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Matter waves with orbital angular momentum: collapse suppression and bistability.

Jasur A. Abdullaev, Anton S. Desyatnikov, Elena A. Ostrovskaya

Published Jan 1, 2011• 0 citations
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Abstract

We explore the influence of the orbital angular momentum on the dynamics of vortex-free elliptic clouds of Bose-Einstein condensates with attractive interatomic interactions. We show that the number of atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves trapped in a radially symmetric harmonic potential. Moreover, rotating anisotropic traps can simultaneously support two differently aligned elliptical matter wave states stabilized against the collapse.

DOI
10.1364/iqec.2011.i847

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We explore the influence of the orbital angular momentum on the dynamics of vortex-free elliptic clouds of Bose-Einstein condensates with attractive interatomic interactions. We show that the number of atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves trapped in a radially symmetric harmonic potential. Moreover, rotating anisotropic traps can simultaneously support two differently aligned elliptical matter wave states stabilized against the collapse.
We explore the influence of the orbital angular momentum on the dynamics of vortex-free elliptic clouds of Bose-Einstein condensates with attractive interatomic interactions. We show that the number of atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves trapped in a radially symmetric harmonic potential. Moreover, rotating anisotropic traps can simultaneously support two differently aligned elliptical matter wave states stabilized against the collapse.
We explore the influence of the orbital angular momentum on the collapse of vortex-free elliptic clouds of Bose–Einstein condensates with a negative scattering length trapped in a radially symmetric harmonic potential. We show that the number of trapped ultracold atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves. Below the threshold the elliptic mode is stable and exhibits periodic oscillations around a stationary rotating state. The frequency of these oscillations is independent of the number of particles and is determined solely by the trapping potential.
In this work we explore, theoretically and numerically, the influence of the OAM on the dynamics and suppression of collapse of trapped matter waves with attractive interatomic interaction. We demonstrate that a radially-symmetric harmonic trap can support elliptically shaped rotating clouds of ultracold atoms which exhibit a collapse-free dynamically stable evolution with the number of particles greatly exceeding the threshold for radially-symmetric fundamental state of the trap. To achieve the suppression of collapse, one needs to increase ellipticity of the trapped state and its rotation (spiraling) velocity, by transferring orbital angular momentum to the matter wave, e.g. imprinting a twisted phase front onto an elliptic BEC cloud. As a result, the critical number of atoms for the collapse raises and the BEC cloud exhibits long-term dynamically stable behavior. The results of numerical simulations are in agreement with the modified collapse threshold for the elliptic BEC states with OAM, predicted by variational analysis.
We investigate vortex solitons in models representing “pancake-shaped” Bose-Einstein condensates (BECs) with attractive interatomic interactions and an anisotropic harmonic trapping potential, or polarization-preserving waveguides, such as a photonic-crystal or radial-bandgap fiber with an elliptically deformed core. Elliptic-vortex states bifurcate from dipole modes. In spite of strongly asymmetric shapes, the elliptic vortices with topological charge 1 are stable in a wide region in their existence domain. The dependence of the stability region on the eccentricity of the elliptic trap is reported. Input circular wave functions with embedded vorticity slowly relax into stationary elliptic vortices, featuring persistent rotation in the course of the evolution. All higher-order vortices are unstable.
This thesis includes theoretical studies regarding stability and manipulation of Bose-Einstein condensates (BECs) of ultra-cold atoms in 2D trapping geometry, as well as formation of steady states of exciton-polariton Bose-Einstein condensates created in solid states. We analyze and numerically model the dynamics and localization of the condensates using mean-field model. Chapter 1 contains an introduction to the physics of ultra-cold atom BEC and excitonpolariton BEC which provides a framework for the work presented in later chapters. In Chapter 2, we consider a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in an ultra-cold atom BEC with attractive interparticle interaction loaded into a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the effective particle approach demonstrate that fast, time-periodic rocking of the two-dimensional optical lattice enables efficient stabilization and manipulation of spatially localized matter wave packets via induced reconfigurable mobility channels. Chapter 3 consists of an investigation of the instability - collapse of a BEC with attractive interactions. In this chapter we explore the influence of an orbital angular momentum on the collapse of vortex-free elliptic clouds of Bose-Einstein condensates trapped in a radially symmetric harmonic potential or a rotating elliptic potential. The results of our analysis show that the number of trapped ultracold atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves in a radially harmonic trap. The results corresponding to a BEC cloud confined in a rotating elliptic trap show that the elongated stationary states can be parallel or perpendicular to the long axis of the trap and display bistable nature. In Chapter 4, we examine spatial localization and dynamical stability of Bose-Einstein condensates of exciton-polaritons in microcavities under the condition of off-resonant spatially inhomogeneous optical pumping both with and without a harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii model for describing an incoherently pumped polariton condensate coupled to an exciton reservoir. We reveal that spatial localization of the steady-state condensate occurs due to effective self-trapping created by the polariton flows, regardless of the presence of the external potential. A ground state of the polariton condensate with repulsive interactions between the quasiparticles represents a dynamically stable bright dissipative soliton. We also investigate the conditions for sustaining spatially localized structures, with nonzero angular momentum, in the form of single-charge vortices. Chapter 5 consider the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic inplane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We show that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultra-cold alkali atoms.
We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.