Optimal control of number squeezing in trapped Bose-Einstein condensates

TL;DR

This paper uses optimal control theory to enhance number squeezing in trapped Bose-Einstein condensates, improving atom interferometry by reducing phase dephasing through optimized splitting protocols.

Contribution

It introduces optimized splitting protocols for low number fluctuations in BECs, analyzing solutions in both Josephson and Fock regimes with two modeling approaches.

Findings

High number squeezing achieved via optimized protocols

Oscillatory tunnel control in Josephson regime

Squeezing due to nonlinear coupling in Fock regime

Abstract

We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.