We develop a systematic theory of quantum fluctuations in the driven parametric oscillator (OPO), including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, in this non-equilibrium quantum phase-transition. In particular, we compute the squeezing spectrum near threshold, and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semiclassical theory.
We address the use of optical parametric oscillator (OPO) to counteract phase-noise in quantum optical communication channels, and demonstrate reduction of phase diffusion for coherent signals travelling through a suitably tuned OPO. In particular, we theoretically and experimentally show that there is a threshold value on the phase-noise, above which OPO can be exploited to squeeze phase noise. The threshold depends on the energy of the input coherent state, and on the relevant parameters of the OPO, i.e. gain and input/output and crystal loss rates.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially non-degenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of OAM modes is mapped on an orbital Poincare sphere, and the modes position on the sphere is spanned by the three orbital parameters. Using the non-degenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere…
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…
Experimental investigation of amplitude and phase quantum correlations in a type II OPO above threshold: from the non-degenerate to the degenerate operation
We report a 65MHz-bandwidth triangular-shaped optical parametric oscillator (OPO) for squeezed vacuum generation at 860nm. The triangle structure of our OPO enables the round-trip length to reach 45mm as a ring cavity, which provides a counter circulating optical path available for introducing a probe beam or generating another squeezed vacuum. Hence our OPO is suitable for the applications in high-speed quantum information processing where two or more squeezed vacua form a complicated interferometer, like continuous-variable quantum teleportation. With a homemade, broadband and low-loss homod…
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 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 report generation and measurement of a squeezed vacuum from a semi-monolithic Fabry-Perot optical parametric oscillator (OPO) up to 100 MHz at 1550 nm. The output coupler of the OPO is a flat surface of a nonlinear crystal with partially reflecting coating, which enables direct coupling with waveguide modules. Using the OPO, we observed 6.2dB of squeezing at 2 MHz and 3.0 dB of squeezing at 100 MHz. The OPO operates at the optimal wavelength to minimize propagation losses in silica waveguides and looks towards solving a bottleneck of downsizing these experiments: that of coupling between a …
We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes, either spatial or temporal, generates both below and above threshold a multimode non-classical state of light consisting of squeezed vacuum states in all the non-oscillating modes. We confirm this prediction by an experiment dealing with the degenerate TEM$_{01}$ and TEM$_{10}$ modes. We show the conservation of non-classical properties when the threshold is crossed. The experiment is made possible by the implementation of a new method to lock the relative phase of the pump and the injected beam.
We present the first measurement of two-mode squeezing between the twin beams produced by a doubly resonant optical parameter oscillator (OPO) in above threshold operation, based on parametric amplification by non degenerate four wave mixing with rubidium $^{85}$Rb. We demonstrate a maximum intensity difference squeezing of -2.7 dB (-3,5 dB corrected for losses) with a pump power of 285 mW and an output power of 12 mW for each beam, operating close to the D1 line of Rb atoms. The possibility to use open cavities combined with the high gain media can provide a strong level of noise compression,…
A particularly simple setup is introduced to study the influence of time-delayed coherent feedback on the optical squeezing properties of the degenerate parametric amplifier (DPA). The possibility for significantly enhanced squeezing is demonstrated both on resonance and in sidebands, at a reduced pump power compared to the case without feedback. We study a broad range of operating parameters and their influence on the characteristic squeezing of the system. A classical analysis of the system dynamics reveals the connection between the feedback-modified landscape of stability and enhanced sque…
Polarization squeezing is shown to occur in non-degenerate parametric amplification of coherent light and the degree of squeezing at interaction time $T$ can be as large as $1-e^{-2T}$. This gives $86.4\%$ polarization squeezing for $T=1$ and $98.2\%$ for $T=2$. One simple case when this occurs is on taking initially plane polarized light having equal amplitudes in the two modes that finally has equal intensities of two circular polarizations. This suggest the experimental settings of parameters to achieve this extent of polarization squeezing in coherent light.
Spin squeezing is one of the most attractive methods for realizing high-precision metrology. In this paper, we propose a protocol for generating spin squeezing in an atomic ensemble via a fully quantum degenerate parametric amplifier. We discuss the properties of generating spin squeezing with and without driving the pump cavity. Numerical simulation results show that the generated spin squeezing strength is sizable, and is able to be comparable to that obtained using a two-axis twisting (TAT) model. Moreover, we demonstrate that the protocol is experimentally feasible by introducing the corre…
We study polarization squeezing of a light beam initially in the coherent state using the nonlinear interaction hamiltonian $ H=k\big(\hat a_{x}^{\dagger2}+{\hat a_{x}}^2\big)$. For the degree of polarization squeezing, we use a definition written in the final form by the authors and also used in earlier papers. We find that the polarization squeezing can be very high and the degree of polarization squeezing can be less than unity by a very small amount. We achieve the polarization squeezing even for very low beam intensity under some conditions involving phase angles in the polarization modes…
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity…
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.
In quantum information systems it is of particular interest to consider the best way in which to use the non-classical resources consumed by that system. Quantum communication protocols are integral to quantum information systems and are amongst the most promising near-term applications of quantum information science. Here we show that a multiplexed, digital quantum communications system supported by comb of vacuum squeezing has a greater channel capacity per photon than a source of broadband squeezing with the same analogue bandwidth. We report on the time-resolved, simultaneous observation o…
Quantized descriptions of nonlinear-optical processes can be relevant from the perspective of developing novel nonclassical sources of light. As a special case, it is useful to characterize light emitted by classically driven systems, since the excitations in many practical cases are laser beams. As a material model, we choose a two-level system. In an earlier work, we investigated photon statistics and intermodal cross-correlations Phys. Rev. A 104(3):033703, (2021), and noted that squeezing is primarily present in specific sets of parameters, corresponding to the degeneracy of hyper-Raman li…
True random number generators (RNGs) are desirable for applications ranging from cryptogra- phy to computer simulations. Quantum phenomena prove to be attractive for physical RNGs due to their fundamental randomness and immunity to attack [1]- [5]. Optical parametric down conversion is an essential element in most quantum optical experiments including optical squeezing [9], and generation of entangled photons [10]. In an optical parametric oscillator (OPO), photons generated through spontaneous down conversion of the pump initiate the oscillation in the absence of other inputs [11, 12]. This q…
We propose and analyse a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyse the threshold behaviour, showing how the normal OPO threshold is changed by the addition of the SHG …
We demonstrate atomic filtering of frequency-degenerate photon pairs from a sub-threshold optical parametric oscillator (OPO). The filter, a modified Faraday anomalous dispersion optical filter (FADOF), achieves 70% peak transmission simultaneous with 57 dB out-of-band rejection and a 445 MHz transmission bandwidth. When applied to the OPO output, only the degenerate mode, containing one-mode squeezed vacuum, falls in the filter pass-band; all other modes are strongly suppressed. The high transmission preserves non-classical continuous-variable features, e.g. squeezing or non-gaussianity, whil…
Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator
Adama Science and Technology University（阿达马科学与技术大学）；Khalifa University of Science and Technology（哈利法科学技术大学）；Durban University of Technology（德班理工大学）；Arba Minch University（阿尔巴明奇大学）
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.
Squeezed light is a quantum resource that can improve the sensitivity of optical measurements. However, existing sources of squeezed light generally require high powers and are not amenable to portability. Here we theoretically investigate an alternative technique for generating squeezing using degenerate four-wave-mixing in atomic vapors. We show that by minimizing excess noise, this technique has the potential to generate measurable squeezing with low powers attainable by a small diode laser. We suggest experimental techniques to reduce excess noise and employ this alternative nonlinear opti…
Using a general Hamiltonian treatment, we theoretically study the generation of degenerate quadrature squeezing in a dual-pumped integrated microring resonator coupled to a waveguide. Considering a dual-pump four-wave mixing configuration in an integrated $\text{Si}_3\text{N}_4$ platform, and following the coupled-mode theory approach, we investigate the effects of parasitic quantum nonlinear optical processes on the generation of squeezed light. Considering five resonance modes in this approach allows us to include the most important four-wave mixing processes involved in such a configuration…
We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in $k$-space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the …
While the squeezing of a propagating field can, in principle, be made arbitrarily strong, the cavity-field squeezing is subject to the well-known 3 dB limit, and thus has limited applications. Here, we propose the use of a fully quantum degenerate parametric amplifier (DPA) to beat this squeezing limit. Specifically, we show that by {\it simply} applying a two-tone driving to the signal mode, the pump mode can, {\it counterintuitively}, be driven by the photon loss of the signal mode into a squeezed steady state with, in principle, an {\it arbitrarily high} degree of squeezing. Furthermore, we…
The theory of quantum feedback networks has recently been developed with the aim of showing how quantum input-output components may be connected together so as to control, stabilize or enhance the performance of one of the subcomponents. In this paper we show how the degree to which an idealized component (a degenerate parametric amplifier in the strong-coupling regime) can squeeze input fields may be enhanced by placing the component in-loop in a simple feedback mechanism involving a beam splitter. We study the spectral properties of output fields, placing particular emphasis on the elastic a…
Hybrid non-degenerate parametric amplifier for a microwave cavity mode and an NV ensemble
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿基谢尔理论物理研究所，NSC KIPT）；Advanced Photonics and Electronics Division, U.S. Army DEVCOM Army Research Laboratory（先进光子学与电子学部门，美国陆军DEVCOM陆军研究实验室）；Department of Physics, University of Massachusetts at Boston（马萨诸塞大学波士顿分校物理系）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（卡尔齐诺夫哈尔科夫国立大学教育与研究所“物理与技术学院”）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气与计算机工程系）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
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…
Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region imm…
