Nonlinear Squeezing Research Articles

Ground State Nature and Nonlinear Squeezing of Gottesman-Kitaev-Preskill States

Ground State Nature and Nonlinear Squeezing of Gottesman-Kitaev-Preskill States

Nonlinear squeezing of stochastic motion

Linearized stochastic nanomechanical systems operating at nonzero temperatures and constant frequency and damping are restricted in their capacity to reduce noise in nonlinear combinations of the canonical variables. Nonlinear dynamics are then required in order to overcome these limits. Here we demonstrate how to make these limits explicit in the form of a threshold for nonlinear squeezing of the motional variables. Noise suppression below the threshold cannot be explained by linearized dynamics and is helpful in low-noise nonlinear devices at an ambient temperature. We predict that a state of the art levitating particle, exposed to cubic or quartic trapping potentials for a short interval will display nonlinear squeezing of stochastic motion that cannot be replicated by linear motion.

Direct Measurement of Higher-Order Nonlinear Polarization Squeezing.

We report on nonlinear squeezing effects of polarization states of light by harnessing the intrinsic correlations from a polarization-entangled light source and click-counting measurements. Nonlinear Stokes operators are obtained from harnessing the click-counting theory in combination with angular-momentum-type algebras. To quantify quantum effects, theoretical bounds are derived for second- and higher-order moments of nonlinear Stokes operators. The experimental validation of our concept is rendered possible by developing an efficient source, using a spectrally decorrelated type-II phase-matched waveguide inside a Sagnac interferometer. Correlated click statistics and moments are directly obtained from an eight-time-bin quasi-photon-number-resolving detection system. Macroscopic Bell states that are readily available with our source show the distinct nature of nonlinear polarization squeezing in up to eighth-order correlations, matching our theoretical predictions. Furthermore, our data certify nonclassical correlations with high statistical significance, without the need to correct for experimental imperfections and limitations. Also, our nonlinear squeezing can identify nonclassicality of noisy quantum states which is undetectable with the known linear polarization-squeezing criterion.

Characterizing Multipartite non-Gaussian Entanglement for a Three-Mode Spontaneous Parametric Down-Conversion Process

Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multi-photon non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing parameters involving accessible higher-order moments of phase-space quadratures. As these parameters can depend on arbitrary operators, we consider their analytical optimization over a set of practical measurements, in order to detect different classes of multipartite non-Gaussian entanglement ranging from fully separable to fully inseparable. We demonstrate that the nonlinear squeezing parameters act as an excellent approximation to the quantum Fisher information within accessible third-order moments. The level of the nonlinear squeezing quantifies the metrological advantage provided by those entangled states. Moreover, by analyzing the above mentioned experiment, we show that our method can be readily used to confirm fully inseparable tripartite non-Gaussian entangled states by performing a limited number of measurements without requiring full knowledge of the quantum state.

Cubic nonlinear squeezing and its decoherence.

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.

Hierarchy of quantum non-Gaussian conservative motion

Mechanical quantum systems embedded in an external nonlinear potential currently offer the first deep excursion into quantum non-Gaussian motion. The Gaussian statistics of the motion of a linear mechanical quantum system, characterised by its mass and a linear-and-quadratic potential, possess a limited capacity to reduce noise in nonlinear variables. This limitation induces thresholds for noise reduction in nonlinear variables beyond which linear mechanical oscillators cannot pass. Squeezing below the thresholds for such variables is relevant for the implementation of nonlinear mechanical devices, such as sensors, processors or engines. First however, quantum non-Gaussian conservative motion must be identified in experiments with diverse nonlinear potentials. For this purpose, we provide sufficient criteria for quantum non-Gaussian motional states in conservative systems based on the observation of squeezing in nonlinear variables. We further extend these criteria to a hierarchy able to recognise the quantum non-Gaussian motion induced via diverse nonlinear potentials through their various capacities to produce nonlinear squeezing.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Generation of quantum states with nonlinear squeezing by Kerr nonlinearity.

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.

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

Quantum non-Gaussian gate is a missing piece to the realization of continuous-variable universal quantum operations in the optical system. In a measurement-based implementation of the cubic phase gate, a lowest-order non-Gaussian gate, non-Gaussian ancillary states that has 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 are 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 the real-time feedforward and are suitable as the ancillary states for the cubic phase gate in time domain. Moreover, by increasing the number of the photons, it is expected that nonlinear squeezing can be further improved. The idea presented here can be readily extended to the higher-order phase gates [P. Marek et al., Phys. Rev. A 97, 022329 (2018)]. As such, this work presents an important step to extend the CV quantum information processing from Gaussian regime to non-Gaussian regime.

Adaptive data-driven nonlinear synchro squeezed transform with single class radial basis function kernel support vector machine applied to wind turbine planetary gearbox fault diagnostics

Planetary stage gears operated at low rotational speed and varying wind speed result variation in load. Variable speed and variable load induce nonstationary operating conditions. Vibration signal measured from Wind power gear transmission systems are embedded with multiple sources of vibration and attenuated considerably as it travels from source of vibration to measuring point. Efficacious multi-component decomposition without mode mixing ensures the accurate fault signature recognition. Synchro squeezing transform is the promising tool that represents the ridges with high resolution in time as well as in frequency axis. An efficient vibration analysis technique, short windowed Fourier synchro squeezing transform with nonlinear radial basis function kernel support vector machine is proposed to detect the mechanical faults in low speed planetary stage of wind turbines. Raw vibration is modeled in time–frequency plane to extract fault pattern signatures effectively with high resolution by adapting an empirical nonlinear tool synchro squeezing transforms. Amplitude modulation and frequency modulation parameters are sculpted from instantaneous amplitude and instantaneous phase, frequency. Hybrid feature space with signal attributes, statistical moments, and randomness measures are extricated from amplitude modulation-frequency modulation components. Single class radial basis function support vector machine is trained with hybrid features. The fault detection accuracy of the proposed method is compared with the standard variants of empirical mode decomposition. The proposed short windowed Fourier synchro squeezing transform-radial basis function kernel support vector machine shows 98.2% accuracy, 98% sensitivity, and 98% specificity.

Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

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.

Metrological Nonlinear Squeezing Parameter.

The well-known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally feasible recipes for a high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and nonclassicality witnesses for complex quantum states.

Semi-analytic modeling of FWM noise in QAM Nyquist-WDM system with phase-conjugated twin waves

Abstract Nonlinear models previously reported for coherent optical fiber transmission have been used to explain the mechanism of nonlinear noise squeezing by phase-conjugated twin waves (PCTW) scheme, but the reduction of four-wave-mixing (FWM) noise by the nonlinearity mitigation method cannot be directly derived from these models for a quasi-symmetric dispersion map, especially when the effect of walk-off between channels is included. Semi-analytic models based on a statistical method are derived herein order to quantify the reduction of FWM noise for quadrature amplitude modulation (QAM) PCTW Nyquist-WDM systems. Our models derived here show that the variance of non-degenerate FWM noise is irrelevant to the number of signal points within a QAM constellation diagram, as is different from the degenerate FWM case. Numerical results by using our models show that even though the effect of walk-off is included, the PCTW scheme is still greatly effective to reduce the impact of FWM noise for a quasi-symmetric map. The performances of central channel for two cases of 16QAM PCTW Nyquist-WDM systems with same total spectral bandwidth and spectral efficiency, 16-channel 32-Gbaud/ch and 32-channel 16-Gbaud/ch, are numerically compared by using our models

多模非对称叠加态光场广义电场分量的高次振幅压缩

多模非对称叠加态光场广义电场分量的高次振幅压缩

Nonlinear Squeezing Time-Frequency Transform and Application in Rotor Rub-Impact Fault Diagnosis

Vibration signal analysis has been proved as an effective tool for condition monitoring and fault diagnosis for rotating machines in the manufacturing process. The presence of the rub-impact fault in rotor systems results in vibration signals with fast-oscillating periodic instantaneous frequency (IF). In this paper, a novel method for rotor rub-impact fault diagnosis based on nonlinear squeezing time-frequency (TF) transform (NSquTFT) is proposed. First, a dynamic model of rub-impact rotor system is investigated to quantitatively reveal the periodic oscillation behavior of the IF of vibration signals. Second, the theoretical analysis for the NSquTFT is conducted to prove that the NSquTFT is suitable for signals with fast-varying IF, and the method for rotor rub-impact fault diagnosis based on the NSquTFT is presented. Through a dynamic simulation signal, the effectiveness of the NSquTFT in extracting the fast-oscillating periodic IF is verified. The proposed method is then applied to analyze an experimental vibration signal collected from a test rig and a practical vibration signal collected from a dual-rotor turbofan engine for rotor rub-impact fault diagnosis. Comparisons are conducted throughout to evaluate the effectiveness of the proposed method by using Hilbert–Huang transform, wavelet-based synchrosqueezing transform (SST), and other methods. The application and comparison results show that the fast-oscillating periodic IF of the vibration signals caused by rotor rub-impact faults can be better extracted by the proposed method.

Nonlinear squeezing time–frequency transform for weak signal detection

Conventional time–frequency analysis methods can characterize the time–frequency pattern of multi-component nonstationary signals. However, it is difficult to detect weak components hidden in complex signals because the time–frequency representation is influenced by the signal amplitude. In this paper, a novel algorithm called nonlinear squeezing time–frequency transform (NSTFT) is proposed to characterize the time–frequency pattern of multi-component nonstationary signals. Most importantly, theoretical analysis shows that the NSTFT method is independent of the signal amplitude and is only relevant to the signal phase, thus it can be used for weak signal detection. Moreover, an improved ridge detection algorithm is proposed in this paper for instantaneous frequency estimation. The experiments on simulated and real-world signals show that the NSTFT method can effectively detect weak components in complex signals, and the comparison study with some other time–frequency analysis methods also shows the advantages of the NSTFT method in weak signal detection.

Balanced homodyne detection with on-off detector systems: Observable nonclassicality criteria

Driven by single photon detection requirements, the theory of arrays of off-on detectors has been developed and applied. However, for a comprehensive characterization of nonclassicality, one also needs phase sensitive properties. This missing link is introduced with the derived theory of phase sensitive click counting measurements. It unifies the balanced homodyne detection for high intensities with the click detection in the few-photon regime. We formulate a hierarchy of nonlinear squeezing conditions to probe quantum effects beyond standard squeezing. Imperfections stemming from fluctuations, detector efficiency, and dark count rates are considered. Experimentally accessible sampling formulas are given. Our theory paves the way towards novel applications of light in quantum metrology.

Wave functions of a new kind of nonlinear single-mode squeezed state

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear single-mode squeezing operators. We derive the wave functions of exp[−(ig/2)(P + P)|0⟩ in the coordinate representation. A new operator's disentangling formula is derived as a by-product.

Fiber-Nonlinearity-Tolerant Superchannel Transmission via Nonlinear Noise Squeezing and Generalized Phase-Conjugated Twin Waves

We present fiber-nonlinearity-tolerant transmission of polarization-division multiplexed binary phase-shift keying (PDM-BPSK) through a nonlinear noise squeezing (NLNS) effect that is achieved by optimized digital electronic dispersion precompensation. With the improved nonlinear tolerance, a 406.6-Gb/s superchannel consisting of eight 37.5-GHz-spaced 32-Gbaud Nyquist-filtered PDM-BPSK signals is transmitted over a 12800-km (160 × 80-km) EDFA-only amplified dispersion-unmanaged nonzero-dispersion-shifted fiber link. We establish a connection between the beneficial NLNS effect and the recently reported phase-conjugated twin wave (PCTW) concept and further generalize the PCTW concept to vector twin waves that are traveling through a fiber link along orthogonal dimensions such as time and space. Moreover, we apply the PCTW concept to wavelength-division-multiplexed (WDM) superchannel transmission by treating the entire WDM superchannel as a twin wave to further mitigate interchannel nonlinear effects. Through numerical simulations, we show that the generalized PCTW technique can effectively mitigate interchannel nonlinear impairments, in addition to mitigating intrachannel nonlinear impairments.

Nonlinear coupling and squeezing in solid-state quantum circuits

We propose an attractive realization of nonlinear coupling of superconducting charge qubit coupled to a transmission-line resonator. Our scheme provides a new approach to produce the strong squeezing effect via a flexible design of the superconducting qubit and mature experimental setup of circuit QED. By properly tuning the external magnetic flux, considerable squeezing can be generated. Strong coupling strength, immunity to noises and suppression of spontaneous emission make our scheme more robust and may be realized with conservative experimental parameters.