Tunneling of trapped-atom Bose condensates
arXiv:cond-mat/0508581 · doi:10.1007/s12043-002-0022-0
Abstract
We obtain the dynamics in number and phase difference, for Bose condensates that tunnel between two wells of a double-well atomic trap, using the (nonlinear) Gross-Pitaevskii equation.The dynamical equations are of the canonical form for the two conjugate variables, and the Hamiltonian corresponds to that of a momentum-shortened pendulum, supporting a richer set of tunneling oscillation modes than for a superconductor Josephson junction, that has a fixed-length pendulum as a mechanical model. Novel modes include "inverted pendulum" oscillations with an average angle of π; and oscillations about a self-maintained population imbalance that we term "macroscopic quantum self-trapping". Other systems with this phase-number nonlinear dynamics include twocomponent (interconverting) condensates in a single harmonic trap, and He^{3}B superfluids in two containers connected by micropores.
This is an overview of some work done with colleagues on the dynamics of tunneling between interacting bosons, with four distinct oscillation modes, understood through a pendulum mechanical analogue. Published in a festschrift a few years ago, it may be of interest, in view of the recent observation of two tunneling modes in double-well Bose-Einstein condensates, by the Heidelberg group of Oberthaler [PRL 95, 010402 (2005)]