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arXiv:2112.01493 · Journal of the Optical Society of America B

Back action evading electro-optical transducer

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

Published Feb 22, 2022• 3 citations
arXivHTMLPDF

Abstract

Electro-optical transducers are utilized for upconversion of radio frequency (RF) signals to the optical frequency domain to study the RF signals with optical tools. The transducers frequently impact the RF system and introduce additional noise, including optical shot noise as well as quantum back action noise, limiting the measurement accuracy. In this paper, we theoretically study a technique based on a high efficiency electro-optical phase modulation effect that allows back action evading detection of an RF field quadrature. The main idea of the proposed method is independent homodyne detection of two (Stokes and anti-Stokes) optical modes. It allows subsequent postprocessing of the detected signals, which, in turn, results in a broadband back action evading measurement leading to the high sensitivity evaluation of the RF signals.

DOI
10.1364/josab.449388

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Electro-optical transducers are utilized for upconversion of radio frequency (RF) signals to the optical frequency domain to study the RF signals with optical tools. The transducers frequently impact the RF system and introduce additional noise, including optical shot noise as well as quantum back action noise, limiting the measurement accuracy. In this paper, we theoretically study a technique based on a high efficiency electro-optical phase modulation effect that allows back action evading detection of an RF field quadrature. The main idea of the proposed method is independent homodyne detection of two (Stokes and anti-Stokes) optical modes. It allows subsequent postprocessing of the detected signals, which, in turn, results in a broadband back action evading measurement leading to the high sensitivity evaluation of the RF signals.
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).].
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.
The influence of measurement back action on electro-optic sampling of electromagnetic quantum fluctuations is investigated. Based on a cascaded treatment of the nonlinear interaction between a near-infrared coherent probe and the mid-infrared vacuum, we account for the generated electric-field contributions that lead to detectable back action. Specifically, we theoretically address two realistic setups, exploiting one or two probe beams for the nonlinear interaction with the quantum vacuum, respectively. The setup parameters at which back action starts to considerably contaminate the measured noise profiles are determined. We find that back action starts to detrimentally affect the signal once the fluctuations due to the coupling to the mid-infrared vacuum become comparable to the base shot noise. Due to the vacuum fluctuations entering at the beam splitter, the shot noise of two incoming probe pulses in different channels is uncorrelated. Therefore, even when the base shot noise dominates the output of the experiment, it does not contribute to the correlation signal itself. However, we find that further contributions due to nonlinear shot-noise enhancement are still present. Ultimately, a regime in which electro-optic sampling of quantum fields can be considered as effectively back-action free is found.
The high-sensitivity quantum detection of a resonant classical force acting on a quantum harmonic oscillator can be significantly improved by employing a resonant optical parametric transducer. This technique leverages the unique properties of parametric interactions to enhance the response of the measurement system while maintaining quantum-limited performance. We demonstrate that such a configuration not only enables quantum back-action evading (BAE) measurements, surpassing the Standard Quantum Limit (SQL) of sensitivity, it also provides a mechanism for noiseless amplification of the classical signal. The key to this enhancement lies in the ability of the parametric transducer to generate and separately measure the upper and lower modulation sidebands induced by the external force. By decoupling and analyzing these sidebands independently, the system becomes capable of amplifying the signal without introducing additional noise, effectively circumventing quantum measurement constraints.
Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.