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arXiv:0710.1702 · Lithuanian Journal of Physics

Formation of solitons in atomic Bose-Einstein condensates by dark-state adiabatic passage

Gediminas Juzeliūnas

Published Jan 1, 2007• 23 citations
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Abstract

We propose a new method of creating solitons in elongated Bose-Einstein condensates (BECs) by sweeping three laser beams through the BEC.If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal π phase slip which can be transferred to the atoms creating a soliton.Using this method it is possible to circumvent the restriction set by the diffraction limit inherent to conventional methods such as phase imprinting.The method allows one to create multicomponent (vector) solitons of the dark-bright form as well as the dark-dark combination.In addition it is possible to create in a controllable way two or more dark solitons with very small velocity and close to each other for studying their collisional properties.

DOI
10.3952/lithjphys.47318

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•Jun 20, 2018•0 citations
We propose a new method of creating solitons in elongated Bose-Einstein condensates (BECs) by sweeping three laser beams through the BEC.If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal π phase slip which can be transferred to the atoms creating a soliton.Using this method it is possible to circumvent the restriction set by the diffraction limit inherent to conventional methods such as phase imprinting.The method allows one to create multicomponent (vector) solitons of the dark-bright form as well as the dark-dark combination.In addition it is possible to create in a controllable way two or more dark solitons with very small velocity and close to each other for studying their collisional properties.
We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a ΛΛΛ-coupled three-level system. Numerical simulations of the corresponding two-component system reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. However, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in, which happens after a few tens of milliseconds after the quench of the optical fields.
We discuss a method to launch gap solitonlike structures in atomic Bose-Einstein condensates confined in optical traps. Bright vector solitons consisting of a superposition of two hyperfine Zeeman sublevels can be created for both attractive and repulsive interactions between the atoms. Their formation relies on the dynamics of the atomic internal ground states in two far-off-resonance counterpropagating $({\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}})$-polarized laser beams that form the optical trap. Numerical simulations show that these solitons can be prepared from a one-component state provided with an initial velocity.
Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.
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 87 Rb. 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 excitations of Bose–Einstein condensates.
We propose and analyze a scheme to create dark solitons and vortices in Bose-Einstein condensates. This is achieved starting from a condensate in the internal state ∣a〉|a〉∣a〉 and transferring the atoms to the internal state ∣b〉|b〉∣b〉 via a Raman transition induced by laser light. By scanning adiabatically the Raman detuning, dark solitons and vortices are created.
In this thesis, we have studied the behavior of two-component dark-bright solitons in multicomponent Bose-Einstein condensates (BECs) analytically and numerically in different situations. We utilized various analytical methods including the variational method and perturbation theory. By imprinting a linear phase on the bright component only, we were able to impart a velocity relative to the dark component and thereby we obtain an internal oscillation between the two components. We find that there are two modes of the oscillation of the dark-bright soliton. The first one is the famous Goldstone mode. This mode represents a moving dark-bright soliton without internal oscillation and is related to the continuous translational symmetry of the underlying equations of motion in the uniform potential. The second mode is the oscillation of the two components relative to each other. We compared the results obtained from the variational method with numerical simulations and found that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments. Also, we studied the binding energy and found a critical value for the breakup of the dark-bright soliton. Building on these results, we have studied another situation where we have the dark-bright soliton oscillate in a harmonic potential. We found for weak trapping the internal modes are nearly independent of center of mass motion of the dark-bright soliton. In contrast, in tighter traps the internal modes couple strongly to the center of mass motion, showing that for dark-bright solitons in a harmonic potential the center of mass and relative degrees of freedom are not independent. We found this result is robust against noise in the initial condition and should, therefore, be experimentally observable. In addition, we have studied the interaction between a moving dark-bright soliton in a uniform background with internal oscillation and a fixed impurity, modeled by a delta function potential. The interaction excites different modes in the system. Our analytical model capture two of these modes: the relative oscillation between the two components, as well as the in-sync oscillation of the widths. The numerical simulations allow further internal modes like out-of-sync oscillations of the soliton widths and even shape deformations of various kinds. We identify regions in parameter space for the transmission, reflection and inelastic scattering of the dark-bright soliton by the potential barrier. We have studied the velocity of dark-bright solitons described with an ansatz that uses one center of mass variable to represent the position of the two components. We found for a dark-bright soliton the maximum velocity is limited by the relative number of atoms in the bright component as compared to the size of the hole or density notch created by the dark component. Above this critical velocity the dark-bright soliton develops internal oscillations, and eventually unbinds and breaks apart.