Unsharp continuous measurement of a Bose-Einstein condensate: full quantum state estimation and the transition to classicality

TL;DR

This paper explores how continuous unsharp measurements influence a Bose-Einstein condensate in a double-well potential, enabling full quantum state estimation and inducing a transition from quantum to classical behavior, especially with inter-atomic interactions.

Contribution

It demonstrates that inter-atomic interactions enable complete quantum state monitoring through unsharp measurements, revealing a quantum-to-classical transition in a BEC.

Findings

Full quantum state estimation is achievable with moderate interactions.

Measurement induces a transition from quantum to mean-field behavior.

Interactions enhance information gain from measurements.

Abstract

We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the back action of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing inter-atomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate inter-atomic interactions, the entire many-body state --modified by the measurement-- is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the inter-atomic interactions enhance the information gained via the measurement.