Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection

Generation of squeezed vacuum state in the millihertz frequency band

The detection of gravitational waves has ushered in a new era of observing the universe. Quantum resource advantages offer significant enhancements to the sensitivity of gravitational wave observatories. While squeezed states for ground-based gravitational wave detection have received marked attention, the generation of squeezed states suitable for mid-to-low-frequency detection has remained unexplored. To address the gap in squeezed state optical fields at ultra-low frequencies, we report on the first direct observation of a squeezed vacuum field until Fourier frequency of 4 millihertz with the quantum noise reduction of up to 8.0 dB, by the employment of a multiple noise suppression scheme. Our work provides quantum resources for future gravitational wave observatories, facilitating the development of quantum precision measurement.

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.

10 dB Quantum-Enhanced Michelson Interferometer with Balanced Homodyne Detection

Future generations of gravitational-wave detectors (GWD) are targeting an effective quantum noise reduction of 10 dB via the application of squeezed states of light. In the last joint observation run O3, the advanced large-scale GWDs LIGO and Virgo already used the squeezing technology, albeit with a moderate efficiency. Here, we report on the first successful 10 dB sensitivity enhancement of a shot-noise limited tabletop Michelson interferometer via squeezed light in the fundamental Gaussian laser mode, where we also implement the balanced homodyne detection scheme that is planned for the third GWD generation. In addition, we achieved a similarly strong quantum noise reduction when the interferometer was operated in higher-order Hermite-Gaussian modes, which are discussed for the GWD thermal noise mitigation. Our results are an important step toward the targeted quantum noise level in future GWDs and, moreover, represent significant progress in the application of nonclassical states in higher-order modes for interferometry, increased spatial resolution, and multichannel sensing.

Squeezed vacuum interaction with an optomechanical cavity containing a quantum well

We investigate a hybrid system consisting of an optomechanical resonator and an optical cavity containing a quantum well. The system is coupled to a squeezed vacuum reservoir. We analyze the effect of the injection of squeezed photons inside the cavity on the intensity spectrum. The system reaches a regime of hybrid resonance where mechanical, excitonic and cavity modes are intermixed. Despite that the optomechanical interaction is the source of the nonlinearity in the system, the optimum squeezing is obtained at the hybrid resonance frequencies. However, when the squeezed vacuum is applied, at these frequencies the minimum squeezing is realized as well as an increase of fluctuations is observed. We show that the squeezed vacuum transforms the coherent states into highly squeezed states of light, and offers a great flexibility to obtain maximal squeezing. Furthermore, a perfect squeezing is predicted.

Squeezed-light-driven force detection with an optomechanical cavity in a Mach-Zehnder interferometer

We analyze the performance of a force detector based on balanced measurements with a Mach–Zehnder interferometer incorporating a standard optomechanical cavity. The system is driven by a coherent superposition of coherent light and squeezed vacuum field, providing quantum correlation along with optical coherence in order to enhance the measurement sensitivity beyond the standard quantum limit. We analytically find the optimal measurement strength, squeezing direction, and squeezing strength at which the symmetrized power spectral density for the measurement noise is minimized below the standard quantum limit. This force detection scheme based on a balanced Mach–Zehnder interferometer provides better sensitivity compared to that based on balanced homodyne detection with a local oscillator in the low frequency regime.

Extending the piezoelectric transducer bandwidth of an optical interferometer by suppressing resonance using a high dimensional IIR filter implemented on an FPGA

This paper considers the application of Field Programmable Gate Array (FPGA)-based infinite impulse response (IIR) filtering to increase the usable bandwidth of a piezoelectric transducer used in optical phase locking. We experimentally perform system identification of the interferometer with the cross-correlation method integrated on the controller hardware. Our model is then used to implement an inverse filter designed to suppress the low frequency resonant modes of the piezoelectric transducer. This filter is realized as a 24th-order IIR filter on the FPGA, while the total input-output delay is kept at 350 ns. The combination of the inverse filter and the piezoelectric transducer works as a nearly flat response position actuator, allowing us to use a proportional-integral (PI) control in order to achieve stability of the closed-loop system with significant improvements over a non-filtered PI control. Finally, because this controller is completely digital, it is straightforward to reproduce. Our control scheme is suitable for many experiments that require highly accurate control of flexible structures.

Quantum Interferometer Combining Squeezing and Parametric Amplification

High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24  dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.

Force measurement in squeezed dissipative optomechanics in the presence of laser phase noise

We investigate the force measurement sensitivity in a squeezed dissipative optomechanics within the free-mass regime under the influence of shot noise (SN) from the photon number fluctuations, laser phase noise from the pump laser, thermal noise from the environment, and optical losses from outcoupling and detection inefficiencies. Generally, squeezed light could generate a reduced SN on the squeezed quadrature and an enlarged quantum backaction noise (QBA) due to the antisqueezed conjugate quadrature. With an appropriate choice of phase angle in homodyne detection, QBA is cancellable, leading to an exponentially improved measurement sensitivity for the SN-dominated regime. By now, the effects of laser phase noise that is proportional to laser power emerge. The balance between squeezed SN and phase noise can lead to an sub-SQL sensitivity at an exponentially lower input power. However, the improvement by squeezing is limited by optical losses because high sensitivity is delicate and easily destroyed by optical losses.

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling

Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

Compact, low-threshold squeezed light source

Strongly squeezed light finds many important applications within the fields of quantum metrology, quantum communication and quantum computation. However, due to the bulkiness and complexity of most squeezed light sources of today, they are still not a standard tool in quantum optics labs. We have taken the first steps in realizing a compact, high-performance 1550 nm squeezing source based on commercially available fiber components combined with a free-space double-resonant parametric down-conversion source. The whole setup, including single-pass second-harmonic generation in a waveguide, fits on a 30 cm×45 cm breadboard and produces 9.3 dB of squeezing at a 5 MHz sideband-frequency. The setup is currently limited by phase noise, but further optimization and development should allow for a 19" sized turn-key squeezing source capable of delivering more than 10 dB of squeezing.

Squeezed vacuum phase control at 2 μm

We demonstrate phase control for vacuum-squeezed light at a 2 μm wavelength, which is a necessary technology for proposed future gravitational wave observatories. The control scheme allowed examination of noise behavior at frequencies below 1 kHz and indicated that squeezing below this frequency was limited by dark noise and scattered light. We directly measure 3.9±0.2  dB of squeezing from 2 kHz to 80 kHz and 14.2±0.3  dB of antisqueezing relative to the shot noise level. The observed maximum level of squeezing is currently limited by photodetector quantum efficiency and laser instabilities at this new wavelength for squeezed light. Accounting for all losses, we conclude the generation of 11.3 dB of squeezing at the optical parametric oscillator.

Gate-controlled phase switching in a parametron

The parametron, a resonator-based logic device, is a promising physical platform for emerging computational paradigms. When the parametron is subject to both parametric pumping and external driving, complex phenomena arise that can be harvested for applications. In this paper, we experimentally demonstrate deterministic phase switching of a parametron by applying frequency tuning pulses. To our surprise, we find different regimes of phase switching due to the interplay between a parametric pump and an external drive. We provide full modeling of our device with numerical simulations and find excellent agreement between model and measurements. Our result opens up new possibilities for fast and robust logic operations within large-scale parametron architectures.

Generation and measurement of a squeezed vacuum up to 100 MHz at 1550 nm with a semi-monolithic optical parametric oscillator designed towards direct coupling with waveguide modules

We report generation and measurement of a squeezed vacuum from a semi-monolithic Fabry-Pérot 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 squeezer and a waveguide.

Dependence of the squeezing and anti-squeezing factors of bright squeezed light on the seed beam power and pump beam noise

We demonstrate the dependence of the squeezing and anti-squeezing factors on the seed beam power at different pump beam noise levels. The results indicate that a seed field injected into the optical parametric amplifier (OPA) dramatically degenerates the squeezing factor due to noise coupling between the pump and seed fields, even if both the pump and seed fields reach the shot noise limit. The squeezing and anti-squeezing factors are immune to the pump beam noise due to no noise coupling when the system operates for the generation of squeezed vacuum states. The squeezing factor degrades gradually as the pump beam intensity noise and seed beam power is increased. The influence of the two orthogonal quadrature variations is mutually independent of each other.

Residual amplitude modulation and its mitigation in wedged electro-optic modulator

We theoretically analyze and experimentally investigate the dependence of residual amplitude modulation (RAM) on the beam radius within the electro-optic crystal (EOC), the wedge angle of the EOC and the overlap efficiency between the extraordinary and ordinary beams, and the overlap efficiency is determined by the distance from the wedge facet to the downstream polarizer. The results show that the RAM with the maximum optical path difference Δ at the edge of light spot presents a sinc-like curve,and the magnitude of Δ is directly proportional to the beam radius and the wedge angle. As a scaling factor, with the decrease of the overlap efficiency between the ordinary and extraordinary beams, the RAM can be further reduced.

Fabrication of Pancharatnam-Berry phase optical elements with highly stable polarization holography

Polarization-dependent diffraction based on Pancharatnam-Berry phase optical elements (PBOEs) offers considerable benefits compared to conventional metasurfaces, such as negligible absorption, nearly 100% diffraction efficiency and an inexpensive fabrication process. Polarization holography is a simple way to fabricate PBOEs, which entails the interference of beams with different polarizations to generate a spatial-varying polarization field. Thus, the quality of recorded PBOEs manifests high sensitivity to the length change and phase shift between polarized beams, usually caused by environmental vibration and air flow. Here, new polarization holography based on modified Sagnac interferometry is developed for fabricating liquid crystal-based PB gratings and lenses, where the pitch of grating and optical power of lens could be easily tuned. This approach offers high tolerance to environmental disturbance during the exposure process. Detailed design parameters are analyzed, and the fabricated PBOEs with high optical quality are also demonstrated.

Improvement of the intensity noise and frequency stabilization of Nd:YAP laser with an ultra-low expansion Fabry-Perot cavity

Continuous-wave, single-frequency, solid-state lasers with long-term frequency stability and low-intensity noise are an essential resource to generate squeezed and entangled states of light. In order to obtain the stable, nonclassical states of light, the frequency of the laser has to be stabilized with a stable reference. Due to the zero expansion property at a certain temperature, an ultra-low expansion (ULE) Fabry-Perot (F-P) cavity with a high finesse can be used as one of the best candidates of the frequency reference. We perform a detailed analysis of an extraordinarily high-frequency stability and ultra-low-intensity noise laser based on an improved cascade Pound-Drever-Hall frequency stabilization to a ULE F-P cavity. The frequency drift of the laser is suppressed to 7.72 MHz in 4 hours, and the noise level of the laser is simultaneously reduced to the quantum noise limit in the frequency below 300 kHz, which provides the possibility for the direct generation of a stable, high-level squeezed state in a lower-frequency region.

Squeezed vacuum states of light for gravitational wave detectors

A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.

Mitigating Mode-Matching Loss in Nonclassical Laser Interferometry

Strongly squeezed states of light are a key technology in boosting the sensitivity of interferometric setups, such as in gravitational-wave detectors. However, the practical use of squeezed states is limited by optical loss, which reduces the observable squeeze factor. Here, we experimentally demonstrate that introducing squeezed states in additional, higher-order spatial modes can significantly improve the observed nonclassical sensitivity improvement when the loss is due to mode-matching deficiencies. Our results could be directly applied to gravitational-wave detectors, where this type of loss is a major contribution.

Detection and perfect fitting of 13.2 dB squeezed vacuum states by considering green-light-induced infrared absorption

We report on a high-level squeezed vacuum state with maximum quantum noise reduction of 13.2 dB directly detected at the pump power of 180 mW. The pump power dependence of the squeezing factor is experimentally exhibited. When considering only loss and phase fluctuation, the fitting results have a large deviation from the measurement value near the threshold. By integrating green-light-induced infrared absorption (GLIIRA) loss, the squeezing factor can be perfectly fitted in the whole pump power range. The result indicates that GLIIRA loss should be thoroughly considered and quantified in the generation of high-level squeezed states.

Quadrature histograms in maximum-likelihood quantum state tomography

Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state and the true state. This paper studies different strategies for determining the histogram bin widths. We show that computation time can be significantly reduced with little loss in the fidelity of the estimated state when the measurement operators corresponding to each histogram bin are integrated over the bin width.

Investigation of residual amplitude modulation in squeezed state generation system

We present an analysis on how the optical parametric oscillator (OPO) detuning and the relative phase drift deteriorate the stability of the squeezed states, including the output power and the squeezed degree, and investigate the influence of RAM on the cavity detuning and the relative phase drift under different cases. Subsequently, the RAM is experimentally measured. In term of the measurement results, we perform a comparative study about RAM's influence on the cavity and phase locking in two cases. As a result, with the error signal extracted from the transmission of the OPO, the output power stability of the squeezed light is greatly improved. With the phase modulation imposed on the signal beam, the long-term stability of the squeezed degree is significantly enhanced.

Orbital-angular-momentum-enhanced estimation of sub-Heisenberg-limited angular displacement with two-mode squeezed vacuum and parity detection

We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number ℓ. This implies that the robustness and the practicability of the system can be improved via raising ℓ without changing mean photon number N.

Quantum squeezing in a modulated optomechanical system

Quantum squeezing, as a typical quantum effect, is an important resource for many applications in quantum technologies. Here we propose a scheme for generating quantum squeezing, including the ponderomotive squeezing and the mechanical squeezing, in an optomechanical system, in which the radiation-pressure coupling and the mechanical spring constant are modulated periodically. In this system, the radiation-pressure interaction can be enhanced remarkably by the modulation-induced mechanical parametric amplification. Moreover, the effective phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir. This ultimately leads to that our scheme can achieve a controllable quantum squeezing. Numerical calculations show that our scheme is experimentally realizable with current technologies.

Spin-Orbit-Coupled Interferometry with Ring-Trapped Bose-Einstein Condensates

We propose a method of atom interferometry using a spinor Bose-Einstein condensate with a time-varying magnetic field acting as a coherent beam splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub-μG scale. We split a ring-trapped condensate, initially in the m_{f}=0 hyperfine state, into superpositions of internal m_{f}=±1 states and condensate superflow, which are spin-orbit coupled. After interrogation, the relative phase accumulation can be inferred from a population transfer to the m_{f}=±1 states. The counterflow generation protocol is adiabatically deterministic and does not rely on coupling to additional optical fields or mechanical stirring techniques. Our protocol can maximize the classical Fisher information for any rotation, magnetic field, or interrogation time and so has the maximum sensitivity available to uncorrelated particles. Precision can increase with the interrogation time and so is limited only by the lifetime of the condensate.

Quantum Transduction with Adaptive Control

Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection, and it can be implemented to realize quantum state transfer between microwave and optical modes.

Detection of stably bright squeezed light with the quantum noise reduction of 12.6 dB by mutually compensating the phase fluctuations

We present a mutual compensation scheme of three phase fluctuations, originating from the residual amplitude modulation (RAM) in the phase modulation process, in the bright squeezed light generation system. The influence of the RAM on each locking loop is harmonized by using one electro-optic modulator (EOM), and the direction of the phase fluctuation is manipulated by positioning the photodetector (PD) that extracts the error signal before or after the optical parametric amplifier (OPA). Therefore a bright squeezed light with non-classical noise reduction of π is obtained. By fitting the squeezing and antisqueezing measurement results, we confirm that the total phase fluctuation of the system is around 3.1 mrad. The fluctuation of the noise suppression is 0.2 dB for 3 h.

Low-noise, transformer-coupled resonant photodetector for squeezed state generation

In an actual setup of squeezed state generation, the stability of a squeezing factor is mainly limited by the performance of the servo-control system, which is mainly influenced by the shot noise and gain of a photodetector. We present a unique transformer-coupled LC resonant amplifier as a photodetector circuit to reduce the electronic noise and increase the gain of the photodetector. As a result, we obtain a low-noise, high gain photodetector with the gain of more than 1.8×10⁵ V/A, and the input current noise of less than 4.7 pA/Hz. By adjusting the parameters of the transformer, the quality factor Q of the resonant circuit is close to 100 in the frequency range of more than 100 MHz, which meets the requirement for weak power detection in the application of squeezed state generation.

Polarization squeezing at the audio frequency band for the Rubidium D1 line

A 2.8-dB polarization squeezing of the Stokes operatorS^₂for the rubidium D₁ line (795 nm) is achieved, with the lowest squeezing band at an audio frequency of 2.6 kHz. It is synthetized by a bright coherent beam and a squeezed vacuum, which are orthogonally polarized and share same frequency. Two methods are applied to support the optical parametric oscillator: an orthogonally-polarized locking beam that precludes residual unwanted interference and quantum noise locking method that locks the squeezing phase. Besides, the usage of low noise balanced detector, mode cleaner and the optical isolator helped to improve the audio frequency detection. The squeezing level is limited by absorption-induced losses at short wavelengths, which is 397.5 nm. The generated polarization squeezed light can be used in a quantum enhanced magnetometer to increase the measurement sensitivity.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Homodyne detection of short-range Doppler radar using a forced oscillator model

This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis.

Qubit-flip-induced cavity mode squeezing in the strong dispersive regime of the quantum Rabi model

Squeezed states of light are a set of nonclassical states in which the quantum fluctuations of one quadrature component are reduced below the standard quantum limit. With less noise than the best stabilised laser sources, squeezed light is a key resource in the field of quantum technologies and has already improved sensing capabilities in areas ranging from gravitational wave detection to biomedical applications. In this work we propose a novel technique for generating squeezed states of a confined light field strongly coupled to a two-level system, or qubit, in the dispersive regime. Utilising the dispersive energy shift caused by the interaction, control of the qubit state produces a time-dependent change in the frequency of the light field. An appropriately timed sequence of sudden frequency changes reduces the quantum noise fluctuations in one quadrature of the field well below the standard quantum limit. The degree of squeezing and the time of generation are directly controlled by the number of frequency shifts applied. Even in the presence of realistic noise and imperfections, our protocol promises to be capable of generating a useful degree of squeezing with present experimental capabilities.

Measurement-Based Linear Optics

A major challenge in optical quantum processing is implementing large, stable interferometers. We offer a novel approach: virtual, measurement-based interferometers that are programed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate postclassical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting.

Estimation of nonclassical independent Gaussian processes by classical interferometry

We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters of an unknown Gaussian process, considering a noisy source of radiation the phase of which is not locked to the pump of the process. We verify the sufficiency of passive optical elements in the interferometer, active optical elements do not improve the quality of the estimation. We also prove the robustness of the method against the noise and loss in both interferometric channels and the sample. The proposed method is suitable even for the case when a source of radiation sufficient for homodyne detection is not available.

Crystallizing highly-likely subspaces that contain an unknown quantum state of light

In continuous-variable tomography, with finite data and limited computation resources, reconstruction of a quantum state of light is performed on a finite-dimensional subspace. In principle, the data themselves encode all information about the relevant subspace that physically contains the state. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace by extracting this information directly from the data for any given unknown quantum state of light and measurement scheme. This procedure makes use of the celebrated statistical principle of maximum likelihood, along with other validation tools, to grow an appropriate seed subspace into the optimal reconstruction subspace, much like the nucleation of a seed into a crystal. Apart from using the available measurement data, no other assumptions about the source or preconceived parametric model subspaces are invoked. This ensures that no spurious reconstruction artifacts are present in state reconstruction as a result of inappropriate choices of the reconstruction subspace. The procedure can be understood as the maximum-likelihood reconstruction for quantum subspaces, which is an analog to, and fully compatible with that for quantum states.

High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared

We report on high-efficiency superconducting nanowire single-photon detectors based on amorphous tungsten silicide and optimized at 1064 nm. At an operating temperature of 1.8 K, we demonstrated a 93% system detection efficiency at this wavelength with a dark noise of a few counts per second. Combined with cavity-enhanced spontaneous parametric downconversion, this fiber-coupled detector enabled us to generate narrowband single photons with a heralding efficiency greater than 90% and a high spectral brightness of 0.6×10⁴ photons/(s·mW·MHz). Beyond single-photon generation at large rate, such high-efficiency detectors open the path to efficient multiple-photon heralding and complex quantum state engineering.

Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency

Squeezed states of light belong to the most prominent nonclassical resources. They have compelling applications in metrology, which has been demonstrated by their routine exploitation for improving the sensitivity of a gravitational-wave detector since 2010. Here, we report on the direct measurement of 15 dB squeezed vacuum states of light and their application to calibrate the quantum efficiency of photoelectric detection. The object of calibration is a customized InGaAs positive intrinsic negative (p-i-n) photodiode optimized for high external quantum efficiency. The calibration yields a value of 99.5% with a 0.5% (k=2) uncertainty for a photon flux of the order 10^{17}  s^{-1} at a wavelength of 1064 nm. The calibration neither requires any standard nor knowledge of the incident light power and thus represents a valuable application of squeezed states of light in quantum metrology.

Reduction of zero baseline drift of the Pound-Drever-Hall error signal with a wedged electro-optical crystal for squeezed state generation

We report an electro-optic modulator (EOM) with a wedged MgO: LiNbO₃ as the modulation crystal to reduce the zero baseline drift (ZBD) of the Pound-Drever-Hall (PDH) error signal. When the input linear polarization is not along the modulation direction, the wedged design can separate the two orthogonal polarizations in space after the EOM and eliminate the interference between the carrier and the two orthogonal sidebands. Therefore, the residual amplitude modulation (RAM) of phase modulation process caused by the input polarization misalignment and the etalon effect can be significantly reduced. The noise power spectrum of phase-modulated light with wedged crystal EOM is suppressed from -24 to -69  dBm, which is much lower than that with conventional EOM. The peak-to-peak value of the ZBD of the PDH error signal is reduced effectively to +70/-50  ppm during the 10 h, which meets the requirements for stable squeezed light generation.

Single-Mode Parametric-Down-Conversion States with 50 Photons as a Source for Mesoscopic Quantum Optics

We generate pulsed, two-mode squeezed states in a single spatiotemporal mode with mean photon numbers up to 20. We directly measure photon-number correlations between the two modes with transition edge sensors up to 80 photons per mode. This corresponds roughly to a state dimensionality of 6400. We achieve detection efficiencies of 64% in the technologically crucial telecom regime and demonstrate the high quality of our measurements by heralded nonclassical distributions up to 50 photons per pulse and calculated correlation functions up to 40th order.

Strong vacuum squeezing from bichromatically driven Kerrlike cavities: from optomechanics to superconducting circuits

Squeezed light, displaying less fluctuation than vacuum in some observable, is key in the flourishing field of quantum technologies. Optical or microwave cavities containing a Kerr nonlinearity are known to potentially yield large levels of squeezing, which have been recently observed in optomechanics and nonlinear superconducting circuit platforms. Such Kerr-cavity squeezing however suffers from two fundamental drawbacks. First, optimal squeezing requires working close to turning points of a bistable cycle, which are highly unstable against noise thus rendering optimal squeezing inaccessible. Second, the light field has a macroscopic coherent component corresponding to the pump, making it less versatile than the so-called squeezed vacuum, characterised by a null mean field. Here we prove analytically and numerically that the bichromatic pumping of optomechanical and superconducting circuit cavities removes both limitations. This finding should boost the development of a new generation of robust vacuum squeezers in the microwave and optical domains with current technology.

Squeezed light from a diamond-turned monolithic cavity

For some crystalline materials, a regime can be found where continuous ductile cutting is feasible. Using precision diamond turning, such materials can be cut into complex optical components with high surface quality and form accuracy. In this work we use diamond-turning to machine a monolithic, square-shaped, doubly-resonant LiNbO3 cavity with two flat and two convex facets. When additional mild polishing is implemented, the Q-factor of the resonator is found to be limited only by the material absorption loss. We show how our monolithic square resonator may be operated as an optical parametric oscillator that is evanescently coupled to free-space beams via birefringent prisms. The prism arrangement allows for independent and large tuning of the fundamental and second harmonic coupling rates. We measure 2.6 ± 0.5 dB of vacuum squeezing at 1064 nm using our system. Potential improvements to obtain higher degrees of squeezing are discussed.

Improvement of vacuum squeezing resonant on the rubidium D1 line at 795 nm

We report on efficient generation of second harmonic laser and single-mode vacuum squeezed light of 795 nm with periodically poled KTiOPO4 (PPKTP) crystals. We achieved 111 mW of ultra-violet (UV) light at 397.5 nm from 191 mW of fundamental light with a PPKTP crystal in a doubling cavity, corresponding to a conversion efficiency of 58.1%. Using the UV light to pump an optical parametric oscillator with a PPKTP crystal, we realized -5.6 dB of a maximum squeezing. We analyzed the pump power dependence of the squeezing level and concluded that the UV light induced losses limit the improvement of the squeezing level. The generated squeezed light has huge potential application in quantum memory and ultra-precise measurement.

Measurement of the squeezed vacuum state by a bichromatic local oscillator

We present the experimental measurement of a squeezed vacuum state by means of a bichromatic local oscillator (BLO). A pair of local oscillators at ±5 MHz around the central frequency ω(0) of the fundamental field with equal power are generated by three acousto-optic modulators and phase-locked technology and used as a BLO. The squeezed vacuum light is detected by a phase-sensitive balanced-homodyne detection with a BLO. The baseband signal around ω(0) combined with a broad squeezed field can be detected with the sensitivity below the shot-noise limit, in which the baseband signal is shifted to the vicinity of 5 MHz (the half of the BLO separation). This work has important applications in quantum state measurement and quantum information.

Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical problems, which might be compromised by improved algorithms or by future quantum computers. State-of-the-art quantum key distribution requires composable security against coherent attacks for a finite number of distributed quantum states as well as robustness against implementation side channels. Here we present an implementation of continuous-variable quantum key distribution satisfying these requirements. Our implementation is based on the distribution of continuous-variable Einstein–Podolsky–Rosen entangled light. It is one-sided device independent, which means the security of the generated key is independent of any memoryfree attacks on the remote detector. Since continuous-variable encoding is compatible with conventional optical communication technology, our work is a step towards practical implementations of quantum key distribution with state-of-the-art security based solely on telecom components.

When quantum key distribution is composed with other secure protocols the overall security has to be guaranteed, which adds further security requirements. Here, the authors demonstrate continuous-variable quantum key distribution with composable security and one-sided-device independence.

Generation of photon-number squeezed states with a fiber-optic symmetric interferometer

We numerically and experimentally demonstrate photon-number squeezed state generation with a symmetric fiber interferometer in an 800-nm wavelength and compared with an asymmetric fiber interferometer, although photon-number squeezed pulses have been generated only with asymmetric interferometers. Even though we obtain -1.0dB squeezing with an asymmetric fiber interferometer, since perfect spectral phase and intensity matching between displacement and signal pulses are achieved with a symmetric fiber interferometer, we obtain better squeezing of -3.1dB. We also numerically calculate and clarify this scheme's usefulness at a 1.55-μm wavelength.

Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing

We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.