Soliton-Sound Interactions in Quasi-One-Dimensional Bose-Einstein Condensates (original) (raw)
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Dark soliton dynamics in confined Bose-Einstein condensates
Dilute atomic Bose-Einstein condensates are inherently nonlinear systems and support solitary wave solutions. An important distinction from optical systems is the inhomogeneous background density, which results from the traps used to confine the atoms. As in optical systems, dark solitary waves in three dimensional geometries are unstable to transverse excitations, which lead to a bending of the dark soliton plane and decay into vortex rings. Highly elongated geometries can now be achieved experimentally, in which the condensate dynamics are effectively one-dimensional, and the motion of the dark soliton is governed by the inhomogeneous longitudinal density. We show that a dark soliton is fundamentally unstable to such a changing background density, by means of numerical simulations of the soliton under various potentials (e.g. steps, ramps, harmonic traps, and optical lattices). This leads to the emission of radiation in the form of sound waves. The power emitted is found to be proportional to the square of the soliton acceleration. The latter quantity is shown to be proportional to the deformation of the apparent soliton profile, arising from the sound field in the region of the soliton. We demonstrate that the ensuing interactions between the soliton and sound field, and therefore the dynamics of the soliton, can be controlled experimentally via manipulation of the emitted sound, achieved by modifying the trap geometry. In this manner, it is possible to induce a rapid decay of the soliton, stabilise the soliton, or even pump energy into the soliton by means of parametric driving.
The motion of a dark soliton is investigated in a one-dimensional dilute Bose–Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the perturbing optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilization of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realized by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.
Parametric Driving of Dark Solitons in Atomic Bose-Einstein Condensates
A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.
Motion of Dark Solitons in Trapped Bose-Einstein Condensates
Physical Review Letters, 2000
We use a multiple time scale boundary layer theory to derive the equation of motion for a dark (or 'grey') soliton propagating through an effectively one-dimensional cloud of Bose-Einstein condensate, assuming only that the background density and velocity vary slowly on the soliton scale. We show that solitons can exhibit viscous or radiative acceleration (anti-damping), which we estimate as slow but observable on experimental time scales.
Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates
Physical Review A, 2010
A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the co-existing soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter timescale than other dissipation mechanisms. Thus, we propose how small realistic modifications to existing experimental set-ups could enable the experimental observation of this decay channel.
Deformation of dark solitons in inhomogeneous Bose-Einstein condensates
A dark soliton becomes unstable when it is incident on a background density gradient, and the induced instability results in the emission of sound. Detailed quantitative studies of sound emission are performed for various potentials, such as steps, linear ramps and Gaussian traps. The amount of sound emission is found to be a significant fraction of the soliton energy for typical potentials. Continuous emission of sound is found to lead to an apparent deformation of the soliton profile. The power emitted by the soliton is shown to be parametrized by the square of the displacement of the centre of mass of the soliton from its density minimum, thus highlighting the significance of the inhomogeneity-induced soliton deformation.
Characterising arbitrary dark solitons in trapped one-dimensional Bose-Einstein condensates
Europhysics Letters, 2021
We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we provide numerical evidence that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we discuss implications for vortex detection in three-dimensional Bose-Einstein condensates.
Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates
Mathematics and Computers in Simulation, 2005
We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.
Dark solitons as quasiparticles in trapped condensates
Physical Review A, 2006
We present a theory of dark soliton dynamics in trapped quasi-one-dimensional Bose-Einstein condensates, which is based on the local density approximation. The approach is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system as well as to arbitrary polynomial traps. In particular, we derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. It is shown that the dependence of the amplitude of oscillations vs the trap frequency (strength) is given by the scaling law X0 ∝ ω −γ where the exponent γ depends on the type of the two-body interactions, on the exponent of the polynomial confining potential, on the density of the condensate and on the initial soliton velocity. Analytical results obtained within the framework of the local density approximation are compared with the direct numerical simulations of the dynamics, showing remarkable match. Various limiting cases are addressed. In particular for the slow solitons we computed a general formula for the effective mass and for the frequency of oscillations.
Generation of dark solitons in oscillating Bose–Einstein condensates
We propose an experimentally tractable setting for observing an "instability" of a repulsive oscillating Bose-Einstein condensate that leads to the generation of dark solitons. We illustrate that when the trap of the condensate (which incorporates a localized impurity) is displaced so that the condensate flow is characterized by an atomic velocity larger than the local speed of sound, dark solitons are generated. The subcritical, near critical and supercritical are analyzed in detail. (D.J. Frantzeskakis). and the generation of bright solitons , the transverse instability of dark solitons [6] and the generation of vortices [7] and robust vortex clusters [8], the generation of Faraday patterns [9], and so on. Additionally, much attention has been paid, both on the theoretical and the experimental sides (see also the discussion and references therein), to the study of dynamical instabilities and their relation to the Landau instability (see also ). The latter instability is known to be a (effectively) "dissipative" mechanism, responsible for the breakup of superfluidity, which also results in the emission of phonon radiation from a superfluid moving with a speed larger 0375-9601/$ -see front matter