Analytical pendulum model for a bosonic Josephson junction

Abstract

We present an analytical description of the tunneling dynamics between two coupled Bose-Einstein condensates in the Josephson regime. The model relies on the classical analogy with a rigid pendulum and focuses on two dynamical modes of this system: Josephson oscillations and Macroscopic Quantum Self-Trapping. The analogy is extended to include an energy difference between the two superfluids caused by an asymmetry in the trapping potential. The model is compatible with the mean-field predictions of the two-mode Bose-Hubbard model. It gives new insights on the mean-field model by involving experimentally measurable parameters with reduced correlations. For agreement with recent experimental observations, we establish heuristic formulas including a dissipation. We conclude with a convincing application of the model to several sets of experimental results.

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction

“…We stress that the standard twomode model [10,13] that captures both Josephson and MQST dynamics of previous experiments [16,18] is out of its validity range due to the considered values of the ratio V 0 /µ and to the thinness of the junctions [38]. Although dissipative effects can be phenomenologically modeled by damped two-mode [21,35,36] and RSJ-circuital models [7], such approaches provide limited insight into the microscopic dissipative processes.…”

Report on scipost_202005_00003v1

“…These oscillations show a rapid damping, accompanied by a narrowing of the distribution function of the phase. To date, no satisfying theoretical explanation of this damping is known [66]. The damping seems incompatable with a description in terms of a translationally invariant sine-Gordon model, which fails to provide a mechanism for the observed strong and rapid damping in both a self-consistent harmonic treatment [67] and in a combination of truncated Wigner and truncated conformal space approaches [68].…”

“…Having obtained a time-dependent probability distribution for the coefficients {f µ,t }, we can directly model experiments: we draw coefficients {f µ,t } from the distribution (69), reconstruct the corresponding eigenvalues (66), and insert these in the time-of-flight density (14) to compute the measured density profile. We note that in the notations used above the set {f µ } contains the non-physical Fourier coefficient f (s,0) .…”

“…where g ± (x) are defined in (17) and are related to the coefficients f µ via (66). Motivated by the experimental data analyses of Refs [21,22,66] we parametrize the interference term (72) as…”

Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates

“…This type of a system, where two subsystems are coupled via tunneling, typically gives rise to Josephson oscillations [29]. Josephson oscillations in Bose-Einstein condensates (BECs) have been studied previously both theoretically [30][31][32][33][34][35][36][37][38] and experimentally [39][40][41]. An interesting effect that has been predicted and observed in such tunnel-coupled systems is the phenomenon of macroscopic self-trapping [32,39].…”