Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

Abstract

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum twomode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.

Tunneling, self-trapping, and manipulation of higher modes of a Bose-Einstein condensate in a double well

“…Ultracold atoms in double wells have been thoroughly studied in the framework of two-mode models, both with an eye towards unveiling Josephson physics [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and as a candidate system to observe macroscopic atomic quantum superpositions [33][34][35][36][37][38][39][40][41][42][43][44]. In this manuscript, we introduce a semiclassical approach that allows one to study effects on the double-well condensate dynamics stemming from a finite population of the excited single-particle states (see Fig.…”

“…Two-mode approaches are conventionally used to model ultracold bosons in double wells [14][15][16][17][18][19][20][21][22][23][27][28][29][30][31][32]. The relevant parameters in such a model are the tunneling energy J and * jeremie.gillet@oist.jp the interaction energy U , together with the total number of atoms N .…”

A SQUID Analog with a Bose-Einstein Condensate

“…A two-mode model that includes the nonlinear interaction in the coupling term [18,20] predicted the critical currents plotted in Fig. 3(a) for three potential depths, showing that the critical current may be varied substantially over the range of atom numbers accessible to the experiment.…”

“…Here, I c ¼ 2E J =@N is the critical normalized current of the double JJ, where E J is the Josephson coupling energy [18,20] and…”

“…, where E C is the capacitance energy [18,20], and z 0 is the population difference when the chemical potential difference…”