Best mean-field for condensates

TL;DR

This paper introduces a generalized mean-field approach for bosonic condensates that allows bosons to occupy multiple states, potentially leading to lower energy solutions than the traditional Gross-Pitaevskii equation.

Contribution

It develops a new variational mean-field method permitting multiple one-particle functions, improving the energy estimate for condensates.

Findings

Mean-field energy can be lower than Gross-Pitaevskii predictions.

Method determines optimal distribution of bosons among multiple states.

Numerical example confirms energy reduction in trapped bosons.

Abstract

The Gross-Pitaevskii equation assumes that all (identical) bosons of a condensate reside in a single one-particle function. Here, we raise the question whether it always provides the best mean-field ansatz for condensates, leading to the lowest mean-field ground state energy. To this end, we derive a mean-field approach allowing for bosons to reside in several different one-particle functions. The number of bosons in each of these functions is a variational parameter minimizing the energy. The energy and one-particle functions at these optimal numbers can be determined directly. A numerical example is presented demonstrating that the mean-field energy of trapped bosons can be below that provided by the Gross-Pitaevskii equation. Implications are discussed.