Dark Solitons In Bose-Einstein Condensates Research Articles

Dynamics of ring dark solitons in Bose-Einstein condensates

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.

Vortex lines attached to dark solitons in Bose-Einstein condensates and boson-vortex duality in 3+1 dimensions

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons.

Dynamics of matter-wave solitons in Bose-Einstein condensates with time-dependent scattering length and complex potentials

We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D) Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) with time-dependent scattering length in varying trapping potentials with feeding/loss term. By performing a modified lens-type transformation, we reduce the GP equation into a classical nonlinear Schrodinger (NLS) equation with distributed coefficients and find its integrable condition. Under the integrable condition, we apply the generalized Jacobian elliptic function method (GJEFM) and present exact analytical solutions which describe the propagation of a bright and dark solitons in BECs. Their stability is examined using analytic method. The obtained exact solutions show that the amplitude of bright and dark solitons depends on the scattering length, while their motion and the total number of BEC atoms depend on the external trapping potential. Our results also shown that the loss of atoms can dominate the aggregation of atoms by the attractive interaction, and thus the peak density can decrease in time despite that the strength of the attractive interaction is increased.

Cosmology and the Korteweg-de Vries equation

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.

Solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic and complex potential

We present two families of analytical solutions of the one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.

Spectroscopy of dark soliton states in Bose Einstein condensates

Experimental and numerical studies of the velocity field of dark solitons in Bose-Einstein condensates are presented. The formation process after phase imprinting as well as the propagation of the emerging soliton are investigated using spatially resolved Bragg-spectroscopy of soliton states in Bose-Einstein condensates of Rubidium87. A comparison of experimental data to results from numerical simulations of the Gross-Pitaevskii equation clearly identifies the flux underlying a dark soliton propagating in a Bose-Einstein condensate. The results allow further optimization of the phase imprinting method for creating collective exitations of Bose-Einstein condensates.

Ring dark solitons and vortex necklaces in Bose-Einstein condensates.

We introduce the concept of ring dark solitons in Bose-Einstein condensates. We show that relatively shallow rings are not subject to the snake instability, but a deeper ring splits into a robust ringlike cluster of vortex pairs, which performs oscillations in the radial and azimuthal directions, following the dynamics of the original ring soliton.

Generation and interaction of solitons in Bose-Einstein condensates

Generation, interaction, and detection of dark solitons in Bose-Einstein condensates are studied. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. We show that solitons slow down significantly when the trap is opened and that soliton phase shifts after binary interactions cannot be observed with present experiments. Finally, motivated by the recent experimental results of Cornish et al. [Phys. Rev Lett. 85, 1795 (2000)], we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.

Controlled generation of dark solitons with phase imprinting.

The generation of dark solitons in Bose-Einstein condensates with phase imprinting is studied by mapping it into the classic problem of a damped driven pendulum. We provide a simple but powerful scheme, designing the phase imprint for various desired outcomes of soliton generation. For a given phase step, we derive a formula for the number of dark solitons traveling in each direction, and examine the physics behind the generation of counterpropagating dark solitons.

Manipulation of Bose-Einstein condensates by dipole potentials

Abstract The coherent manipulation of Bose-Einstein condensates by far blue detuned dipole potentials is discussed. ‘Classical’ atom optical elements, such as mirrors and waveguides, are realized and the dynamics of coherent matter waves interacting with these elements is investigated. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose-Einstein condensates and study their dynamics.

Manipulation of Bose-Einstein condensates by dipole potentials

The coherent manipulation of Bose-Einstein condensates by far blue detuned dipole potentials is discussed. ‘Classical’ atom optical elements, such as mirrors and waveguides, are realized and the dynamics of coherent matter waves interacting with these elements is investigated. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose-Einstein condensates and study their dynamics.

Dark solitons in Bose-Einstein condensates under a slowly varying trap

Dynamics of dark solitons in Bose-Einstein condensates under a slowly varying trap potential is studied with a novel direct perturbation theory for dark solitons.