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Chinese Physics B

Quantum reflection of a Bose–Einstein condensate with a dark soliton from a step potential*

Dongmei Wang, Jian-Chong Xing, Rong Du, Bo Xiong, Tao Yang

Published May 26, 2021• 7 citations
Publisher

Abstract

We study dynamical behaviors of a Bose–Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R s ∼ cos [λ(θ – π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitiv width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.

DOI
10.1088/1674-1056/ac051e

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We study dynamical behaviors of a Bose–Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R s ∼ cos [λ(θ – π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitiv width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.
We study the dynamic behavior of a Bose-Einstein condensate (BEC) containing a dark soliton separately reflected from potential drops and potential barriers. It is shown that for a rapidly varying potential and in a certain regime of incident velocity, the quantum reflection probability displays the cosine of the deflection angle between the incident soliton and the reflected soliton, i.e., R(θ)∼cos⁡2θR(θ) \sim \cos 2θR(θ)∼cos2θ. For a potential drop, R(θ)R(θ)R(θ) is susceptible to the widths of potential drop up to the length of the dark soliton and the difference of the reflection rates between the orientation angle of the soliton θ=0θ=0θ=0 and θ=π/2θ=π/2θ=π/2, δRsδR_sδRs​, displays oscillating exponential decay with increasing potential widths. However, for a barrier potential, R(θ)R(θ)R(θ) is insensitive for the potential width less than the decay length of the matter wave and δRsδR_sδRs​ presents an exponential trend. This discrepancy of the reflectances in two systems is arisen from the different behaviors of matter waves in the region of potential variation.
Abstract We study the quantum reflection of a two-dimensional disk-shaped Bose–Einstein condensate with dark soliton excitation by a square potential barrier. For the given geometry, the dark soliton initially located at the centre of the condensate cloud survives long enough to investigate the reflection process. We show the time evolution of the reflection probability with respect to various widths of the barrier. The asymptotic value of the reflection probability is decreased by the existence of a dark soliton, and is highly sensitive to the initial orientation of the dark soliton, which also affects the excitation properties during the process of condensate and barrier interaction.
The motion characteristics of a Bose–Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross–Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potential in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.
By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose–Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.
We present an analytical study on the dynamics of bright and dark solitons in Bose–Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross–Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.