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arXiv:2508.01080 · Physical Review Letters

Nondestructive Optomechanical Detection Scheme for Bose-Einstein Condensates

Cisco Gooding, Cameron R. D. Bunney, Samin Tajik, Sebastian Erne, Steffen Biermann, Jörg Schmiedmayer, Jorma Louko, William G. Unruh, Silke Weinfurtner

Published Dec 19, 2025• 2 citations
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Abstract

We present a two-tone heterodyne optical readout scheme to extract unequal-time density correlations along an arbitrary stationary interaction path from a pancake-shaped Bose-Einstein condensate, using a modulated laser probe. Analyzing the measurement noise both from imprecision and backaction, we identify the standard quantum limit for the signal-extraction scheme, and examine how a class of two-mode squeezed initial states can be used to push beyond this limit. As an application, we show how the readout scheme can be used for an experimentally feasible realization of acceleration dependence of quantum-vacuum fluctuations in the system, including the analog spacetime circular motion Unruh effect. The scheme is adaptable beyond Bose-Einstein condensates, providing nondestructive access to unequal-time correlations in quantum fluids.

DOI
10.1103/4yfh-tm4f

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•Jul 22, 2016•2 citations
We present a two-tone heterodyne optical readout scheme to extract unequal-time density correlations along an arbitrary stationary interaction path from a pancake-shaped Bose-Einstein condensate, using a modulated laser probe. Analyzing the measurement noise both from imprecision and backaction, we identify the standard quantum limit for the signal-extraction scheme, and examine how a class of two-mode squeezed initial states can be used to push beyond this limit. As an application, we show how the readout scheme can be used for an experimentally feasible realization of acceleration dependence of quantum-vacuum fluctuations in the system, including the analog spacetime circular motion Unruh effect. The scheme is adaptable beyond Bose-Einstein condensates, providing nondestructive access to unequal-time correlations in quantum fluids.
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When one seeks knowledge of the full dynamics of the displacement of a harmonic oscillator, non-commutation of the two mechanical quadratures requires a minimum added noise equal to the mechanical resonator's zero point motion. This fundamental quantum limit (QL) is a distinct bound from the standard quantum limit (SQL) that is often considered in interferometric displacement measurement. The SQL is a consequence of the non-commutation of the probe's quadratures in a specific measurement configuration and is characterized by a tradeoff between shot noise (SN) imprecision and quantum backaction that are uncorrelated. The QL and SQL reach the same limit when probing at the peak mechanical response, but the QL can be a significantly lower bound off resonance. In studies of micro-mechanical motion, there has been great interest in observing quantum backaction and approaching the SQL on mechanical resonance. However, much of what historically motivates SQL research is displacement monitoring over a wide frequency band, such as gravitational wave searches. One long-standing concept for surpassing the SQL is to introduce correlations by changing the readout quadrature as a function of frequency in a technique known as variational readout. Here we harness quantum correlations in the measurement of a macroscopic resonator by modifying the readout quadrature of an optical interferometer. By using an optomechanical device thermalized to a dilution refrigerator, we measure quantum noise far off resonance where we improve upon the off-resonance SQL for our quantum efficiency.