J. Bajer, A. Miranowicz, R. Tanas
It is well known that the optical Kerr effect can be a source of highly squeezed light, however the analytical limit of the noise suppression has not been found yet. The process is reconsidered and an analytical estimation of the optimal quadrature noise level is presented. The validity of the new scaling law is checked numerically and analytically.
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In this Letter we study the evolution of the higher-order squeezing, namely, $n$th-order single-mode squeezing, sum- and difference-squeezing for the codirectional Kerr nonlinear coupler. We show that the amount of squeezing decreases when $n$, i.e. the squeezing order, increases. For specific values of the interaction parameters squeezing factors exhibit a series of revival-collapse phenomena, which become more pronounced when the value of $n$ increases. Sum-squeezing can provide amounts of squeezing greater than those produced by the $n$th higher-order ($n\geq 2$) squeezing for the same valu…
In this Letter we describe a new two-mode system, which consists of Kerr-like medium and down conversion process, called the Kerr-down conversion system. Under a certain condition we can obtain an exact solution of the dynamical equations of motion. For this system we investigate different kinds of quadrature squeezing, e.g., single-mode, two-mode and sum-squeezing. Also we give a more general definition of the principal squeezing. We show that the amounts of nonclassical effects produced by the Kerr-like and down-conversion processes separately are greater than those obtained from the Kerr-do…
Loss tolerant cross-Kerr enhancement via modulated squeezing
通过调制压缩技术增强跨凯尔相互作用，实现容错的光子量子计算中受控相位门的高效实现。
Practical Limits to Single-Mode Vacuum Squeezing with a SNAIL Parametric Amplifier
研究探讨了在SNAIL参量放大器中单模真空压缩的实际限制，发现Kerr非线性对压缩影响不大，主要受限于内部谐振器损耗和微波链路插入损耗。
Kerr-magnon-assisted asymptotic stationary photon-phonon squeezing
提出混合腔磁机械系统中的Kerr磁振子辅助光子-声子压缩方案，通过有效哈密顿量与量子Langevin理论证明可获得超越稳定极限的渐近稳态压缩。
We address quantum estimation of displacement and squeezing parameters by the class of probes made of Gaussian states undergoing Kerr interaction. If we fix the overall energy available to the probe, without posing any constraint on the available Gaussian squeezing, then Gaussian squeezing represents the optimal resource for parameter estimation. On the other hand, in the more realistic case where the amount of Gaussian squeezing is fixed, or even absent, then Kerr interaction turns out to be useful to improve estimation, especially for probe states with large amplitude. Our results indicate t…
Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate …
Quantum squeezing amplification with a weak Kerr nonlinear oscillator
本文通过弱色散非线性振子生成并放大压缩态，利用离散化技术实现量子压缩放大，达到14.6 dB的压缩度和0.28 MHz的压缩速率，为量子传感和信息处理提供新途径。
The interaction of two quantized fields and three-level quantum system in a lambda-type configuration is investigated in the presence of cross-Kerr nonlinearity. We consider three models of coupling for the atom-photon interaction. First, we study the dynamical behavior of the atom-photon entanglement and show that increasing the cross-Kerr nonlinearity results in different behaviors in three considered models. Moreover, it is demonstrated that the two quantized modes can be entangled, on the other hand, by applying a classical driving field to the lower levels. Increasing the classical drivin…
Motivated by quantum experiments with nanomechanical systems, the evolution of a Kerr oscillator with focus on creation of states with a negative Wigner function is investigated. Using the phase space formalism, results are presented that demonstrate an asymptotic behavior in the large squeezing regime for the negativity of a squeezed vacuum state under unitary evolution. The analysis and model are extended to squeezed vacuum states of open systems, adding the decoherence effects of damping and dephasing. To increase experimental relevance, the regime of strong damping is considered. These eff…
In this paper the interaction between a two-level atom and a single-mode field in the $k$-photon Jaynes-Cummings model (JCM) in the presence of Stark shift and Kerr medium is studied. All terms in the respected Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be $f$-deformed. In particular, the effect of the initial state of radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initi…
We apply the Green's function method to determine the global degree of squeezing and the transverse spatial distribution of quantum fluctuations of solitons in Kerr media. We show that both scalar bright solitons and multimode vector solitons experience strong squeezing on the optimal quadrature. For vector solitons, this squeezing is shown to result from an almost perfect anti-correlation between the fluctuations on the two incoherently-coupled circular polarisations.
We analyze an experimental method for creating interesting nonclassical states by processing the entanglement generated when two large coherent states interact in a cross-Kerr medium. We specifically investigate the effects of loss and noise in every mode of the experiment, as well as the effect of "binning" the post-selection outcomes. Even with these imperfections, we find an optimal set of currently-achievable parameters which would allow a proof-of-principle demonstration of number squeezing in states with large mean photon number. We discuss other useful states which can be generated with…
We analyze nonlinear transverse mode coupling in a Kerr medium placed in an optical cavity and its influence on bistability and different kinds of quantum noise reduction. Even for an input beam that is perfectly matched to a cavity mode, the nonlinear coupling produces an excess noise in the fluctuations of the output beam. Intensity squeezing seems to be particularly robust with respect to mode coupling, while quadrature squeezing is more sensitive. However, it is possible to find a mode the quadrature squeezing of which is not affected by the coupling.
We investigate the quantum properties for the codirectional three-mode Kerr nonlinear coupler. We investigate single-, two- and three-mode quadrature squeezing, Wigner function and purity. We prove that this device can provide richer nonclassical effects than those produced by the conventional coupler, i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence on the values of the interaction parameters. In contrast to the conventional Kerr coupler two different forms of cat states can be simultan…
Intracavity squeezing for Kerr QND Measurement scheme
本研究针对克尔量子非破坏测量方案中自相位调制效应限制灵敏度的问题，提出利用探测光束腔内压缩抵消该效应的方法，估算显示可实现单光子灵敏度，适用于光学量子信息处理任务。
We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.
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 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 theory of a three-photon Kerr parametric oscillator
本文研究了由三光子泵浦驱动的非线性Kerr振荡器的量子特性，推导了该相互作用模型的基态的精确和近似解析表达式，并探讨了三光子Kerr参数振荡器如何用于编码抗相位翻转错误的Kerr-猫三能级态。
Squeezed light is one of the resources of photonic quantum technology. Among the various nonlinear interactions capable of generating squeezing, the optical Kerr effect is particularly easy-to-use. A popular venue is to generate polarization squeezing, which is a special self-referencing variant of two-mode squeezing. To date, polarization squeezing generation setups have been very sensitive to fluctuations of external factors and have required careful tuning. In this work, we report on a development of a new all-fibre setup for polarization squeezing generation. The setup consists of passive …
In this paper, we follow our presented model in J. Opt. Soc. Am. B {\bf 30}, 1109--1117 (2013), in which the interaction between a $Λ$-type three-level atom and a quantized two-mode radiation field in a cavity in the presence of nonlinearities is studied. After giving a brief review on the procedure of obtaining the state vector of the atom-field system, some further interesting and important physical features (which are of particular interest in the quantum optics field of research) of the whole system state, i.e., the number-phase entropic uncertainty relation (based on the two-mode Pegg-Bar…
We theoretically analyze the noise transformation of a high power continuouswave light field that is reflected off a critical Kerr non-linear cavity (KNLC). Our investigations are based on a rigorous treatment in the time-domain. Thereby, realistic conditions of a specific experimental environment including optical intra-cavity loss and strong classical driving noise can be modeled for any KNLC. We show that even in the presence of optical loss and driving noise considerable squeezing levels can be achieved. We find that the achievable squeezing levels are not limited by the driving noise but …
The use of a Kerr nonlinearity to generate squeezed light is a well-known way to surpass the quantum noise limit along a given field quadrature. Nevertheless, in the most common regime of weak nonlinearity, a single Kerr resonator is unable to provide the proper interrelation between the field amplitude and squeezing required to induce a sizable deviation from Poissonian statistics. We demonstrate experimentally that weakly coupled bosonic modes allow exploration of the interplay between squeezing and displacement, which can give rise to strong deviations from the Poissonian statistics. In par…
We report on a novel and efficient source of polarization squeezing using a single pass through an optical fiber. Simply passing this Kerr squeezed beam through a carefully aligned lambda/2 waveplate and splitting it on a polarization beam splitter, we find polarization squeezing of up to 5.1 +/- 0.3 dB. The experimental setup allows for the direct measurement of the squeezing angle.
In this paper, we investigate the single mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we investigate quadrature and principal squeezing, Wigner function, quadrature distribution, phase distribution and phase variance. We show that the quadrature squeezing and the phase variance can exhibit collapse-revival and collapse-revival-subrevival phenomena, respectively, based on the values of the detuning parameter. Furthermore, we analytically demonst…
Quantum Dispersive Waves and Multimode Squeezing in Pure-Kerr Parametrically Driven Cavity Solitons
本文首次给出纯Kerr参量驱动腔孤子的多模量子描述，揭示阈值以下的单模和双模压缩以及阈值以上的新型量子色散波，并展示高达20 dB的压缩。
We study the interaction of a nearly resonant linearly polarized laser beam with a cloud of cold cesium atoms in a high finesse optical cavity. We show theoretically and experimentally that the cross-Kerr effect due to the saturation of the optical transition produces quadrature squeezing on both the mean field and the orthogonally polarized vacuum mode. An interpretation of this vacuum squeezing as polarization squeezing is given and a method for measuring quantum Stokes parameters for weak beams via a local oscillator is developed.
Kerr-Filtered Hybrid States from Double-Squeezed Tripartite Interactions
本研究提出利用双压缩与Kerr非线性协同作用，在三方自旋-光子-声子系统中可控生成Kerr滤波混合态，通过增强光子-声子对生成并选择性重塑光子组分，实现混合量子态的工程化。
Strong nanophotonic quantum squeezing exceeding 3.5 dB in a foundry-compatible Kerr microresonator
本研究在代工厂制备的氮化硅微环中实现了3.7 dB的片上量子压缩，证明了该平台在CMOS兼容架构中可实现强量子噪声抑制。
Quantum metrology with a squeezed Kerr oscillator
本文研究 Kerr 非线性振荡器的压缩动力学，提出在正交测量前加入非线性演化的 MAI 协议，以高量子 Fisher 信息实现位移传感灵敏度的显著增强。
We evaluate the squeezing of a probe beam with a transverse Gaussian profile interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and noise functions. The transverse structure is accounted for by averaging atomic functions over the intensity profile. The results of the plane-wave and Gaussian-wave theories are compared. When large squeezing is predicted we find the prediction of the plane-wave model not to be reliable outside the Kerr domain. We give an estimate of the squeezing degradatio…
We theoretically compared quantum noise squeezing differences between silicon and graphene nanoresonators based on experimental structure parameters. The conditions to achieve squeezed states of silicon and graphene have been discussed. According to our theoretical analysis, graphene nanoresonators can obtain a much smaller squeezing factor than silicon, taking advantage of their thin thickness. Both the quantum noise and thermal noise (Brownian motion) of typical monolayer graphene nanoresonator can be reduced by 12.58 dB at T = 5 K with a pump voltage of 5 V.
We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and they remain entangled. By mapping the dynamics onto the Poincare space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.
Frequency-dependent squeezing via Einstein-Podolsky-Rosen entanglement based on silicon nitride microring resonators
本文提出基于氮化硅微环谐振器的EPR纠缠量子频率梳平台，通过选择闲频模式检测角实现频率依赖压缩，为突破量子噪声限制的位移传感提供了集成化方案。
We have considered the interaction of subharmonic light modes with a three-level atom in a closed cavity coupled to a vacuum reservoir. We carry out analysis by normally ordering the vacuum reservoir noise operators. It so happens that there is perfect quadrature squeezing under certain conditions.
We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic chi(3) medium in which self-phase and cross-phase modulation, as well as four--wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the ort…
We present a generalized echo squeezing protocol (GESP) as a generalization of the Schrödinger cat state protocol (SCSP) with the value of the squeezing parameter being an arbitrary number rather than pi/2. We show analytically that over a broad range of the squeezing parameter the sensitivity reaches the Heisenberg limit (HL) within a factor of root-2. For a large number of particles, N, this plateau interval is almost the whole range from zero to pi/2, and the sensitivity is independent of the parity of N. Therefore, it is possible to operate a sensor over a wide interval of the squeezing pa…
We propose a feasible scheme for generation of strongly non-Gaussian states using the cross-Kerr nonlinearity. The resultant states are highly non-classical states of electromagnetic field and exhibit negativity of their Wigner function, sub-Poissonian photon statistics, and amplitude squeezing. Furthermore, the Wigner function has a distinctly pronounced ``banana'' or ``crescent'' shape specific for the Kerr-type interactions, which so far was not demonstrated experimentally. We show that creating and detecting such states should be possible with the present technology using electromagnetical…
We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a chi^3 nonlinear medium. The non-zero response time of the Kerr chi^3 nonlinearity determines the quantum-limited noise figure of chi^3 parametric amplification, as well as the limit on quadrature squeezing. This non-zero response time of the nonlinearity requires coupling of the parametric process to a molecular-vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency non-degenerat…
Phase-Dependent Squeezing in Dual-Comb Interferometry
本研究通过双梳干涉测量实验，观测到相位相关的Kerr孤子压缩现象，验证了量子噪声模型，为量子增强定时应用和高速量子态层析成像提供了新途径。
We demonstrate the generation of broad-band continuous-wave optical squeezing down to 200Hz using a below threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise and detuning fluctuations, present in optical parametric amplifiers have negligible effect on squeezing produced by a below threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational wave detectors.
We consider the quantum effect of slow light dark soliton (SLDS) in a cold atomic gas with defocuing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations, and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are bi-orthogonal and constitute a com…
The signal-to-noise ratio for heterodyne laser radar with a coherent target-return beam and a squeezed local-oscillator beam is lower than that obtained using a coherent local oscillator, regardless of the method employed to combine the beams at the detector.
We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing at very low noise sideband frequencies produced by a single type-II, self-phase-locked, frequency degenerate optical parametric oscillator below threshold. The generated two-mode squeezed vacuum state is preserved for noise frequencies as low as 50 kHz. Designing simple setups able to generate non-classical states of light in the kHz regime is a key challenge for high sensitivity detection of ultra-weak physical effects such as gravitational wave or small beam displacement.
Linearized analysis of dissipative Two Axis Counter Twisting (TACT) squeezing for Metrology
本文分析了退极化信道耗散下的双轴扭转（TACT）自旋压缩，发现耗散须参数上弱于压缩耦合，且压缩须先于测量才能获得计量学增益；关键数学进展是证明含退极化噪声的TACT等价于极化降低且无噪声的TACT，信噪比呈指数增益。
We present a theoretical study of the phase noise, intensity and quadrature squeezing power spectra of the transmitted field of a driven optical cavity containing an interacting one-dimensional Bose-Einstein condensate. We show how the pattern of the output power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to a one-to-one correspondence between the splitting of the peaks in the phase noise power spectrum of the cavity output field and the \textit{s}-wave scattering frequency of the atom-atom interaction, one can measure the…
The Abbe's diffraction limit restricts the resolution of an optical imaging and lithography system. Coherent Rabi oscillation is shown to be able to overcome the diffraction limit in both optical and atom lithography. In previous studies, semiclassical theory is applied where the driving field is treated as a classical light and quantum fluctuation is neglected. Here, we show that the quantum fluctuation may reduce the visibility of the superresolution pattern. However, by squeezing the photon number fluctuation we are able to significantly increase its visibility.
Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system's vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field, in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror, based on our effective Hamiltonian …
We provide a framework for understanding recent experiments on squeezing of a collective atomic pseudo-spin, induced by a homodyne measurement on off-resonant probe light interrogating the atoms. The detection of light decimates the atomic state distribution and we discuss the conditions under which the resulting reduced quantum fluctuations are metrologically relevant. In particular, we consider a dual probe scheme which benefits from a cancelation of classical common mode noise sources such that quantum fluctuations from light and atoms are the main contributions to the detected signal.
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. We show that the irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a l…
We report the measurement of the fluctuations of the two quadratures of the electromagnetic field generated by a quantum conductor, a dc- and ac-biased tunnel junction placed at very low temperature.We observe that the variance of the fluctuations on one quadrature can go below that of vacuum, i.e., that the radiated field is squeezed. This demonstrates the quantum nature of the radiated electromagnetic field.
Squeezing of light's quantum noise requires temporal rearranging of photons. This again corresponds to creation of quantum correlations between individual photons. Squeezed light is a non-classical manifestation of light with great potential in high-precision quantum measurements, for example in the detection of gravitational waves. Equally promising applications have been proposed in quantum communication. However, after 20 years of intensive research doubts arose whether strong squeezing can ever be realized as required for eminent applications. Here we show experimentally that strong squeez…
We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower amplitude noise than states of the same average amplitude excited by a pure harmonic drive; for sufficiently low thermal noise a sub-Poissonian resonator state can be produced. We also calculate the linewidth narrowing that occurs in the limit-cycle states, and show that while the minimum is set by direct phase diffusion, diffusion due to the optical spring e…
We report the demonstration of a magnetometer with noise-floor reduction below the shot-noise level. This magnetometer, based on a nonlinear magneto-optical rotation effect, is enhanced by the injection of a squeezed vacuum state into its input. The noise spectrum shows squeezed noise reduction of about 2 dB spanning from close to 100 Hz to several megahertz. We also report on the observation of two different regimes of operation of such a magnetometer: one in which the detection noise is limited by the quantum noise of the light probe only, and one in which we see additional noise originating…
We examine the quantum states produced through parametric amplification with internal quantum noise. The internal diffusion arises by coupling both modes of light to a reservoir for the duration of the interaction time. The Wigner function for the diffused two-mode squeezed state is calculated. The nonlocality, separability, and purity of these quantum states of light are discussed. In addition, we conclude by studying the nonlocality of two other continuous variable states: the Werner state and the phase-diffused state for two light modes.
Strong Thermomechanical Noise Squeezing Stabilized by Feedback
本文提出通过反馈稳定反压缩正交分量以突破3 dB限制，在高应力氮化硅薄膜谐振器中实现创纪录的17 dB和21 dB热机械噪声压缩，并理论证明在适度低温下可实现量子压缩。
We present experimental and theoretical analysis of quantum fluctuation in a vacuum field in the presence of orthogonal linearly polarized pump field propagating through a Rb vapor cell. Previously reported theoretical and experimental studies provided somewhat contradictory conclusions regarding the possibility to observe the "squeezed vacuum" -- the reduction of vacuum fluctuations below standard quantum limit -- in this system. Here, using the D1 transitions of Rb in a cell without buffer as as an example, we demonstrate that vacuum squeezing is corrupted by incoherent processes (such as sp…
The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
本文在约瑟夫森电路中实现压缩克尔振子，首次通过光谱实验验证其有效哈密顿量，并实现超过99%的量子非破坏读出保真度和相位翻转寿命两个数量级以上的提升，展示了参量驱动哈密顿量工程对硬件高效量子计算的重要性。
Twin-Signal-Recycling (TSR) builds on the resonance doublet of two optically coupled cavities and efficiently enhances the sensitivity of an interferometer at a dedicated signal frequency. We report on the first experimental realization of a Twin-Signal-Recycling Michelson interferometer and also its broadband enhancement by squeezed light injection. The complete setup was stably locked and a broadband quantum noise reduction of the interferometers shot noise by a factor of up to 4\,dB was demonstrated. The system was characterized by measuring its quantum noise spectra for several tunings of …
Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or …
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