2021/01/24 by Asaad R. Sakhel, Asaad R Sakhel, Roger R. Sakhel +1
Physics and Astronomy · #Amplitude #Cold Atom Physics and Bose-Einstein Condensates #Dipole #Gaussian #Optical properties and cooling technologies in crystalline materials #Parametric statistics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Strong Light-Matter Interactions #Trapping #cond-mat.quant-gas
paper · pdf · doi:10.1088/1402-4896/ac0f3a
6 figures, 18 pages
arxiv created 2021/01/24 · openalex created_date 2021/02/01 · openalex publication_date 2021/06/28 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
Abstract Analyzing the energy levels of a trapped Bose–Einstein condensate (BEC) can be difficult when dipole-dipole interactions (DDIs) are present. To address this issue, this study focuses on the parametric resonances (PRs) in the mean-field dynamics of a one-dimensional dipolar BEC (DBEC) over widely varying trapping geometries, with the primary objective of characterizing the energy levels of this system via analytical methods. This is achieved by matching the PR energies to the energy levels of the confining trap using perturbative methods. Further, this research reveals the role of the interplay between DDIs and the trapping geometry in defining the energies and amplitudes of the PRs. The PRs are induced by a negative Gaussian potential with a depth that oscillates with respect to time; DDIs also play a role in this induction. The dynamics of this system are modeled using the time-dependent Gross–Pitaevskii equation (TDGPE), which is numerically solved via the Crank–Nicolson method. The PRs are discussed based on analytical methods. First, we show that PRs similar to the ones obtained from the TDGPE can be reproduced via the Lagrangian variational method. Second, the energies at which the PRs occur are closely matched with the energy levels of the corresponding trap, calculated using the time-independent perturbation theory. Third, the most probable transitions between the trap energy levels yielding PRs are determined based on the time-dependent perturbation theory. The primary contribution of this research is that the energy levels of a DBEC within a complex trapping potential could be characterized.