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arXiv:2311.03060 · Physical Review A

Proposal for observing nonclassicality in highly excited mechanical oscillators by single photon detection

Kai Ryen Bush, Kjetil Børkje

Published Apr 3, 2024• 4 citations
arXivHTMLPDF

Abstract

The preparation of pure quantum states with high degrees of macroscopicity is a central goal of ongoing experimental efforts to control quantum systems. We present a state preparation protocol which renders a mechanical oscillator with an arbitrarily large coherent amplitude in a manifestly nonclassical state. The protocol relies on coherent-state preparation followed by a projective measurement of a single Raman scattered photon, making it particularly suitable for cavity optomechanics. The nonclassicality of the state is reflected by sub-Poissonian phonon statistics, which can be accessed by measuring the statistics of subsequently emitted Raman sideband photons. The proposed protocol would facilitate the observation of nonclassicality of a mechanical oscillator that moves macroscopically relative to motion at the single-phonon level.

DOI
10.1103/physreva.109.043505

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The preparation of pure quantum states with high degrees of macroscopicity is a central goal of ongoing experimental efforts to control quantum systems. We present a state preparation protocol which renders a mechanical oscillator with an arbitrarily large coherent amplitude in a manifestly nonclassical state. The protocol relies on coherent-state preparation followed by a projective measurement of a single Raman scattered photon, making it particularly suitable for cavity optomechanics. The nonclassicality of the state is reflected by sub-Poissonian phonon statistics, which can be accessed by measuring the statistics of subsequently emitted Raman sideband photons. The proposed protocol would facilitate the observation of nonclassicality of a mechanical oscillator that moves macroscopically relative to motion at the single-phonon level.
We show how to use the radiation pressure optomechanical coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state). Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband produces correlated photon-phonon pairs via optomechanical parametric down-conversion. Subsequent detection of a single scattered Stokes photon projects the macroscopic oscillator into a single-phonon Fock state. The nonclassical nature of this mechanical state can be demonstrated by applying a readout laser on the lower sideband to map the phononic state to a photonic mode and performing an autocorrelation measurement. Our approach proves the relevance of cavity optomechanics as an enabling quantum technology.
Adding excitations on a coherent state provides an effective way to observe the nonclassical properties of radiation fields. Here, we describe and analyze how to apply this concept to the motional state of a mechanical oscillator and present a full scheme to prepare non-Gaussian phonon-added coherent states of the mechanical motion in cavity optomechanics. We first generate a mechanical coherent state using electromagnetically induced transparency. We then add a single phonon onto the coherent state via optomechanical parametric down-conversion combined with single-photon detection. We validate this single-phonon-added coherent state by using a red-detuned beam and reading out the state of the optical output field. This approach allows us to verify nonclassical properties of the phonon state, such as sub-Poissonian character and quadrature squeezing. We further show that our scheme can be directly implemented using existing devices, and is generic in nature and hence applicable to a variety of systems in opto- and electromechanics.
Here we show that quantum states of a mechanical oscillator can be generated in an optomechanical analog of the micromaser in the absence of any atomlike subsystem, thus exhibiting single-atom masing effects in a system composed solely of oscillator components. In the regime where the single-photon coupling strength is on the order of the cavity decay rate, a cavity mode with at most a single-excitation present gives rise to sub-Poissonian oscillator limit-cycles that generate quantum features in the steady state just above the renormalized cavity resonance frequency and mechanical sidebands. The merger of multiple stable limit-cycles markedly reduces these nonclassical signatures. Varying the cavity-resonator coupling strength, corresponding to the micromaser pump parameter, reveals transitions for the oscillator phonon number that are the hallmark of a micromaser. The connection to the micromaser allows for a physical understanding of how nonclassical states arise in this system and how best to maximize these signatures for experimental observation.
Recognized as a potential resource for quantum technologies and a possible test bed for fundamental physics, the control and preparation of nonclassical states of mechanical oscillators have been explored extensively. Within optomechanics, quantum state synthesis can be realized by entangling photonic and phononic degrees of freedom followed by optical detection. Single-photon detection enables one of the most powerful forms of such heralded quantum state preparation, permitting the creation of single-phonon states when applied to conventional cavity optomechanical systems. As the complexity of optomechanical systems increases, single-photon detection may provide heralded access to a larger class of exotic quantum states. Here, we examine the quantum dynamics of optomechanical systems that permit forward Brillouin scattering, where a single-phonon mode mediates transitions between a collection of equally spaced optical resonances. Solving both the Schrodinger equation and the Lindblad master equation for this system, we find that initial states comprised of single photons or weak laser pulses evolve into complex quantum states where the frequency of single-photon states and the phonon occupation number are entangled. Physically, these interactions permit a single photon to scatter to lower frequencies, where phonon excitation occurs for each scattering event. Combining this result with frequency filtering, we show how single-photon detection can herald selected multiphonon Fock states, even in the presence of optical losses. We also present an approach for quantum tomography of the heralded phonon states, which in the form of a state swap from the phononic to photonic domain enables on-demand generation of multiphoton Fock states.
The investigation of macroscopic quantum phenomena is a current active area of research that offers significant promise to advance the forefronts of both fundamental and applied quantum science. Utilising the exquisite precision and control of quantum optics provides a powerful toolset for generating such quantum states where the types and 'size' of the states that can be generated are set by the experimental parameter regime available and the resourcefulness of the protocol applied. In this work we present a new multistep scheme to 'grow' macroscopic superposition states of motion of a mechanical oscillator via cavity quantum optomechanics. The scheme consists of a series of optical pulses interacting with a mechanical mode via radiation-pressure followed by photon-counting measurements. The multistep nature of our protocol allows macroscopic superposition states to be prepared with a relaxed requirement for the single-photon optomechanical coupling strength. To illustrate the experimental feasibility of our proposal, we quantify how initial mechanical thermal occupation and mechanical decoherence affects the non-classicality and macroscopicity of the states generated and show that our scheme is resilient to optical loss. The advantages of this protocol provide a promising path to grow non-classical mechanical quantum states to a macroscopic scale under realistic experimental conditions.
We present a proposal to prepare the macroscopic superposition states of a mechanical oscillator in an optomechanical system with quadratic coupling. By coherently driving the optomechanical cavity with an external field, a Kerr-type interaction among phonons is induced. The macroscopic mechanical superposition can be generated by exploiting the Kerr nonlinearity in the mechanical oscillator, just as the generation of a nonclassical state of light in a Kerr medium. One merit of our proposal is that the Kerr nonlinearity can be strongly enhanced by adjusting the amplitude of the driving field. The influence of the system damping on the realization of mechanical non-Gaussian state is discussed by the negativity of the Wigner function. The results show that the macroscopic superposition states are robust against the mechanical thermal noise.