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arXiv:2008.11130 · Physical Review A

Quantum nondemolition photon counting with a hybrid electromechanical probe

Junjie Liu, Hsing-Ta Chen, Dvira Segal

Published Dec 7, 2020• 7 citations
arXivHTMLPDF

Abstract

Quantum nondemolition (QND) measurements of photons is a much pursued endeavor in the field of quantum optics and quantum information processing. Here, we propose a hybrid optoelectromechanical platform that integrates a cavity system with a hybrid electromechanical probe for QND photon counting. Building upon a mechanical-mode-mediated nonperturbative electro-optical dispersive coupling, our protocol performs the QND photon counting measurement by means of the current-voltage characteristics of the probe. In particular, we show that the peak voltage shift of the differential conductance is linearly dependent on the photon occupation number, thus providing a sensitive measure of the photon number, especially in the strong optomechanical coupling regime. Given that our proposed hybrid system is compatible with state-of-the-art experimental techniques, we discuss its implementations and anticipate applications in quantum optics and polariton physics.

DOI
10.1103/physreva.102.061501

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Quantum nondemolition (QND) measurements of photons is a much pursued endeavor in the field of quantum optics and quantum information processing. Here, we propose a hybrid optoelectromechanical platform that integrates a cavity system with a hybrid electromechanical probe for QND photon counting. Building upon a mechanical-mode-mediated nonperturbative electro-optical dispersive coupling, our protocol performs the QND photon counting measurement by means of the current-voltage characteristics of the probe. In particular, we show that the peak voltage shift of the differential conductance is linearly dependent on the photon occupation number, thus providing a sensitive measure of the photon number, especially in the strong optomechanical coupling regime. Given that our proposed hybrid system is compatible with state-of-the-art experimental techniques, we discuss its implementations and anticipate applications in quantum optics and polariton physics.
In the field of cavity optomechanics, proposals for quantum nondemolition (QND) measurements of phonon number provide a promising avenue by which one can study the quantum nature of nanoscale mechanical resonators. Here we investigate these QND measurements for an optomechanical system whereby quadratic coupling arises due to shared symmetries between a single optical resonance and a mechanical mode. We establish a relaxed limit on the amount of linear coupling that can exist in this type of system while still allowing for QND measurements of mechanical Fock states. The ability to perform optomechanical QND measurements of this nature would allow one to probe the decoherence of these mesoscopic states, providing an experimental test bed for quantum collapse theories.
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the atomic medium explicitly depends on the number n of photons during the process of transient state dynamics, the measurement on the change of transmission of the probe field can be used for QND measurement of small photon number, and thus create the photon Fock states in particular single-photon state in a heralded way.
Detailed understanding of physical measurements is essential for devising efficient metrological strategies and measurement-feedback schemes, as well as finding fundamental limitations on measurement sensitivity. In the quantum regime, measurements modify the state of the system of interest through measurement backaction as a direct consequence of the Heisenberg principle. In cavity optomechanics and electromechanics, a plethora of strategies exist for measuring the mechanical motion using electromagnetic fields, each leading to different competition between measurement imprecision and backaction. While this range of techniques allows broad applications of optomechanical and electromechanical devices, it makes direct comparison of different measurement methods difficult. We develop a formalism for quantifying the performance of optomechanical measurements using a few relevant figures of merit. Our approach is inspired by similar characterizations in quantum optics and quantifies the main properties of quantum measurements -- the ability to distinguish different quantum states and preservation of signal in the presence of measurement noise. We demonstrate our concept on the most common optomechanical measurements -- displacement detection, coherent quantum noise cancellation, and quantum nondemolition measurements -- and perform detailed analysis of errors in optomechanical nondemolition measurements. This newly acquired knowledge allows us to propose a strategy for quantum nondemolition measurements in levitodynamics using coherent scattering. Our results complement existing knowledge of linear optomechanical interactions and open the way to new understanding of optomechanical measurements, thus allowing also novel applications of optomechanical devices in fundamental physics and quantum technologies.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.
A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.