A general formalism is given in quantum optics within a ring cavity, in which a non-linear material is stored. The method is Feynman graphical one, expressing the transition amplitude or S-matrix in terms of propagators and vertices. The propagator includes the additional damping effect via the non-linear material as well as the reflection and penetration effects by mirrors. Possible application of this formalism is discussed, in estimating the averaged number of produced photons, Husimi function, and the observables to examine beyond the squeezing mechanism of photons.
This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real line, that is, a transformation capable to diminish (or enhance) the mean square deviation of a centered distribution. As it is discussed, the definition of such an operator on finite dimensional vector spaces is not a trivial matter, but, on the other hand, has obvious connections with problems such as spin squeezing and (finite) quantum state reproduction.
A monochromatic double-mode coherent light endowed with orthogonally polarized photons propagating collinearly is studied in Degenerate Parametric Amplification. Generation of Hidden Optical- Polarized States is shown by non-zero values of Index of Hidden Optical-Polarization. Squeezing in HOPS is demonstrated by recognizing a Squeezing function. The Non-Classical feature of HOPS is observed by 'degree of Hidden Optical-Polarization' which attains non-classical value 'greater than unity'. The dynamical nature of Generation, Squeezing and Non-Classicality are numerically presented.
We present the first demonstration of all-optical squeezing in an on-chip monolithically integrated CMOS-compatible platform. Our device consists of a low loss silicon nitride microring optical parametric oscillator (OPO) with a gigahertz cavity linewidth. We measure 1.7 dB (5 dB corrected for losses) of sub-shot noise quantum correlations between bright twin beams generated in the microring four-wave-mixing OPO pumped above threshold. This experiment demonstrates a compact, robust, and scalable platform for quantum optics and quantum information experiments on-chip.
We analyze a fiber-optic gyroscope design enhanced by the injection of quantum-optical squeezed vacuum into a fiber-based Sagnac interferometer. In the presence of fiber loss, we compute the maximum attainable enhancement over a classical, laser-driven fiber-optic gyroscope in terms of the angular velocity estimate variance from a homodyne measurement. We find a constant enhancement factor that depends on the degree of squeezing introduced into the system but has diminishing returns beyond $10$--$15$ dB of squeezing. Under a realistic constraint of fixed total fiber length, we show that segmen…
Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher order antibunching, higher order squeezing, higher order two-mode and multi-mode entanglement in the asymmetric nonlinear optical c…
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed lig…
Experimental investigation of the effect of dispersion on squeezing generation in a synchronously pumped optical parametric oscillator
Università degli Studi di Milano（米兰大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所米兰分部）；Istituto di Fotonica e Nanotecnologie – CNR（光子与纳米技术研究所-国家研究委员会）
We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot …
We present squeezing and anti-squeezing spectra of the output from a degenerate optical parametric oscillator (OPO) network arranged in different coherent quantum feedback configurations. One OPO serves as a quantum plant, the other as a quantum controller. The addition of coherent feedback enables shaping of the output squeezing spectrum of the plant, and is found to be capable of pushing the frequency of maximum squeezing away from the optical driving frequency and broadening the spectrum over a wider frequency band. The experimental results are in excellent agreement with the developed theo…
We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is applied to the two-photon algebra and the corresponding algebra eigenstates are studied by using the Fock-Bargmann analytic representation. This formalism yields a unified analytic approach to various types of single-mode photon states generated by squeezing and displacing transformations.
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part of this work we study the symplectic structure associated with linear canonical transformations. After reviewing salient mathematical properties of the symplectic group in a pedagogical way, we introduce the squeezing formalism, and show how any linear dynamics can be cast in terms of an invariant representation. In the second part, we apply these results to…
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 have developed an optical parametric amplification module for quadrature squeezing with input and output ports coupled with optical fibers for both fundamental and second harmonic. The module consists of a periodically poled LiNbO${}_{3}$ ridge waveguide fabricated with dry etching, dichroic beamsplitters, lenses and four optical fiber pigtales. The high durability of the waveguide and the good separation of squeezed light from a pump beam by the dichroic beamsplitter enable us to inject intense continuous-wave pump light with the power of over 300 mW. We perform $-$4.0${\pm}$0.1 dB of nois…
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.
Optical squeezing mediated by levitated oscillators at their quantum ground state
CNR-INO（意大利国家研究委员会红外光学研究所）；Dipartimento di Fisica e Astronomia, Univ. Di Firenze（佛罗伦萨大学物理与天文系）；INFN, Sezione di Firenze（意大利国家核物理研究院佛罗伦萨分部）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
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 …
In analogy with the spin-squeezing inequality of Wang and Sanders [Physical Review A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields, and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly-solvable experimental scenario employing polarization- squeezed light from an optical parametric oscillator (OPO) and find that any two photons separated by less than the OPO coherence time are polarization entangled. The polarization entanglement is robust aga…
We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the -3dB limit in the noise reduction, associated to parametric resonance, with a best experimental result of -7.4dB. In a moderately cooled system, our technique can be efficiently exploited to produce strong squeezing of …
We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dy…
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric non…
We demonstrate quantum correlations in the transverse plane of continuous wave light beams by producing -4.0 dB, -2.6 dB and -1.5 dB of squeezing in the TEM00, TEM10 and TEM20 Hermite- Gauss modes with an optical parametric amplifier, respectively. This has potential applications in quantum information networking, enabling parallel quantum information processing. We describe the setup for the generation of squeezing and analyze the effects of various experimental issues such as mode overlap between pump and seed and nonlinear losses.
A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating wave approximations and the adiabatic approximation. Using this formalism we deduce both the conditional and unconditional state of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions stressing the import…
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining -internal- fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expres…
Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this paper we report its first experimental demonstration that well agrees with the theory taking into account time delays and losses in the coherent feedback loop. The results clarify both the benefit and the limitation of coherent feedback control in a practical situation.
We implement the squeezing operation as a genuine quantum gate, deterministically and reversibly acting `online' upon an input state no longer restricted to the set of Gaussian states. More specifically, by applying an efficient and robust squeezing operation for the first time to non-Gaussian states, we demonstrate a two-way conversion between a particle-like single-photon state and a wave-like superposition of coherent states. Our squeezing gate is reliable enough to preserve the negativities of the corresponding Wigner functions. This demonstration represents an important and necessary step…
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 study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for Hadamard gate when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.
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…
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we …
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We find the fidelity for Hadamard gate and compute the purity of the final state when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate that in contradiction to the case of the systematic control errors the stochastic ones lead to decoherence of the final state. In the small errors limit we derive a simple formulae connecting the gate fidelity and the purity of the final state.
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…
In recent experiments, the re-thermalization time of the mechanical resonator is stated as the limiting factor for quantum applications of optomechanical systems. To explain the origin of this limitation, an analytical nonlinear investigation supported by the recent successful experimental laser cooling parameters is carried out in this work. To this end, the effects of geometrical and the optical nonlinearities on the squeezing are studied and are in a good agreement with the experimental results. It appears that highly squeezed state are generated where these nonlinearities are minimized and…
We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase-matched, resulting in exponential enhancement of squeezing. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. A simplified model indicates ~10 dB of squeezing should be achievable with current laboratory parameters.
We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon is not critical as it is independent of the system parameters and, in particular, of the existence of bifurcations. This result is a consequence of the spatial symmetry breaking introduced by the dissipative structure. Effects that could degrade the squeezing level are considered.
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…
A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the non-classical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.
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 propose an all-optical approach to achieve optical nonreciprocity on a chip by quantum squeezing one of two coupled resonator modes. By parametric pumping a nonlinear resonator unidirectionally with a classical coherent field, we squeeze the resonator mode in a selective direction due to the phase-matching condition, and induce a chiral photon interaction between two resonators. Based on this chiral interresonator coupling, we achieve an all-optical diode and a three-port quasi-circulator. By applying a second squeezed-vacuum field to the squeezed resonator mode, our nonreciprocal device al…
We show that squeezing is an irreducible resource which remains invariant under transformations by linear optical elements. In particular, we give a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled sta…
Linear optical realizations of Bell state measurement (BSM) on two single-photon qubits succeed with probability $p_s$ no higher than $0.5$. However pre-detection quadrature squeezing, i.e., quantum noise limited phase sensitive amplification, in the usual linear-optical BSM circuit, can yield ${p_s \approx 0.643}$. The ability to achieve $p_s > 0.5$ has been found to be critical in resource-efficient realizations of linear optical quantum computing and all-photonic quantum repeaters. Yet, the aforesaid value of $p_s > 0.5$ is not known to be the maximum achievable using squeezing, thereby lea…
Intensity squeezing, i.e., photon number fluctuations below the shot noise limit, is a fundamental aspect of quantum optics and has wide applications in quantum metrology. It was predicted in 1979 that the intensity squeezing could be observed in resonance fluorescence from a two-level quantum system. Yet, its experimental observation in solid states was hindered by inefficiencies in generating, collecting and detecting resonance fluorescence. Here, we report the intensity squeezing in a single-mode fibre-coupled resonance fluorescence single-photon source based on a quantum dot-micropillar sy…
Quantum projection noise will soon limit the best achievable precision of optical atomic clocks based on lattice-confined neutral atoms. Squeezing the collective atomic pseudo-spin via measurement of the clock state populations during Ramsey interrogation suppresses the projection noise. We show here that the lattice laser field can be used to perform ideal quantum non-demolition measurements without clock shifts or decoherence and explore the feasibility of such an approach in theory with the lattice field confined in a ring-resonator. Detection of the motional sideband due to the atomic vibr…
We present a scheme for generating and manipulating three-mode squeezed states with genuine tripartite entanglement by injecting single-mode squeezed light into an array of coupled optical waveguides. We explore the possibility to selectively generate single-mode squeezing or multimode squeezing at the output of an elliptical waveguides array, determined solely by the input light polarization. We study the effect of losses in the waveguides array and show that quantum correlations and squeezing are preserved for realistic parameters. Our results show that arrays of optical waveguides are suita…
By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys. Rev. A {\bf 71}, 042308 (2005) \cite{Filip05.pra}), we experimentally demonstrate a universal, deterministic and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a …
Optical satellite links open up new prospects for realizing quantum physical experiments over unprecedented length scales. We analyze and affirm the feasibility of detecting quantum squeezing in an optical mode with homodyne detection of only one bit resolution, as is found in satellites already in orbit. We show experimentally that, in combination with a coherent displacement, a binary homodyne detector can still detect quantum squeezing efficiently even under high loss. The sample overhead in comparison to non-discretized homodyne detection is merely a factor of 3.3.
The detection of kilohertz-band gravitational waves promises discoveries in astrophysics, exotic matter, and cosmology. To improve the kilohertz quantum noise-limited sensitivity of interferometric gravitational-wave detectors, we investigate nondegenerate internal squeezing: optical parametric oscillation inside the signal-recycling cavity with distinct signal-mode and idler-mode frequencies. We use an analytic Hamiltonian model to show that this stable, all-optical technique is tolerant to decoherence from optical detection loss and that it, with its optimal readout scheme, is feasible for b…
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the particle production though being reversible in time. We associate this state a non-dissipative classical fluctuations and study their trigger to develop the coherent state which can be classical if sufficiently developed. The Schwinger-Keldysh in-in formalism yields the classical Langevin equation including the fluctuation force which faithfully reflects th…
Cavity-QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, an…
We study the effect of photothermal fluctuations on squeezed states of light through the photo-refractive effect and thermal expansion in a degenerate optical parametric amplifier (OPA). We also discuss the effect of the photothermal noise in various cases and how to minimize its undesirable consequences. We find that the photothermal noise in the OPA introduces a significant amount of noise on phase squeezed beams, making them less than ideal for low frequency applications such as gravitational wave (GW) interferometers, whereas amplitude squeezed beams are relatively immune to the phototherm…
We demonstrate an unconditional high-fidelity teleporter capable of preserving the broadband entanglement in an optical squeezed state. In particular, we teleport a squeezed state of light and observe $-0.8 \pm 0.2$dB of squeezing in the teleported (output) state. We show that the squeezing criterion translates directly into a sufficient criterion for entanglement of the upper and lower sidebands of the optical field. Thus, this result demonstrates the first unconditional teleportation of broadband entanglement. Our teleporter achieves sufficiently high fidelity to allow the teleportation to b…
The spectra and generalized eigenfunctions of the hyperbolic and parabolic generators of the standard representation of SU(1,1) in the one-mode boson Hilbert space are derived. The eigenfunctions are given in three different forms, corresponding to the coordinate, photon number, and Fock-Bargmann representations of the state vectors. The possible spectra of general second degree Hamiltonians are determined. Some corresponding results in the two-mode case are also given. - In the Appendix we prove completeness and orthonormality relations for the polynomials giving the number representation exp…
