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arXiv:2401.04066 · Physical Review Research

Generation of classical non-Gaussian states by squeezing a thermal state into nonlinear motion of levitated optomechanics

Rafael Muffato, Tiberius Georgescu, Jack Homans, Thiago Guerreiro, Q. Wu, Diana A. Chisholm, Matteo Carlesso, Mauro Paternostro, Hendrik Ulbricht

Published Feb 18, 2025• 11 citations
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Abstract

We report on an experiment achieving the dynamical generation of non-Gaussian states of motion of a levitated optomechanical system. We access intrinsic Duffing-like nonlinearities by thermal squeezing of an oscillator's state of motion by rapidly switching the frequency of its trap. We characterize the experimental non-Gaussian state versus expectations from simulations and give prospects for the emergence of genuine nonclassical features.

DOI
10.1103/physrevresearch.7.013171

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We report on an experiment achieving the dynamical generation of non-Gaussian states of motion of a levitated optomechanical system. We access intrinsic Duffing-like nonlinearities by thermal squeezing of an oscillator's state of motion by rapidly switching the frequency of its trap. We characterize the experimental non-Gaussian state versus expectations from simulations and give prospects for the emergence of genuine nonclassical features.
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.
Abstract A nanoparticle optically levitated in vacuum represents a macroscopic mechanical oscillator that can be virtually decoupled from its thermal environment, providing a unique testbed for exploring the transition between classical and quantum dynamical regimes. It is generally assumed that such a levitated particle is confined and oscillates in a parabolic optical potential where its state is described by a Gaussian distribution in the phase space. However, real-world experiments are performed in optical potentials with weak nonlinear distortions that drive the motion into a non-Gaussian state. Such a state requires additional parameters for the full characterization, and direct quantitative comparison with the ideal Gaussian states is not straightforward. Here, we focus on the most common weak nonlinearity of Duffing type, in which the oscillation frequency decreases with the square of the amplitude of nanoparticle's oscillations. This dependence gives rise to spiral-shaped, squeezed non-Gaussian states. Given the particular observed symmetry of the phase-space distributions, we use the concept of Fermat's spiral and propose a nonlinear transformation of normalized phase-space coordinates that transforms this spiral state into a squeezed Gaussian-like state, which can be directly compared with the states of a stochastic harmonic oscillator. For comparison, we evaluate a nonlinear squeezing metric that can be used also in quantum regimes. The proposed approach can be extended to other nonlinearities of the confining potential with an explicit dependence of the oscillation frequency on the amplitude of the motion.
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.
Controlling the state of motion of optically levitated nanoparticles is crucial for the advancement of precision sensing, fundamental tests of physics, and the development of hybrid classical-quantum technologies. Experimentally, such control can be achieved by pulsed modifications of the optical potential confining the nanoparticle. Most frequently, the applied potential pulses are parabolic in nanoparticle position, and they expand/squeeze or displace the initial Gaussian state of motion to a modified Gaussian state. The time-dependent mean values and covariance matrix of the phase-space variables can fully characterize such a state. However, quasi-parabolic optical potentials with added weak Duffing-type nonlinearity, encountered in real-world experiments, can generally distort the state of motion to a non-Gaussian one, for which the description based solely on the mean values and covariance matrix fails. Here, we introduce a nonlinear transformation of the phase-space coordinates using the concept of Fermat's spiral, which effectively removes the state distortion induced by the Duffing-type nonlinearity and enables characterization of the state of motion by the standard Gaussian-state metrics. Comparisons of the experimental data with theoretical models show that the proposed coordinate transformation can recover the ideal behavior of a harmonic oscillator even after extended evolution of the system in the nonlinear potential. The presented scheme enables the separation of the effects of the applied state manipulation, the system's gradual thermalization, and the nonlinearity of the confinement on the experimentally observed dynamics of the system, thereby facilitating the design of advanced protocols for levitated optomechanics.
We study an optomechanical system for the purpose of generating a nonclassical mechanical state when a mechanical oscillator is quadratically coupled to a single-mode cavity field driven by a squeezed optical field. The system corresponds to a regime where the optical dissipation dominates both the mechanical damping and the optomechanical coupling. We identify that multiphonon processes emerge in the optomechanical system and show that a mechanical oscillator prepared in the ground state will evolve into an amplitude-squared squeezed vacuum state. The Wigner distribution of the steady state of the mechanical oscillator is non-Gaussian exhibiting quantum interference and fourfold symmetry. This nonclassical mechanical state, generated via reservoir engineering, can be used for quantum correlation measurements of the position and momentum of the mechanics below the standard quantum limit.