Bose-Einstein Condensate Tunneling: The Gross-Pitaevskii Equation

Abstract

AbstractThe Gross-Pitaevskii equation that has had a great deal of success in the analysis of the dynamics of Bose-Einstein condensates was pointed out to be identical in form to the nonlinear Schrödinger equation. As a consequence of this fact, tunneling dynamics of condensates in traps turned out to be described by the DNLSE. The work of Raghavan and his collaborators that put the connection to good use a couple of decades ago was described briefly. Using a similar bridge connecting disparate fields of study, new results found in the nonresonant nonlinear dimer during my writing of this book were ported over to BEC systems and experiments were proposed that can delicately probe tunneling dynamics. Examples of topics studied were the similarities and differences between the time evolution that would obtain for degenerate and nondegenerate systems both near and far from critical points; how static energy mismatch can be manipulated to make the self-trapping and the amplitude transitions coincide with each other; and how critical points and critical lines move in parameter space as one changes the initial distribution between the traps. The validity of the Gross-Pitaevskii equation relative to the exact quantum dynamics was studied with the help of accurate numerical quantum calculations along the lines of analogous investigations for the polaron problem. Initial states used were coherent in the Sudarshan-Glauber sense. An exercise was outlined in great detail for the reader to attempt to approach the problem analytically in terms of a series expansion in orders of the reciprocal of the number of atoms in the condensate.KeywordsBose-Einstein condensate tunnelingAnalysis from and validity of the Gross-Pitaevskii mean field equationMovement of critical points and lines in parameter space