Bose-Einstein condensation in harmonic double wells

TL;DR

This paper investigates Bose-Einstein condensation in split harmonic traps, analyzing how well separation and interactions influence the critical temperature and thermodynamics of the system.

Contribution

It provides a detailed numerical and analytical study of BEC in double-well harmonic traps, including effects of interactions on the condensation temperature.

Findings

Condensation temperature shifts from T_c^{(0)}(N) to T_c^{(0)}(N/2) with increasing well separation.

Repulsive interactions can increase the critical temperature for large well splitting.

Numerical results agree with semiclassical approximations for large particle numbers.

Abstract

We discuss Bose-Einstein condensation in harmonic traps where the confinement has undergone a splitting along one direction. We mostly consider the 3D potentials consisting of two cylindrical wells separated a distance 2a along the z-axis. For ideal gases, the thermodynamics of the confined bosons has been investigated performing exact numerical summations to describe the major details of the transition and comparing the results with the semiclassical density-of-states approximation. We find that for large particle number and increasing well separation, the condensation temperature evolves from the thermodynamic limit value T_c^{(0)}(N) to T_c^{(0)}(N/2). The effects of adding a repulsive interaction between atoms has been examined resorting to the Gross-Pitaevskii-Popov procedure and it is found that the shift of the condensation temperature exhibits different signs according to the separation between wells. In particular, for sufficiently large splitting, the trend opposes the well known results for harmonic traps, since the critical temperature appears to increase with growing repulsion strength.