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Physical Review A

Matter-wave solitons in heteronuclear atomic Bose-Einstein condensates with synchronously controllable interactions and potentials

Cai-Ying Ding, Xiao-Fei Zhang, Dun Zhao, Hong‐Gang Luo, Weixi Liu

Published Nov 28, 2011• 9 citations
Publisher

Abstract

We investigate exact matter-wave soliton pairs of two-component heteronuclear atomic Bose-Einstein condensates with tunable interactions and harmonic potentials by using a combination of the homogeneous balance principle and the $F$-expansion technique. Our results show that exact matter-wave soliton pairs are asymmetric where their existence requires some restrictive conditions corresponding to experimentally controllable interactions and harmonic potential parameters. In contrast to homonuclear systems, the potentials for two components in heteronuclear systems are different, which is due to the mass of two components being unequal. Considering two explicit situations of the interaction parameters, we further explore the collision dynamics of the soliton pairs with opposite velocities by synchronously controlling the interaction and potential parameters. The collision dynamics occur during and after the simultaneous evaporative cooling of two condensates. The results show that collisions are elastic and that the solitons after the collision can keep their identities. In addition, we find that the amplitudes of the soliton pairs periodically grow with time during the cooling process and, for the same initial conditions, the collision time of the soliton pair without gain is delayed compared with that with gain. We also discuss how to observe these new phenomena in future experiments.

DOI
10.1103/physreva.84.053631

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We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose—Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.
We present a family of exact vector-soliton solutions for the coupled nonlinear Schr\"odinger equations with tunable interactions and harmonic potential, and then apply the model to investigate the dynamics of solitons and collisions between two orthogonal solitons in the case with equal interaction parameters. Our results show that the exact vector-soliton solutions can be obtained with arbitrary tunable interactions as long as a proper harmonic potential is applied. The dynamics of solitons can be controlled by the Feshbach resonance and the collisions are essentially elastic and do not depend on the initial conditions.
We investigate the dynamics of matter-wave solitons in Bose–Einstein condensates with a time-dependent complicated potential, which is composed of a linear, a harmonic and a complex potential of arbitrary form. This system is characterized by the time dependence of all the parameters of the complicated potential. A unified transformation is derived and exact soliton solutions are obtained analytically. Our results show that the dynamical evolution of the solitons can be dramatically affected by the complicated potential; the collisions between two solitons are essentially elastic in the absence of complex potential. Moreover, it is found that the number of atoms in the soliton can be effectively controlled by a proper choice of the external complex potential.
By using the split-step fast Fourier transform (SSFFT) method, we numerically study the collision properties between two bright solitons in the growth Bose–Einstein condensates (BECs) with different interaction strengths under a harmonic potential. It is shown that the soliton’s collision property of the condensates can be controlled by adjusting the gain term, the initial position and the interaction strength between atoms. The number of collisions of the two bright solitons decreases first, then increases, with increasing the values of the gain term. As the initial distance between solitons increases, the number of collisions between the two bright solitons is reduced, and the first collision time is also postponed. The increase in interaction strength between atoms delays the collision time of the two bright solitons. Meanwhile, a critical interaction strength between atoms is found, the amplitude of the soliton’s first collision peak increases slowly when the interaction strength is less than the critical value, but the amplitude increases sharply when the interaction strength is more than the critical value.
Considering time-dependence of both interactions and external potential, we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation. It is found that for a closed external potential, the soliton-soliton distance is decreased with nonlinearly increased interactions, while the amplitude of each soliton increases and its width decreases. For linearly increased interactions but nonlinearly decreased external potential, especially, the atom transfer between two solitons is observed, different from previous theory of no atom transfer in solitons collision in a fixed external potential. In addition, it is shown that the collisional type, such as head-on, “chase", or collision period between two solitons, can be controlled by tuning both interactions and external potential. The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.