Brownian motion of solitons in a Bose–Einstein condensate

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongatedRb87Bose–Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton’s diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

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Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates

Mathematical Problems in Engineering ◽

10.1155/2020/4632434 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Ming Wang ◽

Guo-Liang He

Keyword(s):

Soliton Solutions ◽

Auxiliary Function ◽

Einstein Condensate ◽

Polarization Parameter ◽

One Dimension ◽

Pitaevskii Equation ◽

Bose Einstein Condensate ◽

The One ◽

Bose Einstein ◽

Two Peaks

In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.

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Bose polaron as an instance of quantum Brownian motion

Quantum ◽

10.22331/q-2017-09-27-30 ◽

2017 ◽

Vol 1 ◽

pp. 30 ◽

Cited By ~ 41

Author(s):

Aniello Lampo ◽

Soon Hoe Lim ◽

Miguel Ángel García-March ◽

Maciej Lewenstein

Keyword(s):

Brownian Motion ◽

Langevin Equation ◽

Degrees Of Freedom ◽

Interaction Strength ◽

Einstein Condensate ◽

Generalized Langevin Equation ◽

Quantum Gas ◽

Quantum Brownian Motion ◽

Bose Einstein Condensate ◽

Bose Einstein

We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.

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