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Physical Review A

Transfer of non-Gaussian quantum states of mechanical oscillator to light

Radim Filip, Andrey A. Rakhubovsky

Published Nov 3, 2015• 13 citations
Publisher

Abstract

Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

DOI
10.1103/physreva.92.053804

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Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
Abstract High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures. We test the method numerically by analyzing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test. The method paves a road for experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.
Optomechanics with levitated nanoparticles is a promising way to combine very different types of quantum non-Gaussian aspects induced by continuous dynamics in a nonlinear or time-varying potential with the ones coming from discrete quantum elements in dynamics or measurement. First, it is necessary to prepare quantum non-Gaussian states using both methods. The nonlinear and time-varying potentials have been widely analyzed for this purpose. However, feasible preparation of provably quantum non-Gaussian states in a single mechanical mode using discrete photon detection has not been proposed yet for optical levitation. We explore pulsed optomechanical interactions combined with non-linear photon detection techniques to approach mechanical Fock states and confirm their quantum non-Gaussianity. We also predict the conditions under which the optomechanical interaction can induce multiple-phonon addition processes, which are relevant for nnn-phonon quantum non-Gaussianity. The practical applicability of quantum non-Gaussian states for sensing phase-randomized displacements is shown. Besides such applications, generating quantum non-Gaussian states of levitated nanoparticles can help to study fundamental questions of quantum thermodynamics, and macroscopic quantum effects.
Abstract Optomechanics with levitated nanoparticles is a promising way to combine very different types of quantum non-Gaussian aspects induced by continuous dynamics in a nonlinear or time-varying potential with the ones coming from discrete quantum elements in dynamics or measurement. First, it is necessary to prepare quantum non-Gaussian states using both methods. The nonlinear and time-varying potentials have been widely analyzed for this purpose. However, feasible preparation of provably quantum non-Gaussian states in a single mechanical mode using discrete photon detection has not been proposed yet for optical levitation. We explore pulsed optomechanical interactions combined with non-linear photon detection techniques to approach mechanical Fock states and confirm their quantum non-Gaussianity. We also predict the conditions under which the optomechanical interaction can induce multiple-phonon addition processes, which are relevant for n-phonon quantum non-Gaussianity. The practical applicability of quantum non-Gaussian states for sensing phase-randomized displacements is shown. Besides such applications, generating quantum non-Gaussian states of levitated nanoparticles can help to study fundamental questions of quantum thermodynamics, and macroscopic quantum effects.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
Abstract Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian ancilla. A necessary condition for a nonlinear phase state to implement a nonlinear phase gate is that noise in a selected nonlinear quadrature should decrease below the level of classical states. A reduction of the variance in this nonlinear quadrature below the ground state of the ancilla, a type of nonlinear squeezing, is the resource embedded in these non-Gaussian states and a figure of merit for nonlinear quantum processes. Quantum optomechanics with levitating nanoparticles trapped in nonlinear optical potentials is a promising candidate to achieve such resources in a flexible way. We provide a scheme for reconstructing this figure of merit, which we call nonlinear squeezing, in standard linear quantum optomechanics, analysing the effects of mechanical decoherence processes on the reconstruction and show that all mechanical states which exhibit reduced noise in this nonlinear quadrature are nonclassical.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear χ2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong χ3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.