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Bulletin of the American Physical Society

Transition properties of a Bose-Einstein condensate confined by a laser in a Laguerre-Gaussian mode

Thomas G. Akin, Sharon A. Kennedy, Jeremy Marzoula, Jason S. Alexander, E. Abraham

Published May 27, 2010• 0 citations
OpenAlex

Abstract

•Our trap is generated from the AC Stark effect induced by a laser in higherorder Laguerre-Gaussian modes detuned both to the red and blue of the resonance frequency. • Common practice is to make an harmonic expansion about the outer node of the LG geometry. •Here, we compare the effects of including the potential in its entirety. •We present experimental results for a Bose gas trapped in the LG dipole trap. •A dipole trap is arises from the AC Stark effect, whose potential takes the form:

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•Our trap is generated from the AC Stark effect induced by a laser in higherorder Laguerre-Gaussian modes detuned both to the red and blue of the resonance frequency. • Common practice is to make an harmonic expansion about the outer node of the LG geometry. •Here, we compare the effects of including the potential in its entirety. •We present experimental results for a Bose gas trapped in the LG dipole trap. •A dipole trap is arises from the AC Stark effect, whose potential takes the form:
We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order $\ensuremath{\ell}$ allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a ``finger'' or of a ``hockey puck'' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.
Abstract This study investigates the formation and dynamics of solitons in Bose–Einstein condensates (BECs) within dark traps generated by two crossed Laguerre–Gaussian (LG) beams with varying azimuthal indices ℓ . As the index ℓ increases, the potential transitions from a harmonic trap when ℓ = 1 to a square-well potential for larger values of ℓ . This transition allows us to study a range of soliton dynamics under different confinement conditions while maintaining the same BEC volume. Through the derivation of the Gross-Pitaevskii equation (GPE) and under these specific conditions in both one-dimensional and two-dimensional configurations, we explore the dynamics of solitons across multiple scenarios. The study examines two primary methods for solitons generation: the temporal modulation of the scattering length and the implementation of an initial potential barrier that is subsequently removed. The results indicate that the trap shape plays a critical role in the generation and interaction dynamics of solitons. In harmonic traps, solitons exhibit a behavior different from those observed in anharmonic traps, where the dynamics is significantly influenced by the azimuthal index of the trap. The ability to control soliton dynamics in BECs holds significant promise for applications in quantum technologies, precision sensing, and the exploration of fundamental quantum phenomena.
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.
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.