# Two-Step Production of Resonant Bose-Einstein Condensates

## TL;DR

This paper proposes a two-step method for producing resonant Bose-Einstein condensates that maximizes transfer probability by using an intermediate scattering length, addressing challenges like heating and losses.

## Contribution

It introduces a novel two-step scheme with an optimal intermediate scattering length for efficient resonant BEC production.

## Key findings

- Optimal intermediate scattering length is approximately 3.16N^{-2/3} times the harmonic oscillator length.
- Maximum transfer probability is about 1.03N^{-1/6}.
- Two-step process improves stability and efficiency over sudden quench methods.

## Abstract

Producing a substantial and stable resonant Bose-Einstein condensate (BEC) has proven to be a challenging experimental task due to heating and three-body losses that may occur even before the gas comes to thermal equilibrium. In this paper, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths may not be the best way to prepare a resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between $0$ and $\infty$, which serves to maximize the transfer probability of $N$ bosons of mass $m$ in a harmonic trap with frequency $\omega$. We find that the intermediate scattering length should be $a\approx3.16N^{-2/3}\sqrt{\hbar/(m\omega)}$ to produce an optimum transition probability of $1.03N^{-1/6}$.