Collective Excitation Interferometry with a Toroidal Bose-Einstein Condensate

TL;DR

This paper introduces an acoustic interferometer using a toroidal Bose-Einstein condensate to measure rotation, demonstrating key experimental techniques and analyzing noise sources, with potential for compact inertial sensing despite current noise limitations.

Contribution

It presents the first experimental demonstration of a sound-wave-based interferometer in a toroidal BEC for rotation measurement, including analysis methods and noise characterization.

Findings

Successfully excited counter-propagating sound waves in BEC

Measured frequency splitting and precession due to rotation

Identified atom shot noise as dominant measurement noise

Abstract

The precision of compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here, we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counter-propagating sound waves within the condensate and use \emph{in situ} absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\sim \mbox{rad}\, \mbox{s}^{-1}/\sqrt{\mbox{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at $10^4 - 10^6$ times higher density and in a volume $10^9$ times smaller than free-falling atom interferometers.