Generation of squeezed states by parametric down conversion

Wavelength-tunable and high-heralding-efficiency quantum photon source in a birefringent phase-matched lithium niobate waveguide

Lithium niobate (LN) is a birefringent material, where the strong birefringence thermo-optic effect is promising for the generation of a quantum photon source with a widely tunable wavelength. Here, we demonstrate birefringent phase matching in a 20-mm-long waveguide fabricated on a 5-μm-thick x-cut lithium niobate on insulator (LNOI). The waveguide is deviated from the optical axis of LN by an angle of 53.5∘, enabling the phase matching between telecom and visible wavelengths. The phase-matching wavelength of this device can be thermally tuned with rate of 0.6 nm/K. We demonstrate the type-1 spontaneous parametric downconversion to generate photon pairs with a brightness of 4.7 MHz/mW and a coincidence-to-accidental ratio of up to 2.8 × 105. Furthermore, the heralded single photon is obtained from the photon pair with an efficiency of 13.8% and a count rate of up to 37.8 kHz.

Precise wavelength alignment of second-harmonic generation in thin-film lithium niobate resonators

Second-harmonic generation (SHG) plays a significant role in modern photonic technology. Integrated photonic resonators fabricated with thin-film lithium niobate can achieve ultrahigh efficiencies by combining small mode volumes with high material nonlinearity. Cavity-enhanced SHG requires accurate phase and frequency matching conditions, where fundamental and second-harmonic wavelengths are both on resonance. However, this double-resonance condition can typically be realized only at a fixed random wavelength due to the high sensitivity of photonic resonances to the device geometry and fabrication variations. Here, we propose a novel method that can achieve the double-resonance condition over a large wavelength range. We combine thermal-optic and electro-optic (EO) effects to realize the separate tuning of fundamental and second-harmonic resonances. We demonstrated that the optimum SHG efficiency can be maintained over a wavelength range that exceeds the limit achievable with only thermal tuning. With this flexible tuning capability, we further show the precise alignment of SHG wavelengths of two separate thin-film lithium niobate resonators without sacrificing efficiencies.

Concurrent Spin Squeezing and Light Squeezing in an Atomic Ensemble

Squeezed spin states and squeezed light are both key resources for quantum metrology and quantum information science, but have been separately investigated in experiments so far. Simultaneous generation of these two types of quantum states in one experiment setup is intriguing but remains a challenging goal. Here, we propose a novel protocol based on judiciously engineered symmetric atom-light interaction, and report proof-of-principle experimental results of concurrent spin squeezing of 0.61±0.09  dB and light squeezing of 0.65_{-0.10}^{+0.11}  dB in a hot atomic ensemble. The squeezing process is deterministic, yielding fixed squeezing directions for both the light field and the collective atomic spin. Furthermore, the squeezed light modes lie in the multiple frequency sidebands of a single spatial mode. This new type of dual squeezed state is applicable for quantum enhanced metrology and quantum networks. Our method can be extended to other quantum platforms such as optomechanics, cold atoms, and trapped ions.

Squeezing enhancement by suppression of noise through a resonant interferometric coupler

We propose an integrated resonant structure to enhance squeezing by dual-pump spontaneous four-wave mixing (SFWM) while simultaneously suppressing parametric noise due to parasitic processes. The structure relies on a resonant interferometric coupler that allows one to engineer the field enhancement on-demand in the spectral region of interest. We analyze the different configurations in which the structure can operate, and we calculate the generated squeezing. We show that our device can overcome the intrinsic squeezing limit of a single-ring resonator.

Improving the Stationary Entanglement of a Laguerre-Gaussian Cavity Mode with a Rotating Mirror via Nonlinear Cross-Kerr Interactions and Parametric Interactions

Quantum entanglement is essential in performing many quantum information tasks. Here, we theoretically investigate the stationary entanglement between a Laguerre-Gaussian (LG) cavity field and a rotating end mirror in an LG-cavity optorotational system with a nonlinear cross-Kerr (CK) interaction and a degenerate optical parametric amplifier (OPA). We calculate the logarithmic negativity of the system to quantify the stationary entanglement. We examine the influence of various system parameters such as the cavity detuning, the strength of the nonlinear CK interaction, the parametric gain and phase of the OPA, the power of the input Gaussian laser, the topological charge of the LG-cavity field, the mass of the rotating end mirror, and the ambient temperature on the stationary entanglement. Under the combined effect of the nonlinear CK interaction and the OPA, we find that the stationary entanglement can be substantially enhanced at lower Gaussian laser powers, smaller topological charges of the LG-cavity field, and larger masses of the rotating end mirror. We show that the combination of the nonlinear CK interaction and the OPA can make the stationary entanglement more robust against the ambient temperature.

Digital Homodyne and Heterodyne Detection for Stationary Bosonic Modes

Homo- and heterodyne detection are fundamental techniques for measuring propagating electromagnetic fields. However, applying these techniques to stationary fields confined in cavities poses a challenge. As a way to overcome this challenge, we propose to use repeated indirect measurements of a two-level system interacting with the cavity. We demonstrate numerically that the proposed measurement scheme faithfully reproduces measurement statistics of homo- or heterodyne detection. The scheme can be implemented in various physical architectures, including circuit quantum electrodynamics. Our results pave the way for implementation of quantum algorithms requiring linear detection of stationary modes, including quantum verification protocols.

A review of gallium phosphide nanophotonics towards omnipotent nonlinear devices

Gallium phosphide (GaP) has been increasingly prioritized, fueled by the enormous demands in visible light applications such as biomedical and quantum technologies. GaP has garnered tremendous attention in nanophotonics thanks to its high refractive index, indirect bandgap width of 2.26 eV, lattice perfectly matched with silicon, and omnipotent and competitive nonlinear optical properties. Herein, we review the progress and application of GaP in nanoscale devices over the past two decades. The material properties of bulk GaP are first listed, followed by a summary of the methodologies for fabricating nanoscale devices and related integration techniques. Then, we digest the operational mechanisms across different GaP-based devices on their optical linear responses. Following this, we categorize the GaP nonlinear optical effects into multiple aspects including second-harmonic generation, four-wave mixing, Kerr optical frequency combs, etc. Ultimately, we present a perspective on GaP nanophotonics in the context of coexisting and competing modes of various nonlinear effects. We believe that a comprehensive overview of unique GaP will propel these nanophotonic devices toward a mature state, underpinning foundational understanding and leveraging practical innovations.

Experimental enhancement of six-beam quantum squeezing by phase-sensitive cascaded four-wave mixing processes

We experimentally realize the enhancement of six-beam quantum squeezing by utilizing a six-beam phase-sensitive amplifier (PSA) based on cascaded four-wave mixing processes. Compared to the intensity-difference squeezing (IDS) of about 5.03 or 5.09 dB generated by a six-beam phase-insensitive amplifier (PIA), the six-beam IDS generated by the six-beam PSA is enhanced to about 6.64 dB. The intrinsic interference of six-beam PSA induces this enhancement. In addition, we investigate the dependence of IDS generated by the six-beam PSA and PIAs on the powers of two pump beams. The results show that the IDS of six-beam PSA is always better than that of six-beam PIAs. Our scheme may find potential applications in high-precision multi-parameter quantum metrology.

Parametric magnon transduction to spin qubits

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Single-mode squeezed-light generation and tomography with an integrated optical parametric oscillator

Quantum optical technologies promise advances in sensing, computing, and communication. A key resource is squeezed light, where quantum noise is redistributed between optical quadratures. We introduce a monolithic, chip-scale platform that exploits the χ(2) nonlinearity of a thin-film lithium niobate (TFLN) resonator device to efficiently generate squeezed states of light. Our system integrates all essential components-except for the laser and two detectors-on a single chip with an area of one square centimeter, reducing the size, operational complexity, and power consumption associated with conventional setups. Using the balanced homodyne measurement subsystem that we implemented on the same chip, we measure a squeezing of 0.55 decibels and an anti-squeezing of 1.55 decibels. We use 20 milliwatts of input power to generate the parametric oscillator pump field by using second harmonic generation on the same chip. Our work represents a step toward compact and efficient quantum optical systems posed to leverage the rapid advances in integrated nonlinear and quantum photonics.

Single-frequency optical parametric oscillator intracavity-pumped by a visible VECSEL for low-noise down-conversion to 1.55 µm

We report, to the best of our knowledge, the first optical parametric oscillator (OPO) pumped by a visible AlGaInP-based vertical-external-cavity surface-emitting laser (VECSEL). Tunable emission over 1155-1300 nm in the signal and 1474-1718 nm in the idler are observed by temperature adjustment of a 40 mm-long 5%-MgO:PPLN crystal intracavity-pumped at 690 nm. When optimized for low oscillation threshold, and by implementing resonant idler output-coupling (TOC = 1.7%), extracted output powers of 26.2 mW (signal) and 5.6 mW (idler; one-way) are measured, corresponding to a total down-conversion efficiency and extraction efficiency of 70.2% and 43%, respectively. Further, a total down-conversion efficiency of 72.1% is achieved in the absence of idler output-coupling. Of particular interest for high-precision applications, including quantum optics experiments and squeezed light generation, high stability and single-frequency operation are also demonstrated. We measure RMS stabilities of 0.4%, 1.8% and 2.3% for the VECSEL fundamental, signal and idler, with (resolution-limited) frequency linewidths of 2.5 MHz (VECSEL) and 7.5 MHz (signal and idler).

Near-resonant twin-beam generation from degenerate four-wave mixing in hot 133Cs vapor enabled by field-dressed energy levels

Squeezed light near an atomic resonance is beneficial for efficient atom-light quantum interfaces. It is desirable but challenging to directly generate in atoms due to excess noise from spontaneous emission and reabsorption. Here, we report on the use of energy-level modulation to actively control atomic coherence and interference in degenerate four-wave mixing (DFWM) and then to enhance the DFWM gain process for the generation of near-resonant squeezed twin beams. With this technique, we obtain a -2.6 dB intensity-difference squeezing detuned 100 MHz from the D1 F = 4 to F' = 4 transition of 133Cs.

Quantum correlation in a nano-electro-optomechanical system enhanced by an optical parametric amplifier and Coulomb-type interaction

In this paper, we investigated the quantum correlation of nano-electro-optomechanical system enhanced by an optical parametric amplifier (OPA) and Coulomb-type interaction. In particular, we consider a hybrid system consisting of a cavity and two charged mechanical oscillators with an OPA, where the optical cavity mode is coupled with a charged mechanical oscillator via radiation pressure, and the two charged mechanical oscillators are coupled through a Coulomb interaction. We use logarithmic negativity to quantify quantum entanglement, and quantum discord to measure the quantumness correlation between the two mechanical oscillators. We characterize quantum steering using the steerability between the two mechanical oscillators. Our results show that the presence of OPA and strong Coulomb coupling enhances the quantum correlations between the two mechanical oscillators. In addition, Coulomb interactions are more prominent in quantum correlations. Besides, in the presence of OPA, the maximum amount of quantum entanglement, quantum steering, and quantum discord were achieved between the two mechanical oscillators is greater than in the absence of OPA. Moreover, a proper phase choice of the optical field driving the OPA enhances quantum correlations under suitable conditions. We obtain quantum entanglement confines quantum steering and quantum discord beyond entanglement. Furthermore, quantum entanglement, quantum steering, and quantum discord decrease rapidly with increasing temperature as a result of decoherence. In addition, quantum discord persists at higher temperature values, although the quantum entanglement between the systems also vanishes completely. Our proposed scheme enhances quantum correlation and proves robust against fluctuations in the bath environment. We believe that the present scheme of quantum correlation provides a promising platform for the realization of continuous variable quantum information processing.

On the equivalence between squeezing and entanglement potential for two-mode Gaussian states

The maximum amount of entanglement achievable under passive transformations by continuous-variable states is called the entanglement potential. Recent work has demonstrated that the entanglement potential is upper-bounded by a simple function of the squeezing of formation, and that certain classes of two-mode Gaussian states can indeed saturate this bound, though saturability in the general case remains an open problem. In this study, we introduce a larger class of states that we prove saturates the bound, and we conjecture that all two-mode Gaussian states can be passively transformed into this class, meaning that for all two-mode Gaussian states, entanglement potential is equivalent to squeezing of formation. We provide an explicit algorithm for the passive transformations and perform extensive numerical testing of our claim, which seeks to unite the resource theories of two characteristic quantum properties of continuous-variable systems.

Integrated quantum optical phase sensor in thin film lithium niobate

The quantum noise of light, attributed to the random arrival time of photons from a coherent light source, fundamentally limits optical phase sensors. An engineered source of squeezed states suppresses this noise and allows phase detection sensitivity beyond the quantum noise limit (QNL). We need ways to use quantum light within deployable quantum sensors. Here we present a photonic integrated circuit in thin-film lithium niobate that meets these requirements. We use the second-order nonlinearity to produce a squeezed state at the same frequency as the pump light and realize circuit control and sensing with electro-optics. Using 26.2 milliwatts of optical power, we measure (2.7 ± 0.2)% squeezing and apply it to increase the signal-to-noise ratio of phase measurement. We anticipate that photonic systems like this, which operate with low power and integrate all of the needed functionality on a single die, will open new opportunities for quantum optical sensing.

Quantum-Enhanced Absorption Spectroscopy with Bright Squeezed Frequency Combs

Absorption spectroscopy is a widely used technique that permits the detection and characterization of gas species at low concentrations. We propose a sensing strategy combining the advantages of frequency modulation spectroscopy with the reduced noise properties accessible by squeezing the probe state. A homodyne detection scheme allows the simultaneous measurement of the absorption at multiple frequencies and is robust against dispersion across the absorption profile. We predict a significant enhancement of the signal-to-noise ratio that scales exponentially with the squeezing factor. An order of magnitude improvement beyond the standard quantum limit is possible with state-of-the-art squeezing levels facilitating high precision gas sensing.

Experimental realization of multimode nonlinear parametric amplification from cascading four-wave mixing of dressed atoms

The nonlinear parametric process is of great significance for achieving high-quality coherent optical signals and quantum correlated photons. With the development of classical and quantum information processing, the study of the properties of parametric processes is evolving in complex scenarios of multimode, which is limited in conventional nonlinear media due to strict phase matching, e.g. nonlinear crystals. Here we study the dressing-energy-level-cascaded four-wave mixing process to generate multimode optical parametric signals. Via cascading double-Λ type configuration of ⁸⁵Rb D₁ line, the non-degenerate energy-level-cascaded FWM is constructed to generate multimode self-parametric amplification. Moreover, with the dressing effects based on atomic coherence, the spatial and frequency multimode characteristics of energy-level-cascaded FWM parametric amplification, i.e., the modes number and pattern, are actively modulated by the pump fields detuning. Also, the spatial modes from the coupling of two coexisting spontaneous parametric FWMs can be controlled to reach tremendous scalability via the atomic coherence and Kerr non-linearity. The atomic coherence effects and unique phase-matching symmetry nature allow flexible modulation of the multimode property of the generated parametric signals within a nonlinear device, which paves a way for multimode classical and quantum information processing.

Squeezed states generation by nonlinear plasmonic waveguides: a novel analysis including loss, phase mismatch and source depletion

In this article, a full numerical method to study the squeezing procedure through second harmonic generation process is proposed. The method includes complex nonlinear coupling coefficient, phase mismatch, and pump depletion. Attention has been also paid to the effects of accumulated noises in this work. The final form of the numerical formula seems to be much simpler than the analytical solutions previously reported. The function of this numerical method shows that it works accurately for different mechanisms of squeezed state generations and does not suffer from instabilities usually encountered even for non-uniform, coarse steps. The proposed method is used to examine the squeezing procedure in an engineered nonlinear plasmonic waveguide. The results show that using the nonlinear plasmonic waveguide, it is possible to generate the squeezed states for the pump and the second harmonic modes with high efficiency in a propagation length as short as 2 mm which is much shorter than the needed length for the traditional nonlinear lithium niobate- based optical waveguides being of the order of 100 mm. This new method of squeezed states generation may find applications in optical communication with a noise level well below the standard quantum limit, in quantum teleportation, and in super sensitive interferometry.

Optimizing the generation of polarization squeezed light in nonlinear optical fibers driven by femtosecond pulses

Bright squeezed light can be generated in optical fibers utilizing the Kerr effect for ultrashort laser pulses. However, pulse propagation in a fiber is subject to nonconservative effects that deteriorate the squeezing. Here, we analyze two-mode polarization squeezing, which is SU(2)-invariant, robust against technical perturbations, and can be generated in a polarization-maintaining fiber. We perform a rigorous numerical optimization of the process and the pulse parameters using our advanced model of quantum pulse evolution in the fiber that includes various nonconservative effects and real fiber data. Numerical results are consistent with experimental results.

Multistep Two-Copy Distillation of Squeezed States via Two-Photon Subtraction

Squeezed states are nonclassical resources of quantum cryptography and photonic quantum computing. The higher the squeeze factor, the greater the quantum advantage. Limitations are set by the effective nonlinearity of the pumped medium and energy loss on the squeezed states produced. Here, we experimentally analyze for the first time the multistep distillation of squeezed states that in the ideal case can approach an infinite squeeze factor. Heralded by the probabilistic subtraction of two photons, the first step increased our squeezing from 2.4 to 2.8 dB. The second step was a two-copy Gaussification, which we emulated. For this, we simultaneously measured orthogonal quadratures of the distilled state and found by probabilistic postprocessing an enhancement from 2.8 to 3.4 dB. Our new approach is able to increase the squeeze factor beyond the limit set by the effective nonlinearity of the pumped medium.

Direct Measurement of Higher-Order Nonlinear Polarization Squeezing

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

Electro-Optical Sampling of Single-Cycle THz Fields with Single-Photon Detectors

Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing.

Optical-cavity mode squeezing by free electrons

The generation of nonclassical light states bears a paramount importance in quantum optics and is largely relying on the interaction between intense laser pulses and nonlinear media. Recently, electron beams, such as those used in ultrafast electron microscopy to retrieve information from a specimen, have been proposed as a tool to manipulate both bright and dark confined optical excitations, inducing semiclassical states of light that range from coherent to thermal mixtures. Here, we show that the ponderomotive contribution to the electron-cavity interaction, which we argue to be significant for low-energy electrons subject to strongly confined near-fields, can actually create a more general set of optical states, including coherent and squeezed states. The postinteraction electron spectrum further reveals signatures of the nontrivial role played by A 2 terms in the light-matter coupling Hamiltonian, particularly when the cavity is previously excited by either chaotic or coherent illumination. Our work introduces a disruptive approach to the creation of nontrivial quantum cavity states for quantum information and optics applications, while it suggests unexplored possibilities for electron beam shaping.

Enhancement of Optomechanical Squeezing of Light Using the Optical Coherent Feedback

A coherent feedback scheme is used to enhance the degree of squeezing of the output field in a cavity optomechanical system. In the feedback loop, a beam splitter (BS) plays the roles of both a feedback controller and an input-output port. To realize effective enhancement, the output quadrature should take the same form as the input quadrature, and the system should operate at the deamplification situation in the meantime. This can be realized by choosing an appropriate frequency-dependent phase angle for the generalized quadrature. Additionally, both the transmissivity of the BS and the phase factor induced by time delays in the loop affect optical squeezing. For the fixed frequency, the optimal values of transmissivity and phase factor can be used to achieve the enhanced optical squeezing. The effect of optical losses on squeezing is also discussed. Optical squeezing is degraded by the introduced vacuum noise owing to the inefficient transmission in the loop. We show that the enhancement of squeezing is achievable with the parameters of the current experiments.

Optimal bright multimode quantum squeezing via multi-seeding energy-level cascaded four-wave mixing

Quantum Squeezing is one of the most important quantum resources in quantum optics and quantum information. In particular, multimode quantum squeezing, with ultra-low quantum fluctuations and quantum correlations amongst many optical modes, is essential for realizing multipartite entanglement and quantum precision measurements. In this paper, we propose an all-optically controlled scheme to generate three-mode bright quantum correlated beams from energy-level cascaded four-wave mixing (ELC-FWM). By using a linear modes transform approach, the input-output relation and the covariance matrix of the produced states are obtained. Moreover, single-, double- and triple-seeding conditions are investigated to measure the quantum squeezing properties. We find that various permutations of two- and three-mode quadrature squeezing can be generated and optimized to reach the corresponding limit, via only modulating the ratio of the multiple seeds, without need of any post-operating linear optics, e.g., beam splitters. Such weak seeding light controlled scheme suggests the modulation and the optimization of multimode quantum states might be operated at photons-level, providing a reconfigurable and integrated strategy for complex quantum information processing and quantum metrology.

Intensity instability and correlation in amplified multimode wave mixing

The dynamics of optical nonlinearity in the presence of gain and feedback can be complex leading to chaos in certain regimes. Temporal, spectral, spatial, or polarization instability of optical fields can emerge from chaotic response of an optical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ^{(2)}$$\end{document}χ(2) or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ^{(3)}$$\end{document}χ(3) nonlinear medium placed between two cavity mirrors or before a single feedback mirror. The complex mode dynamics, high-order correlations, and transition to instability in these systems are not well known. We consider a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ^{(3)}$$\end{document}χ(3) medium with amplified four-wave mixing process and study noise and correlation between multiple optical modes. Although individual modes show intensity instability, we observe relative intensity noise reduction close to the standard quantum noise, limited by the camera speed. We observe a relative noise reduction of more than 20 dB and fourth-order intensity correlation between four spatial modes. More than 100 distinct correlated quadruple modes can be generated using this process.

Efficient Quadrature Squeezing from Biexcitonic Parametric Gain in Atomically Thin Semiconductors

Modification of electromagnetic quantum fluctuations in the form of quadrature squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity makes it possible to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with conventional third-order nonlinear materials that rely on far off-resonant nonlinearities. Furthermore, the squeezing bandwidth is found to be in the range of several meV. These results identify atomically thin semiconductors as a promising candidate for on-chip squeezed-light sources.

Cubic nonlinear squeezing and its decoherence

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators below threshold for all possible up-to-quadratic Hamiltonians, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often more vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. Therefore, a stability of nonlinear squeezing is essential. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters which can be optimized and adjusted to achieve the maximal robustness for the potential applications.

Squeezed light generated with hyperradiance without nonlinearity

We propose that the squeezed light accompanied by hyperradiance is induced by quantum interference in a linear system consisting of a high-quality optical cavity and two coherently driven two-level qubits. When two qubits are placed in the cavity with a distance of integer multiple and one-half of wavelengths (i.e., they have the opposite coupling coefficient to the cavity), we show that squeezed light is generated in the hyperradiance regime under the conditions of strong coupling and weak driving. Simultaneously, Klyshko's criterion alternates up and down at unity when the photon number is even or odd. Moreover, the orthogonal angles of the squeezed light can be controlled by adjusting the frequency detuning between the driving field and the qubits. It can be implemented in a variety of quantum systems, including but not limited to two-level systems such as atoms, ions, quantum dots in single-mode cavities.

Generation of Long-Term Stable Squeezed Vacuum States Using Dither-Locking Technique

We report the generation of long-term stable squeezed vacuum states at 1064 nm using a degenerate optical parametric amplifier (DOPA) with a periodically poled KTiOPO4 crystal (PPKTP). The OPA is pumped by a 532 nm light produced by frequency doubling the fundamental light with a bow-tie enhancement second harmonic generator (SHG). When the DOPA and relative phases are locked using a dither-locking method, the squeezed vacuum states are stably measured over 2 h at 11 MHz. The highly compact and simple squeezed light source is suitable for applications in quantum optics experiments.

Remote preparation and manipulation of squeezed light

Remote state preparation enables one to create and manipulate a quantum state based on the shared entanglement between distant nodes. Here, we experimentally demonstrate remote preparation and manipulation of squeezed light. By performing a homodyne projective measurement on one mode of the continuous variable entangled state at Alice's station, a squeezed state is created at Bob's station. Moreover, rotation and displacement operations are applied on the prepared squeezed state by changing the projective parameters on Alice's state. We also show that the remotely prepared squeezed state is robust against loss and N - 1 squeezed states can be remotely prepared based on an N-mode continuous variable Greenberger-Horne-Zeilinger-like state. Our results verify the entanglement-based model used in security analysis of quantum key distribution with continuous variables and have potential application in remote quantum information processing.

Unravelling the non-classicality role in Gaussian heat engines

At the heart of quantum thermodynamics lies a fundamental question about what is genuine "quantum" in quantum heat engines and how to seek this quantumness, so that thermodynamical tasks could be performed more efficiently compared with classical protocols. Here, using the concept of P-representability, we define a function called classicality, which quantifies the degree of non-classicality of bosonic modes. This function allows us to explore the role of non-classicality in quantum heat engines and design optimal protocols for work extraction. For two specific cycles, a quantum Otto and a generalised one, we show that non-classicality is a fundamental resource for performing thermodynamic tasks more efficiently.

Enhancing vacuum squeezing via magnetic field optimization

In this paper, we report on -3.5±0.2 dB vacuum squeezing (corresponding to -4.2±0.2 dB with loss correction) at 795 nm via the polarization self-rotation (PSR) effect in rubidium vapor by applying a magnetic field, whose direction is perpendicular to the propagation and polarization of the pump light. Compared with the case without the magnetic field, whose optimal squeezing degree is about -1.5 dB, this weak magnetic field can enhance the PSR effect and ultimately increase the squeezing degree. This compact squeezed light source can be potentially utilized in quantum protocols in which atomic ensembles are involved, such as in quantum memory, atomic magnetometers and quantum interferometers.

Generation of Schrödinger cat states with Wigner negativity using a continuous-wave low-loss waveguide optical parametric amplifier

Continuous-wave (CW) squeezed light is used in the generation of various optical quantum states, and thus is a fundamental resource of fault-tolerant universal quantum computation using optical continuous variables. To realize a practical quantum computer, a waveguide optical parametric amplifier (OPA) is an attractive CW squeezed light source in terms of its THz-order bandwidth and suitability for modularization. The usages of a waveguide OPA in quantum applications thus far, however, are limited due to the difficulty of the generation of the squeezed light with a high purity. In this paper, we report the first observation of Wigner negativity of the states generated by a heralding method using a waveguide OPA. We generate Schrödinger cat states at the wavelength of 1545 nm with Wigner negativity using a quasi-single-mode ZnO-doped periodically poled LiNbO₃ waveguide module we developed. Wigner negativity is regarded as an important indicator of the usefulness of the quantum states as it is essential in the fault-tolerant universal quantum computation. Our result shows that our waveguide OPA can be used in wide range of quantum applications leading to a THz-clock optical quantum computer.

Improving the Stochastic Feedback Cooling of a Mechanical Oscillator Using a Degenerate Parametric Amplifier

Cooling of a macroscopic mechanical resonator to extremely low temperatures is a necessary condition to observe a variety of macroscopic quantum phenomena. Here, we study the stochastic feedback cooling of a mechanical resonator in an optomechanical system with a degenerate optical parametric amplifier (OPA). In the bad-cavity limit, we find that the OPA can enhance the cooling of the movable mirror in the stochastic feedback cooling scheme. The movable mirror can be cooled from 132 mK to 0.033 mK, which is lower than that without the OPA by a factor of about 5.

Topological optical parametric oscillation

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in nonequilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two dimensional systems as well as in the corner modes of a higher order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out-of-equilibrium and reveals their intriguing behavior in the quantum regime.

Helstrom Bound for Squeezed Coherent States in Binary Communication

In quantum information processing, using a receiver device to differentiate between two non-orthogonal states leads to a quantum error probability. The minimum possible error is known as the Helstrom bound. In this work, we study the conditions for state discrimination using an alphabet of squeezed coherent states and compare them with conditions using the Glauber-Sudarshan, i.e., standard, coherent states.

Squeezing Light via Levitated Cavity Optomechanics

Squeezing light is a critical resource in both fundamental physics and precision measurement. Squeezing light has been generated through optical-parametric amplification inside an optical resonator. However, preparing the squeezing light in an optomechanical system is still a challenge for the thermal noise inevitably coupled to the system. We consider an optically levitated nano-particle in a bichromatic cavity, in which two cavity modes could be excited by the scattering photons of the dual tweezers, respectively. Based on the coherent scattering mechanism, the ultra-strong coupling between the cavity field and the torsional motion of nano-particle could be achieved for the current experimental conditions. With the back-action of the optically levitated nano-particle, the broad single-mode squeezing light can be realized in the bad cavity regime. Even at room temperature, the single-mode light can be squeezed for more than 17 dB, which is far beyond the 3 dB limit. The two-mode squeezing light can also be generated, if the optical tweezers contain two frequencies, one is on the red sideband of the cavity mode, the other is on the blue sideband. The two-mode squeezing can be maximized near the boundary of the system stable regime and is sensitive to both the cavity decay rate and the power of the optical tweezers.

Cosmological particle production: a review

This article will review quantum particle creation in expanding universes. The emphasis will be on the basic physical principles and on selected applications to cosmological models. The needed formalism of quantum field theory in curved spacetime will be summarized, and applied to the example of scalar particle creation in a spatially flat Universe. Estimates for the creation rate will be given and applied to inflationary cosmology models. Analog models which illustrate the same physical principles and may be experimentally realizable are also discussed.

Entangled sideband control scheme via frequency-comb-type seed beam

We report a control scheme of entangled sideband modes without coherent amplitude by employing a frequency-comb-type seed beam. In this scheme, each tooth of the frequency comb serves as a control field for the corresponding downconversion mode. Consequently, all the degrees of freedom can be actively controlled, and the entanglement degrees are higher than 6.7 dB for two pairs of sidebands. We believe that this scheme provides a simple solution for the control of sideband modes, which could be further applied to achieve compact channel multiplexing quantum communications.

A squeezed quantum microcomb on a chip

The optical microresonator-based frequency comb (microcomb) provides a versatile platform for nonlinear physics studies and has wide applications ranging from metrology to spectroscopy. The deterministic quantum regime is an unexplored aspect of microcombs, in which unconditional entanglements among hundreds of equidistant frequency modes can serve as critical ingredients to scalable universal quantum computing and quantum networking. Here, we demonstrate a deterministic quantum microcomb in a silica microresonator on a silicon chip. 40 continuous-variable quantum modes, in the form of 20 simultaneously two-mode squeezed comb pairs, are observed within 1 THz optical span at telecommunication wavelengths. A maximum raw squeezing of 1.6 dB is attained. A high-resolution spectroscopy measurement is developed to characterize the frequency equidistance of quantum microcombs. Our demonstration offers the possibility to leverage deterministically generated, frequency multiplexed quantum states and integrated photonics to open up new avenues in fields of spectroscopy, quantum metrology, and scalable, continuous-variable-based quantum information processing.

Numerical Simulations on Polarization Quantum Noise Squeezing for Ultrashort Solitons in Optical Fiber with Enlarged Mode Field Area

Broadband quantum noise suppression of light is required for many applications, including detection of gravitational waves, quantum sensing, and quantum communication. Here, using numerical simulations, we investigate the possibility of polarization squeezing of ultrashort soliton pulses in an optical fiber with an enlarged mode field area, such as large-mode area or multicore fibers (to scale up the pulse energy). Our model includes the second-order dispersion, Kerr and Raman effects, quantum noise, and optical losses. In simulations, we switch on and switch off Raman effects and losses to find their contribution to squeezing of optical pulses with different durations (0.1–1 ps). For longer solitons, the peak power is lower and a longer fiber is required to attain the same squeezing as for shorter solitons, when Raman effects and losses are neglected. In the full model, we demonstrate optimal pulse duration (~0.4 ps) since losses limit squeezing of longer pulses and Raman effects limit squeezing of shorter pulses.

Enhancement of microwave squeezing via parametric down-conversion in a superconducting quantum circuit

We propose an experimentally accessible superconducting quantum circuit, consisting of two coplanar waveguide resonators (CWRs), to enhance the microwave squeezing via parametric down-conversion (PDC). In our scheme, the two CWRs are nonlinearly coupled through a superconducting quantum interference device embedded in one of the CWRs. This is equivalent to replacing the transmission line in a flux-driven Josephson parametric amplifier (JPA) by a CWR, which makes it possible to drive the JPA by a quantized microwave field. Owing to this design, the PDC coefficient can be considerably increased to be about tens of megahertz, satisfying the strong-coupling condition. Using the Heisenberg-Langevin approach, we numerically show the enhancement of the microwave squeezing in our scheme. In contrast to the JPA, our proposed system becomes stable around the critical point and can generate stronger transient squeezing. In addition, the strong-coupling PDC can be used to engineer the photon blockade.

First Demonstration of 6 dB Quantum Noise Reduction in a Kilometer Scale Gravitational Wave Observatory

Photon shot noise, arising from the quantum-mechanical nature of the light, currently limits the sensitivity of all the gravitational wave observatories at frequencies above one kilohertz. We report a successful application of squeezed vacuum states of light at the GEO 600 observatory and demonstrate for the first time a reduction of quantum noise up to 6.03±0.02  dB in a kilometer scale interferometer. This is equivalent at high frequencies to increasing the laser power circulating in the interferometer by a factor of 4. Achieving this milestone, a key goal for the upgrades of the advanced detectors required a better understanding of the noise sources and losses and implementation of robust control schemes to mitigate their contributions. In particular, we address the optical losses from beam propagation, phase noise from the squeezing ellipse, and backscattered light from the squeezed light source. The expertise gained from this work carried out at GEO 600 provides insight toward the implementation of 10 dB of squeezing envisioned for third-generation gravitational wave detectors.

Characterization of quantum squeezing generated from the phase-sensitive and phase-insensitive amplifiers in the ultra-low average input photon number regime

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

Squeezed-Light Interferometry on a Cryogenically Cooled Micromechanical Membrane

Squeezed states of light reduce the signal-normalized photon counting noise of measurements without increasing the light power and enable fundamental research on quantum entanglement in hybrid systems of light and matter. Squeezed states of light have high potential to complement cryogenically cooled sensors, whose thermal noise is suppressed below the quantum noise of light by operation at low temperature. They allow us to reduce the optical heat load on cooled devices by lowering the light power without losing measurement precision. Here, we demonstrate the squeezed-light position sensing of a cryo-cooled micromechanical membrane. The sensing precision is improved by up to 4.8 dB below photon counting noise, limited by optical loss, at a membrane temperature of about 20 K. We prove that realizing a high interference contrast in a cryogenic Michelson interferometer is feasible. Our setup is the first conceptual demonstration towards the envisioned European gravitational-wave detector, the "Einstein telescope," which is planned to use squeezed states of light together with cryo-cooled mirror test masses.

Hybrid two-mode squeezing of microwave and optical fields using optically pumped graphene layers

A measurable quadrature of a squeezed quantum state manifests a small uncertainty below the Heisenberg limit. This phenomenon has the potential to enable several extraordinary applications in quantum information, metrology and sensing, and other fields. Several techniques have been implemented to realize squeezed electromagnetic states, including microwave fields and optical fields. However, hybrid squeezed modes (that incorporate both microwave and optical fields) have not yet been proposed despite their vital functionality to combine the two worlds of quantum superconducting systems and photonics systems. In this work, for the first time, we propose a novel approach to achieve two-mode squeezing of microwave and optical fields using graphene based structure. The proposed scheme includes a graphene layered structure that is driven by a quantum microwave voltage and subjected to two optical fields of distinct frequencies. By setting the optical frequency spacing equal to the microwave frequency, an interaction occurs between the optical and microwave fields through electrical modulation of the graphene conductivity. We show that significant hybrid two-mode squeezing, that includes one microwave field and one optical field, can be achieved. Furthermore, the microwave frequency can be tuned over a vast range by modifying the operation parameters.

Dissipative bosonic squeezing via frequency modulation and its application in optomechanics

The dissipative squeezing mechanism is an effective method to generate the strong squeezing, which is important in the precision metrology. Here, we propose a practical method to achieve arbitrary bosonic squeezing via introducing frequency modulation into the coupled harmonic resonator model. We analyze the effect of frequency modulation and give the analytical and numerical squeezing results, respectively. To measure the accurate dynamic squeezing in our proposal, we give a more general defination of the relative squeezing degree. Finally, the proposed method is extended to generate the strong mechanical squeezing (>3 dB) in a practical optomechanical system consisting of a graphene mechanical oscillator coupled to a superconducting microwave cavity. The result indicates that the strong mechanical squeezing can be effectively achieved even when the mechanical oscillator is not initially in its ground state. The proposed method expands the study on nonclassical state and does not need the bichromatic microwave driving technology.