610

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Bose-Einstein condensates (BECs) are in many ways similar to laser light. In Fox-Li-type simulations, which involve free evolution of a two-dimensional BEC in combination with periodic focusing and localized loss, we model here numerically the BEC equivalent of transverse aspects of laser resonators. We discuss possible experimental realizations in the form of periodic series of light pulses interacting with the BEC. We show that such experiments can result in trapped, structurally stable, modes analogous to Hermite-Gaussian laser modes. This outlines a new way of trapping BECs and illustrates further the analogy between BECs and laser light.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
The interesting question if and how can Bose-Einstein condensation (BEC) occur with photons has received a boost by a recent experiment that reported on the observation of photon-BEC condensation in an optical microcavity [1]. Here we present a different laser light condensation (LC) phenomenon [2], while discussing and questioning the meaning and the possibility to observe thermal photon-BEC in laser cavities. LC is a classical condensation effect that is based on very different grounds than the regular BEC. Its “energy” levels are measured in a loss-gain scale inherent in laser cavities, where the “ground-state” is the lowest-loss mode, and noise has the role of temperature. The loss scale gives a power occupation hierarchy and power spectra similar to Bose-Einstein statistics with an effective chemical potential parameter and eventually laser light-condensation (LC) which is formally very similar to BEC in a potential-well [3].
Summary form only given. The production of tight toroidal traps, or rings, for Bose-Einstein condensates (BECs) opens up the way to a variety of both fundamental and applied studies. By providing tight transverse confinement one can produce a quasi-one-dimensional motion for the BEC on a ring, which allows for studies of vortices and persistent currents. On the applied side, such mesoscopic rings could be used for rotation sensing via the Sagnac effect for counter-propagating atoms around the ring. In this paper, we show that Laguerre-Gaussian (LG) laser modes of high azimuthal mode index l and containing one radial ring can be used to create tight confined optical dipole traps for 2D BECs.
The properties of Bose–Einstein condensates in an external potential produced by a laser light field are discussed. Considered are the condensates embedded in periodic lattices produced by standing laser waves and the condensates confined within 'optical traps' near the focus of a traveling wave. Observations of the Mott transition in a periodic lattice are described, as are experiments on atoms near the Feshbach resonance and experiments on the condensates in a double potential well, which permit investigating the tunnel dynamics of condensate phases.