Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1904.00772 · New Journal of Physics

Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

Darren W. Moore, Andrey A. Rakhubovsky, Radim Filip

Published Nov 1, 2019• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ab5690

Related papers

Generation of quantum states with nonlinear squeezing by Kerr nonlinearity

Šimon Bräuer, Petr Marek

In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.

arXiv:2105.05189•Optics Express•Jun 16, 2021•19 citations

Nonlinear Squeezing for Measurement-Based Non-Gaussian Operations in Time Domain

Shunya Konno, A. Sakaguchi, Warit Asavanant +6 more

Quantum non-Gaussian gate is a missing piece to the realization of continuous-variable universal quantum operations in an optical system. In a measurement-based implementation of the cubic phase gate, a lowest-order non-Gaussian gate, non-Gaussian ancillary states that have a property we call nonlinear squeezing are required. This property, however, has never been experimentally verified. In this paper, we generate a superposition between a vacuum state and a single-photon state whose nonlinear squeezing is maximized by the optimization of the superposition coefficients. The nonlinear squeezing is observed via real-time quadrature measurements, meaning that the generated states are compatible with real-time feedforward and are suitable as ancillary states for the cubic phase gate in the time domain. Moreover, by increasing the number of photons, it is expected that nonlinear squeezing can be further improved. The idea presented here can be readily extended to higher-order phase gates [P. Marek et al., Phys. Rev. A 97, 022329 (2018)]. As such, this work presents an important step to extend continuous-variable quantum information processing from Gaussian regime to non-Gaussian regime.

arXiv:2011.14576•Physical Review Applied•Feb 10, 2021•33 citations

Stroboscopic high-order nonlinearity for quantum optomechanics

Andrey A. Rakhubovsky, Radim Filip

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.

arXiv:1904.00773•npj Quantum Information•Jul 29, 2021•18 citations

Cubic nonlinear squeezing under decoherence

Vojtěch Kala, Petr Marek, Radim Filip

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often those most vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters that can be optimized and adjusted to achieve the maximal robustness for the potential applications.

•Jul 13, 2021•0 citations

Cubic nonlinear squeezing and its decoherence

Vojtěch Kala, Radim Filip, Petr Marek

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic Hamiltonians, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often more vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. Therefore, a stability of nonlinear squeezing is essential. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters which can be optimized and adjusted to achieve the maximal robustness for the potential applications.

arXiv:2107.06036•Optics Express•Jul 20, 2022•18 citations

Optical squeezing mediated by levitated oscillators at their quantum ground state

A. Pontin, Q. Deplano, F. Marino +1 more

We demonstrate optical squeezing below the shot-noise level generated through the interaction of an optical cavity field with two center-of-mass modes of a levitated nanoparticle, simultaneously cooled to occupation numbers well below unity. By analyzing the quadrature fluctuations of the cavity output through heterodyne detection, we resolve the full spectral covariance matrix of the optical field and map regions of sub-shot-noise squeezing as a function of detection phase and frequency. Operating in the resolved sideband and strong coupling regime where mechanical modes hybridize with the optical mode, we observe consistent squeezing in the band 70-95 kHz with a lowest variance of 0.98 (2$\%$ below vacuum fluctuations). We thus demonstrate optical squeezing mediated by multiple mechanical oscillators in their quantum ground state, bridging mechanical quantum control with non-classical light and establishing levitated optomechanics as a platform for multimode quantum interactions.

quant-pharXiv:2604.26790•Physical Review A•Apr 30, 2026•0 citations
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.
In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.
Quantum non-Gaussian gate is a missing piece to the realization of continuous-variable universal quantum operations in an optical system. In a measurement-based implementation of the cubic phase gate, a lowest-order non-Gaussian gate, non-Gaussian ancillary states that have a property we call nonlinear squeezing are required. This property, however, has never been experimentally verified. In this paper, we generate a superposition between a vacuum state and a single-photon state whose nonlinear squeezing is maximized by the optimization of the superposition coefficients. The nonlinear squeezing is observed via real-time quadrature measurements, meaning that the generated states are compatible with real-time feedforward and are suitable as ancillary states for the cubic phase gate in the time domain. Moreover, by increasing the number of photons, it is expected that nonlinear squeezing can be further improved. The idea presented here can be readily extended to higher-order phase gates [P. Marek et al., Phys. Rev. A 97, 022329 (2018)]. As such, this work presents an important step to extend continuous-variable quantum information processing from Gaussian regime to non-Gaussian regime.
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.
Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often those most vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters that can be optimized and adjusted to achieve the maximal robustness for the potential applications.
Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic Hamiltonians, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often more vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. Therefore, a stability of nonlinear squeezing is essential. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters which can be optimized and adjusted to achieve the maximal robustness for the potential applications.
We demonstrate optical squeezing below the shot-noise level generated through the interaction of an optical cavity field with two center-of-mass modes of a levitated nanoparticle, simultaneously cooled to occupation numbers well below unity. By analyzing the quadrature fluctuations of the cavity output through heterodyne detection, we resolve the full spectral covariance matrix of the optical field and map regions of sub-shot-noise squeezing as a function of detection phase and frequency. Operating in the resolved sideband and strong coupling regime where mechanical modes hybridize with the optical mode, we observe consistent squeezing in the band 70-95 kHz with a lowest variance of 0.98 (2%\%% below vacuum fluctuations). We thus demonstrate optical squeezing mediated by multiple mechanical oscillators in their quantum ground state, bridging mechanical quantum control with non-classical light and establishing levitated optomechanics as a platform for multimode quantum interactions.