M. Bhattacharya, P. -L. Giscard, P. Meystre
We consider a small partially reflecting vibrating mirror coupled dispersively to a single optical mode of a high finesse cavity. We show this arrangement can be used to implement quantum squeezing of the mechanically oscillating mirror.
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We present a protocol to generate a large degree of squeezing of a boson (light) field mode strongly coupled to a two-level system in the dispersive regime. Our protocol exploits the strong dispersive coupling to introduce a time dependent frequency change of the boson field. With an appropriately timed sequence of sudden frequency changes, the quantum noise fluctuations in one quadrature of the field can be reduced well below the standard quantum limit, with a correspondingly increased uncertainty in the orthogonal quadrature. Even in the presence of realistic noise and imperfections, the pro…
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…
A conventional optomechanical system is composed of a mechanical mode and an optical mode interacting through a linear optomechanical coupling (LOC). We study how the presence of quadratic optomechanical coupling (QOC) in the conventional optomechanical system affects the system's stability and optical quadrature squeezing. We work in the resolved side-band limit with a high quality factor mechanical oscillator. In contrast to the conventional optomechanical systems, we find that strong squeezing of the cavity field can be achieved in presence of QOC along with LOC at lower pump powers and at …
It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s-ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s-ordered quasipr…
We present a hybrid optomechanical scheme to achieve dynamical squeezing of position quadrature of a mesoscopic mechanical oscillator, that can be externally controlled by classical fields. A membrane-in-the-middle set up is employed, in which an atom in $Λ$ configuration is considered to be trapped on either side of the membrane inside the cavity. We show that a considerable amount of squeezing (beyond the 3 dB limit) can be achieved that is not affected by the decay of the cavity and the spontaneous emission of the atom. Squeezing depends upon the initial preparation of atomic states. Furthe…
Generation of squeezed light and optomechanical instability for dissipative type of opto- mechanical coupling is theoretically addressed for a cavity with the input mirror, serving as a mechanical oscillator, or an equivalent system. The problem is treated analytically for the case of resonance excitation or small detunings, mainly focusing on the bad cavity limit. A qualitative difference between the dissipative and purely dispersive coupling is reported. In particular, it is shown that, for the purely dissipative coupling in the bad cavity regime, the backaction is strongly reduced and the s…
We study the von Neumann entropy of the partial trace of a system of two two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanish…
We study an optomechanical system consisting of an optical cavity and movable mirror coupled through dispersive linear optomechanical coupling (LOC) and quadratic optomechanical coupling(QOC). We work in the resolved side band limit with a high quality factor mechanical oscillator in a strong coupling regime. We show that the presence of QOC in the conventional optomechanical system (with LOC alone) modifies the mechanical oscillator's frequency and reduces the back-action effects on mechanical oscillator. As a result of this the fluctuations in mechanical oscillator can be suppressed below st…
Squeezing for dispersive readout of NV magnetometer
本文针对金刚石NV磁力计色散读出系统，分析其噪声与损耗源，提出采用探测微波场压缩态的方案，可在室温下提升器件性能。
In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down converted frequency.
We show that squeezing of a nanomechanical mirror can be generated by injecting broad band squeezed vacuum light and laser light into the cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum momentum squeezing of the movable mirror, the squeezing parameter of the input light should be about 1. We can obtain more than 70% squeezing. Besides, for a fixed squeezing parameter, decreasing the temperature of the environment or increasing the laser power increases the momentum squeezing. We find very large squeezing with respect to thermal fluctuations, for ins…
This work analyses the quantum properties of counter-propagating twin beams generated by a Mirrorless Optical Parametric Oscillator in the continuous variable regime. Despite the lack of the filtering effect of a cavity, we show that in the vicinity of its threshold it may generate high levels of narrowband squeezing and Einstein-Podolsky-Rosen (EPR) correlation, completely comparable to what can be obtained in standard optical parametric oscillators.
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 present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive) atom-cavity couplings, on a potentially equal footing. We focus on a regime where the dispersive coupling is very large and find that the steady state of the system can in fact be a strongly spin-squeezed Dicke state, $|N/2,0\rangle$, of the atomic ensemble. These states offer Heisenberg-limited metrological properties and feature genuine multipartite entanglement am…
We study the squeezing as well as the statistical properties of the output radiation from a degenerate parametric oscillator coupled to a squeezed vacuum reservoir employing the stochastic differential equations associated with the normal ordering. It is found that the degree of squeezing of the output radiation is less than the corresponding cavity radiation. However, for output radiation the correlation of the quadrature operators evaluated at different times also exhibits squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the squeezing s…
Quantum coherent feedback control is a measurement-free control method fully preserving quantum coherence. In this paper we show how time-delayed quantum coherent feedback can be used to control the degree of squeezing in the output field of a cavity containing a degenerate parametric oscillator. We focus on the specific situation of Pyragas-type feedback control where time-delayed signals are fed back directly into the quantum system. Our results show how time-delayed feedback can enhance or decrease the degree of squeezing as a function of time delay and feedback strength.
We propose a simple scheme to measure squeezing and phase properties of a harmonic oscillator. We treat in particular the case of a the field, but the scheme may be easily realized in ion traps. It is based on integral transforms of measured atomic properties as atoms exit a cavity. We show that by measuring atomic polarizations it is possible, after a given integration, to measure several properties of the field.
Quantum Squeezing Effects in Coupled van der Pol Oscillators
该研究针对量子领域同步易被噪声掩盖的问题，在两个耦合范德波尔振荡器中引入压缩哈密顿量，增强非经典效应、量子关联并提升同步动力学鲁棒性，为量子同步提供了更优方案。
Exponentially Improved Dispersive Qubit Readout with Squeezed Light
本文提出将注入外部压缩与腔内压缩结合用于色散量子比特读出，可在任意测量时间内使信噪比指数级提升，并在短时测量中以两倍压缩参数进一步指数改善，为量子纠错和容错量子计算提供快速高保真读出方案。
In this paper, we investigate theoretically the quantum state transfer in a laser driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources …
In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be …
We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane/mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions…
We consider the thermodynamic properties of the squeezed vacuum state of a frequency--modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work and the degree of nonadiabaticity of the frequency transformation. We furthermore determine the optimal modulation that leads to maximal squeezing, and discuss its implementation as well as the detection of squeezing in single cold ion traps.
Dynamically enhancing qubit-photon interactions with anti-squeezing
本研究利用简并参量振荡器的压缩态放大场涨落，在超导电路实验中以5.5 dB压缩量实现量子比特-光子色散相互作用两倍增强，验证了量子比特-光子相互作用的原位动态控制，为增强相互作用的实验平台提供新方向。
Optical squeezing mediated by levitated oscillators at their quantum ground state
研究通过悬摆纳米颗粒的中心质量模与光学腔场相互作用，实现低于Shot噪声的光学压缩，展示多机械振荡器在量子基态下的压缩效应，建立悬摆光机作为多模量子交互平台。
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…
Fast quantum squeezing of a nanomechanical oscillator with an inverted potential
本文提出利用光学倒置势阱对室温真空光悬浮二氧化硅纳米颗粒的摆动模式进行指数加速压缩，在250纳秒内实现低于真空涨落11 dB的量子压缩，为机械运动量子压缩和量子增强传感提供新范式。
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。
In a series of articles we studied the quantum properties of a degenerate optical parametric oscillator tuned to the first family of transverse modes at the subharmonic. We found that, for a cavity having rotational symmetry respect to the optical axis, a TEM$_{10}$ mode with an arbitrary orientation in the transverse plane is emitted above threshold. We proved then that quantum noise induces a random rotation of this bright TEM$_{10}$ mode in the transverse plane, while the mode orthogonal to it, the so-called dark mode, has perfect quadrature squeezing irrespective of the distance to thresho…
We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the othe…
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。
Advances in the emerging field of coherent quantum feedback control (CQFC) have led to the development of new capabilities in the areas of quantum control and quantum engineering, with a particular impact on the theory and applications of quantum optical networks. We consider a CQFC network consisting of two coupled optical parametric oscillators (OPOs) and study the squeezing spectrum of its output field. The performance of this network as a squeezed-light source with desired spectral characteristics is optimized by searching over the space of model parameters with experimentally motivated bo…
Frequency shifts heralding ground state squeezing and entanglement of two coupled harmonic oscillators
研究通过频率位移揭示两个耦合谐振子的基态压缩和纠缠，展示量子特性在经典系统中的表现。
Quantum squeezing in a nonlinear mechanical oscillator
本研究通过参数驱动超导量子比特实现千兆赫机械谐振器的基态压缩，并利用失谐耦合引入可调非线性，构建机械压缩克尔振子，制备非高斯量子态，为量子计量和传感提供新途径。
In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a …
The squeezing effect arises in the interacting qubit-oscillator system is studied with the presence of a parametric oscillator in the Rabi model. Based on the generalized rotating wave approximation which works well in the wide range of coupling strength as well as detuning, the analytically derived approximate energy spectrum is compared with the numerically determined spectrum of the Hamiltonian. For the initial state of the bipartite system, the dynamical evolution of the reduced density matrix corresponding to the oscillator is obtained by partial tracing over the qubit degree of freedom. …
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement…
We demonstrate a diode-laser-pumped system for generation of quadrature squeezing and polarization squeezing. Due to their excess phase noise, diode lasers are challenging to use in phase-sensitive quantum optics experiments such as quadrature squeezing. The system we present overcomes the phase noise of the diode laser through a combination of active stabilization and appropriate delays in the local oscillator beam. The generated light is resonant to the rubidium D1 transition at 795nm and thus can be readily used for quantum memory experiments.
Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predi…
We observe -9.01$\pm$0.14 dB of squeezing and +15.12$\pm$0.14 dB of antisqueezing with a local oscillator phase locked in homodyne measurement. In reference [1], two main factors are pointed out which degrade the observed squeezing level: phase fluctuation in homodyne measurement and intracavity losses of an optical parametric oscillator for squeezing. We have improved the phase stability of homodyne measurement and have reduced the intracavity losses. We measure pump power dependences of the squeezing and antisqueezing levels, which show good agreement with theoretical calculations taking acc…
It is shown that each one of the Lie algebras su(1,1) and su(2) determine the spectrum of the radial oscillator. States that share the same orbital angular momentum are used to construct the representation spaces of the non-compact Lie group SU(1,1). In addition, three different forms of obtaining the representation spaces of the compact Lie group SU(2) are introduced, they are based on the accidental degeneracies associated with the spherical symmetry of the system as well as on the selection rules that govern the transitions between different energy levels. In all cases the corresponding gen…
We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic interaction. This impacts …
The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement back action leads to squeezing and entanglement of the quantized density oscillations. In particular, we show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of non-targeted modes of the system.
Applications of Spin-Dependent Generalized Squeezing in Hybrid Spin-Oscillator Quantum Processors
本文提出并研究混合自旋-振子量子处理器中自旋依赖广义压缩的4种应用，为该平台的高保真量子计算与传感奠定基础。
Generation of strong mechanical squeezing through the joint effect of two-tone driving and parametric pumping
本研究提出在光机械系统中利用双色调驱动与参数泵浦的协同机制，高效制备强机械压缩，打破3 dB极限，且对热噪声和衰减具有鲁棒性。
In this paper, we theoretically propose and investigate a feasible experimental scheme for realizing the dynamical Casimir effect (DCE) of phonons in an optomechanical setup formed by a ground-state precooled mechanical oscillator (MO) inside a Fabry-P{é}rot cavity, which is driven by an amplitude-modulated classical laser field in the dispersive (far-detuned) regime. The time modulation of the driving field leads to the parametric amplification of the mechanical vacuum fluctuations of the MO, which results in the generation of Casimir phonons over time scales longer than the cavity lifetime. …
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fi…
We study entanglement dynamics in dispersive optomechanical systems consisting of two optical modes and a mechanical oscillator inside an optical cavity. The two optical modes interact with the mechanical oscillator, but not directly with each other. The appearance of optical entanglement witnesses non-classicality of the oscillator. We study the dependence of the entanglement dynamics with the optomechanical coupling, the mean photon number in the cavity and the oscillator temperature. An experimental realization with ultracold atomic ensembles is proposed.
The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems as promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings and thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles to observe squeezing for gi…
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 n…
We consider a star network consisting of N oscillators coupled to a central one which in turn is coupled to an infinite set of oscillators (reservoir), which makes it leaking. Two of the N + 1 normal modes are dissipating, while the remaining N - 1 lie in a frequency range which is more and more squeezed as the coupling strengths increase, which realizes synchronization of the single parts of the system.
Unique Steady-State Squeezing in a Driven Quantum Rabi Model
本文提出了一种在量子拉比模型和Dicke模型中产生稳态压缩的理论，通过消除自旋动力学导出抽象谐振子，实现了具有时间无关不确定性的独特压缩，可应用于连续背作用规避测量。
Local-oscillator-agnostic squeezing detection
本文提出了一种无需本地振荡器的压缩态检测方法，通过部分正常排列的概念，实现对光子系统量子特性的评估。
Generalized squeezing rotating-wave approximation (GSRWA) is proposed by employing both the displacement and the squeezing transformations. A solvable Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a qubit coupled to oscillators experiment, a well-defined Schrödinger-cat-like entangled state is given by the displaced-squeezed oscillator state instead of the original displaced state. For the isotropic Rabi case, the mean photon number and the ground-state energy are expressed analytically with additional squeezing terms, exhibiting a substantial improvement of the GS…
In this work, the dynamics of the deformed one-dimensional harmonic oscillator with minimal length uncertainty is examined and the analytical solutions for time evolution of position and momentum operators are presented in which the rough approximation that neglects the higher order terms in BakerHausdor lemma is avoided. Based on these analytical solutions the uncertainties for position and momentum operators are calculated in a coherent state, and an unexpected squeezing effect in both coordinate and momentum directions is found in comparison with ordinary harmonic oscillator. Obviously such…
Squeezing equivalence of quantum harmonic oscillators under different frequency modulations
本文将量子谐振子在不同频率调制下的压缩等价性从零压缩推广到非零压缩情形，并分别给出数值求解与解析求解两类方法，揭示其与压缩态生成及 shortcuts to adiabaticity 的联系。
We investigate nonlinear effects in an electromechanical system consisting of a superconducting charge qubit coupled to transmission line resonator and a nanomechanical oscillator, which in turn is coupled to another transmission line resonator. The nonlinearities induced by the superconducting qubit and the optomechanical coupling play an important role in creating optomechanical entanglement as well as the squeezing of the transmitted microwave field. We show that strong squeezing of the microwave field and robust optomechanical entanglement can be achieved in the presence of moderate therma…
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。
We show that an ensemble of identical d-level atoms can be efficiently described by d-1 collective oscillator degrees of freedom in the vicinity of a product state with all atoms in the same, but otherwise arbitrary single-particle state. We apply our description to two different kinds of spin squeezing: (i) when each spin-F atom is individually squeezed without creating interatomic entanglement and (ii) when a particular collective atomic oscillator mode is squeezed via quantum non-demolition (QND) measurement and feedback. When combined in sequence, the order of the two methods is relevant i…
Continuous-time quantum harmonic oscillator state engineering
本文利用李代数方法，基于旋转、位移和压缩三种基本操作，推导了时变驱动量子谐振子的时间演化，并提出了一种直观构建态工程协议的方法，适用于参数慢速和快速变化。
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