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Physical Review A

Theory of a mode-locked atom laser with toroidal geometry

P. D. Drummond, Antonios Eleftheriou, Kerson Huang, Karen V. Kheruntsyan

Published Apr 13, 2001• 19 citations
Publisher

Abstract

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to $\ensuremath{\Elzxh}/2.$ It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

DOI
10.1103/physreva.63.053602

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We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to \ensuremath\Elzxh/2.\ensuremath{\Elzxh}/2.\ensuremath\Elzxh/2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.
We consider a possible technique for mode-locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to \hbar/2. It emerges naturally, when the condensate is stirred at the soliton velocity, and subsequently outcoupled with a periodic Raman pulse-train. The result is a replicating coherent field inside the atom laser. We give a numerical demonstration of the generation and stabilization of the soliton.
In order to manufacture a modelocked, pulsed atom laser, we suggest the idea of making use of the atom-atom repulsion in a BEC to form a toroidal soliton which can then form a reproducible, coherent waveform. The relevant solitons have the form of a kink, or phase-singularity in the nonlinear Schrodinger equation. We suppose that the atoms are all trapped in a deep, toroidal magnetic trap with the central repulsive core potential induced by a blue-detuned laser. We investigate the case of an atom laser environment with a uniform gain provided by the super-saturation technique. We also assume that there is a periodic loss, provided by a synchronized Raman output coupling laser, and show that this combination of gain and periodic loss leads to stable circulating dark solitons.
We demonstrate the feasibility of generation of quasi-stable counter-propagating solitonic structures in an atomic Bose–Einstein condensate confined in a realistic toroidal geometry, and identify optimal parameter regimes for their experimental observation. Using density engineering we numerically identify distinct regimes of motion of the emerging macroscopic excitations, including both solitonic motion along the azimuthal ring direction, such that structures remain visible after multiple collisions even in the presence of thermal fluctuations, and snaking instabilities leading to the decay of the excitations into vortical structures. Our analysis, which considers both mean field effects and fluctuations, is based on the ring trap geometry of Murray et al (2013 Phys. Rev. A 88 053615 ).
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.
Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensates are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. We also explore different proposed particle pictures considering the ring as a moving particle and find, where appropriate, results in very good qualitative and also reasonable quantitative agreement with the numerical findings.