Classical versus quantum dynamics of the atomic Josephson junction

TL;DR

This paper compares classical mean-field and quantum dynamics of atomic Bose-Einstein condensates in double-well potentials, highlighting quantum phenomena like collapses, revivals, and Schrödinger cat states that are absent in classical models.

Contribution

It introduces a simple quantum scheme based on Raman-Nath equations to analyze quantum dynamics and explores excitation methods, revealing quantum effects beyond mean-field approximations.

Findings

Quantum revivals occur after wave packet collapses.

Single energy eigenstates can be excited, including Schrödinger cat states.

Quantum phenomena like Bloch oscillations and Bragg resonances are identified.

Abstract

We compare the classical (mean-field) dynamics with the quantum dynamics of atomic Bose-Einstein condensates in double-well potentials. The quantum dynamics are computed using a simple scheme based upon the Raman-Nath equations. Two different methods for exciting a non-equilbrium state are considered: an asymmetry between the wells which is suddenly removed, and a periodic time oscillating asymmetry. The first method generates wave packets that lead to collapses and revivals of the expectation values of the macroscopic variables, and we calculate the time scale for these revivals. The second method permits the excitation of a single energy eigenstate of the many-particle system, including Schroedinger cat states. We also discuss a band theory interpretation of the energy level structure of an asymmetric double-well, thereby identifying analogies to Bloch oscillations and Bragg resonances. Both the Bloch and Bragg dynamics are purely quantum and are not contained in the mean-field treatment.