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Journal of Experimental and Theoretical Physics Letters

On the Validity of the One-Dimensional Description for Ring Polariton Bose–Einstein Condensates

K. D. Dyadkin, M. A. Posazhenkov, N. Voronova

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This work is motivated by the active surge in research on ring Bose–Einstein condensates of exciton polaritons, including those with artificially created defects (barriers). Currently, such systems are primarily described within a one-dimensional approach, taking into account that the order parameter depends only on the azimuthal angle. In this work, the profiles of a polariton ring Bose–Einstein condensate in the stationary case have been numerically simulated using the two-dimensional Gross–Pitaevskii equation. The radial profiles of the ground-state wavefunction are obtained for ring confinement potentials of various depths and widths, which have been used to calculate effectively one-dimensional interaction constants for various particle densities in the condensate. The results have been compared with analytical expressions for the linear limit and for a ring of a large radius, and the validity range for these simplified analytical descriptions have been determined.

DOI
10.1134/s0021364025609637

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This work is motivated by the active surge in research on ring Bose–Einstein condensates of exciton polaritons, including those with artificially created defects (barriers). Currently, such systems are primarily described within a one-dimensional approach, taking into account that the order parameter depends only on the azimuthal angle. In this work, the profiles of a polariton ring Bose–Einstein condensate in the stationary case have been numerically simulated using the two-dimensional Gross–Pitaevskii equation. The radial profiles of the ground-state wavefunction are obtained for ring confinement potentials of various depths and widths, which have been used to calculate effectively one-dimensional interaction constants for various particle densities in the condensate. The results have been compared with analytical expressions for the linear limit and for a ring of a large radius, and the validity range for these simplified analytical descriptions have been determined.
The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.
Abstract Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose–Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross–Pitaevskii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom–atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.
We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped targetlike trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [R. Mathew, A. Kumar, S. Eckel, F. Jendrzejewski, G. K. Campbell, M. Edwards, and E. Tiesinga, Phys. Rev. A 92, 033602 (2015)]. In addition to the ground-state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These configurations are obtained from a systematic bifurcation analysis starting from the linear, small atom density, limit. We study the stability and, when unstable, the dynamics of the most basic configurations. Often these lead to vortical dynamics inside the ring persisting over long time scales in our numerical experiments. To illustrate the relevance of the identified states, we showcase how such dark-soliton configurations (even the unstable ones) can be created in laboratory condensates by using phase-imprinting techniques.
Considered as a fundamental step for the development of the atomic laser and quantum computing, as well as the theoretical explanation of super fluidity, the Bose- Einstein condensate (BEC) has emerged as one of the most important topics in modern physics. This project is devoted to the analysis of a condensate based on exciton-polaritons. This BEC is characterized by a high critical temperature of condensation (about 20 K) and non-equilibrium dynamics. A mathematical model called complex Gross- Pitaevskii equation (cGPE) is used to describe its behavior. The steady state solutions of the cGPE are studied and a numerical method based on a collocation method is proposed in order to find these solutions. Once the steady state solutions are found, a linear stability analysis is performed, demonstrating that the steady state solutions become unstable as the pumping spot radius increases. Finally, the manifestations of these instabilities are analyzed by direct simulation of the cGPE, using a second order time-splitting spectral method. As a result, it is possible to see the formation of quantum vortices, which increase in number as the pumping spot radius increases.
We study vortex ring solutions of the Gross-Pitaevskii equation for Bose-Einstein condensates confined in toroidal traps. Analogously to the Feynman-Onsager ansatz for a single vortex line, we assume a condensate wavefunction that describes a quantized vortex ring. This leads to a modified Gross-Pitaevskii equation that incorporates vortex ring solutions. By numerically solving this equation, we have obtained the density profiles and the vortex core structure. We have also calculated the nucleation energy of a vortex ring, and have analyzed its dependence on the ring position. Finally, a qualitative description of the vortex ring dynamics is presented.
We present a theoretical description of Bogolyubov-type excitations of exciton-polariton Bose-Einstein condensates (BECs) in semiconductor microcavities. For a typical two-dimensional (2D) BEC we focus on two limiting cases, the weak- and strong-coupling regimes, where a perturbation theory and the Thomas-Fermi approximation, respectively, are valid. We calculate integrated scattering intensity spectra for probing the collective excitations of the condensate in both considered limits. Moreover, in relation to recent experiments on optical modulation allowing localization of condensates in a trap with well-controlled shape and dimensions, we study the quasi-one-dimensional (1D) motion of the BEC in microwires and report the corresponding Bogolyubov excitation spectrum. We show that in the 1D case the characteristic polariton-polariton interaction constant is expressed as ${g}_{1}=3\ensuremath{\lambda}\mathcal{N}/(2{L}_{y})$ ($\ensuremath{\lambda}$ is the 2D polariton-polariton interaction parameter in the cavity, N\mathcal{N}N the number of the particles, and Ly{L}_{y}Ly​ the wire cavity width). We reveal some interesting features for 2D and 1D Bogolyubov spectra for both repulsive $(\ensuremath{\lambda}>0)$ and attractive $(\ensuremath{\lambda}<0)$ interactions.