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Physica Scripta

Coupled dynamics of polaron and Bose–Einstein condensate in a parabolic potential

Sh. Mardonov, Eugene Ya. Sherman

Published Dec 7, 2020• 2 citations
Publisher

Abstract

Abstract We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.

DOI
10.1088/1402-4896/abd120

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Abstract We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.
The concept of polaron quasiparticles was first introduced in the pioneering papers by Landau and Feynman in the 1930s and 1940s. It describes the phenomenon of an external particle producing a bound state in an embedded medium. Since then, the study of polaron quasiparticles has been an active area of research in condensed matter physics, with a wide range of applications in magnetic phenomena and lattice deformation properties. In this paper, we provide a comprehensive review of the polaron quasiparticle phenomenon, including its historical origins, theoretical developments, and current research. We also study the various applications of polaron quasiparticles in condensed matter physics, including in magnetic phenomena and lattice deformation properties. The review concludes with an outlook on future directions of research in this field. In particular, we study the motion of external embedded particles in a quasi-two-dimensional Bose–Einstein condensate confined by the quantum harmonic oscillator. We found that the dynamics of attracting particles with static Bose–Einstein condensate exhibit circular and precessional elliptic trajectories due to centripetal force. Polaron-forming embedded particles in the condensate lead to a strongly nonlinear trajectory of the polaron and dynamics of condensate depending on the initial parameters of the condensate and polaron.
We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.
We investigate the dynamics of the plane wave state in one-dimensional spin-tensor-momentum coupled Bose-Einstein condensate. By using the Gaussian variational approximation, we first derive the equations of motion for the variational parameters, including the center-of-mass coordinate, momentum, amplitude, width, chirp, and relative phase. These variational parameters are coupled together nonlinearly by the spin-tensor-momentum coupling, Raman coupling, and the spin-dependent atomic interaction. By minimizing the energy with respect to the variational parameters, we find that the ground state is a biaxial nematic state, the momentum of the ground state decreases monotonically with the increase of the strength of the Raman coupling, and the parity of real part of the ground-state wave function is opposite to that of the imaginary part. The linear stability analysis shows that the ground state is dynamically stable under a perturbation, and exhibits three different oscillation excitation modes, the frequencies of which are related to the strength of the Raman coupling, the aspect ratio of the harmonic trap, and the strength of the atomic interaction. By solving the equations of motion for the variational parameters, we find that the system displays periodical oscillation in the dynamical evolution. These variational results are also confirmed by the direct numerical simulations of the Gross-Pitaevskii equations, and these findings reveal the unique properties given by the spin-tensor-momentum coupling.
Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation and the interference of two quantum wave packets decay in time owing to mutual interaction, which is analogous to the decoherence in quantum mechanics of many particles.
We study the collision dynamics of two Bose–Einstein condensates, with their dynamical wave functions modeled by a set of coupled, time-dependent Gross–Pitaevskii equations. In an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest, with a small separation about the center of an anisotropic harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing.
We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.