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arXiv:2105.02532 · Physical Review A

Broadband dichromatic variational measurement

Sergey P. Vyatchanin, Albert I. Nazmiev, Andrey B. Matsko

Published Aug 24, 2021• 7 citations
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Abstract

The standard quantum limit (SQL) of a classical mechanical force detection results from quantum backaction impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous broadband backaction, avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of the mirrors of an optical Michelson-Sagnac interferometer (MSI). The interferometer with the movable mirror is an optomechanical transducer able to support the polychromatic probe field. The method involves a dichromatic optical probe resonant with the MSI modes and having frequency separation equal to the mechanical frequency. We show that analyzing each of the harmonics of the probe reflected from the mechanical system separately and postprocessing the measurement results allows excluding the backaction in a broad frequency band and measuring the force with sensitivity better than the SQL.

DOI
10.1103/physreva.104.023519

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The standard quantum limit (SQL) of a classical mechanical force detection results from quantum backaction impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous broadband backaction, avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of the mirrors of an optical Michelson-Sagnac interferometer (MSI). The interferometer with the movable mirror is an optomechanical transducer able to support the polychromatic probe field. The method involves a dichromatic optical probe resonant with the MSI modes and having frequency separation equal to the mechanical frequency. We show that analyzing each of the harmonics of the probe reflected from the mechanical system separately and postprocessing the measurement results allows excluding the backaction in a broad frequency band and measuring the force with sensitivity better than the SQL.
The standard quantum limit (SQL) of a classical mechanical force detection results from quantum back action perturbing evolution of a mechanical system. In this paper we show that usage of a multidimensional optical transducer may enable a broadband quantum back action evading measurement. We study theoretically a corresponding technique of measurement of a resonant signal force acting on a linear mechanical oscillator coupled to a generic optical system with three optical modes with separation nearly equal to the mechanical frequency. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other modes. By detecting optimal quadrature components of the optical modes and postprocessing the measurement results we are able to exclude the back action in a broad frequency band and characterize the force with sensitivity better than the SQL. We show that the proposed scheme is similar to the multidimensional system containing quantum-mechanics-free subsystems which can evade the SQL using the idea of the so-called negative mass [M. Tsang and C. M. Caves, Phys. Rev. X 2, 031016 (2012).].
A broadband multidimensional variational measurement allows overcoming the Standard Quantum Limit (SQL) of a classical mechanical force detection for a mechanical oscillator. In this measurement quantum back action, which perturbs the evolution of a mechanical oscillator, can be completely removed in a broad detection frequency band after post-processing. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other optical modes, which have the frequency separation with the central mode equal to the mechanical frequency. To realize such a scheme in practice one either needs to use a very long optical interferometer or should utilize optical modes belonging to different mode families. In the second case the modes have different geometries and their coupling with the mechanical mode is not identical. Here we analyze a general case of the non-symmetric measurement scheme, in which the coupling strengths with the light modes are not equal to each other, and take into account optical losses. We found that the back action can be completely excluded from the measurement result in the case of the asymmetric lossless system. The nonzero loss limits the sensitivity. An experimental implementation of the proposed scheme is discussed.
Broadband multidimensional variational measurement allows overcoming the standard quantum limit (SQL) in detecting a classical mechanical force acting on a mechanical oscillator. In this measurement quantum back action, which perturbs the evolution of a mechanical oscillator, can be completely removed in a broad frequency band after post-processing. In this paper we show that optical losses inside the cavity restrict back action exclusion due to the loss noise. We also analyze the effect of two-photon (nondegenerate) and conventional (degenerate) squeezing in order to improve sensitivity with accounting for optical losses. We consider mainly internal squeezing.
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.
Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the trade-off between the probe’s shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work, we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as variational readout, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And, more generally, our result is a salient example of how correlations can aid sensing in the presence of backaction.
The Standard Quantum Limit (SQL) in classical force detection using mechanical systems arises from quantum back-action, which disturbs the oscillator’s evolution during measurement. We present a theoretical analysis of a scheme that enables broadband back-action evading (BAE) force sensing by employing a multidimensional optical transducer. The proposed system consists of a mechanical oscillator coupled to an optical structure supporting three distinct optical modes, with mode spacing approximately matched to the mechanical resonance. The central mode is coherently pumped, and the signal is extracted by monitoring the light emitted from the adjacent sideband modes. By selecting appropriate optical quadratures for detection and applying tailored post-processing to the measurement data, our approach suppresses back-action noise across a wide frequency range, enabling sensitivity beyond the SQL. The architecture can be interpreted as a composite system hosting quantum-mechanics-free subsystems (QMFS), which effectively isolate the measured observable from quantum fluctuations by exploiting correlations akin to those found in systems with engineered “negative mass” response. We also show that the adjacent sideband modes are entangled and discuss possible methods for detecting this entanglement. This configuration opens a promising route toward high-precision quantum metrology without being constrained by quantum measurement noise.