Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID

TL;DR

This paper develops and tests an interferometric method to measure the in-situ phase difference in a toroidal Bose-Einstein condensate, demonstrating its accuracy through theoretical, numerical, and experimental analysis.

Contribution

It introduces a novel atomic analog of the rf-SQUID using spiral interference patterns to measure phase drops in BECs, supported by comprehensive theoretical and experimental validation.

Findings

The interferometer accurately measures in-situ phase drops.

Single-particle and mean-field models explain spiral formation.

Interactions affect expansion time scales for phase measurement.

Abstract

We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop.