Squeezing in the audio gravitational-wave detection band

Quantum Enhanced Balanced Heterodyne Readout for Differential Interferometry

Conventional heterodyne readout schemes are now under reconsideration due to the realization of techniques to evade its inherent 3 dB signal-to-noise penalty. The application of high-frequency, quadrature-entangled, two-mode squeezed states can further improve the readout sensitivity of audio-band signals. In this Letter, we experimentally demonstrate quantum-enhanced heterodyne readout of two spatially distinct interferometers with direct optical signal combination, circumventing the 3 dB heterodyne signal-to-noise penalty. Applying a high-frequency, quadrature-entangled, two-mode squeezed state, we show further signal-to-noise improvement of an injected audio band signal of 3.5 dB. This technique is applicable for quantum-limited high-precision experiments, with application to searches for quantum gravity, searches for dark matter, gravitational wave detection, and wavelength-multiplexed quantum communication.

Characterizing two-mode-squeezed light from four-wave mixing in rubidium vapor for quantum sensing and information processing

We present a study of homodyne measurements of two-mode, vacuum-seeded, quadrature-squeezed light generated by four-wave mixing in warm rubidium vapor. Our results reveal that the vacuum squeezing can extend down to measurement frequencies of less than 1 Hz, and the squeezing bandwidth, similar to the seeded intensity-difference squeezing measured in this system, reaches up to approximately 20 MHz for typical pump parameters. By dividing the squeezing bandwidth into smaller frequency bins, we show that different sideband frequencies represent independent sources of two-mode squeezing. These properties are useful for quantum sensing and quantum information processing applications. We also investigate the impact of group velocity delays on the correlations in the system, which allows us to optimize the useful spectrum.

Heterodyne laser Doppler vibrometer with squeezed light enhancement

An important feature of a heterodyne laser Doppler vibrometer (LDV) is the possibility of measuring an optical path length oscillation at a frequency f at a choosable frequency fhet ± f, at which the photo-electric measurement shows an optical quantum noise that is significantly greater than the detector dark noise. The full-squeezed light enhancement of a heterodyne LDV's signal-to-noise ratio has not been achieved so far. Here we use a sideband spectrum that is squeezed around fhet = 40 MHz and demonstrate the squeezing-enhanced measurement of an optical path length vibration at f = 1 MHz of about 3.5 dB while fully maintaining the signal power. The proof of principle we provide will enable the realization of ultra-precise LDVs over an extended signal bandwidth for probes or environments that require low intensities.

Lithium niobate waveguide squeezer with integrated cavity length stabilisation for network applications

We report a titanium indiffused waveguide resonator featuring an integrated electro-optic modulator for cavity length stabilisation that produces close to 5 dB of squeezed light at 1550 nm (2.4 dB directly measured). The resonator is locked on resonance for tens of minutes with 70 mW of SH light incident on the cavity, demonstrating that photorefraction can be mitigated. Squeezed light production concurrent with cavity length stabilisation utilising the integrated EOM is demonstrated. The device demonstrates the suitability of this platform for squeezed light generation in network applications, where stabilisation to the reference field is typically necessary.

Loss-tolerant and quantum-enhanced interferometer by reversed squeezing processes

Reversed nonlinear dynamics is predicted to be capable of enhancing the quantum sensing in unprecedented ways. Here, we report the experimental demonstration of a loss-tolerant (external loss) and quantum-enhanced interferometer. Two cascaded optical parametric amplifiers are used to judiciously construct an interferometry with two orthogonal squeezing operation. As a consequence, a weak displacement introduced by a test cavity can be amplified for measurement, and the measured signal-to-noise ratio is better than that of both conventional photon shot-noise limited and squeezed-light assisted interferometers. We further confirm its superior loss-tolerant performance by varying the external losses and comparing with both conventional photon shot-noise limited and squeezed-light assisted configurations, illustrating the potential application in gravitational wave detection.

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.

Squeezing in Gravitational Wave Detectors

Injecting optical squeezed states of light, a technique known as squeezing, is now a tool for gravitational wave detection. Its ability to reduce quantum noise is helping to reveal more gravitational wave transients, expanding the catalog of observations in the last observing run. This review introduces squeezing and its history in the context of gravitational-wave detectors. It overviews the benefits, limitations and methods of incorporating squeezing into advanced interferometers, emphasizing the most relevant details for astrophysics instrumentation.

Phase locking of squeezed vacuum generated by a single-pass optical parametric amplifier

In high-precision optical measurements, squeezed vacuum states are a promising resource for reducing the shot noise. To utilize a squeezed vacuum, it is important to lock the phase of the local oscillator (LO) to the squeezed light. The coherent control sideband (CCSB) scheme has been established for the precise phase locking, while the previous CCSB scheme was designed for the squeezed vacuum generated with an optical parametric oscillator (OPO). Thus the previous CCSB scheme is not applicable to squeezing by a single-pass optical parametric amplifier (OPA), which is attractive for generating broadband squeezed vacuum states. In this study, we propose a variant of CCSB scheme, which is applicable to the squeezing by single-pass OPA. In this scheme, we inject pump light and frequency-shifted signal light into an OPA crystal in the same way as the previous CCSB scheme. The parametric process in the OPA crystal generates a squeezed vacuum, amplifies the signal light, generates an idler light, and causes the pump depletion reflecting the interference of the amplified signal light and the idler light. Through the lock-in detection of the pump depletion, we can phase-lock the injected signal light to the pump light. Then, after the heterodyne detection of the signal and the idler light, we get the error signal of LO and realize the precise phase locking of LO to the squeezed quadrature. We show the feasibility of the proposed scheme by deriving the signal-to-noise ratio (SNR) of the modulated pump signal. We experimentally demonstrate the proposed scheme on pulsed squeezing by a single-pass OPA.

Automated source of squeezed vacuum states driven by finite state machine based software

In the last few decades, much effort has been made for the production of squeezed vacuum states in order to reduce quantum noise in the audio-frequency band. This technique has been implemented in all running gravitational-wave interferometric detectors and helped to improve their sensitivity. While the detectors are acquiring data for astrophysical observations, they must be kept in the operating condition, also called "science mode," that is, a state that requires the highest possible duty-cycle for all the instrumental parts and controls. We report the development of a highly automated setup for the generation of optical squeezed states, where all the required control loops are supervised by a software based on finite state machines; we took special care to grant ease of use, stability of operation, and possibility of auto-recovery. Moreover, the setup has been designed to be compatible with the existing software and hardware infrastructure of the Virgo detector. In this paper, we discuss the optical properties of this squeezing setup, the locking techniques, and the automation algorithms.

Controllable continuous variable quantum state distributor

To scale quantum information processing, quantum state distributors are an indispensable technology in quantum networks. We present a universal scheme of a continuous variable quantum state distributor that performs point-to-multipoint distributions via quantum teleportation with partially disembodied transport. The fidelity of the state at the output nodes can be conveniently manipulated as needed by engineering the correlation noise of the Einstein-Podolsky-Rosen (EPR) beam. For a 1→2 distributor, controllable distributions were demonstrated by manipulating the squeezing factor of EPR entanglement. The fidelities of the two receivers gradually changed from (2/3, 2/3) to (0.95, 0.17) corresponding to the transition from symmetric to asymmetric quantum cloning.

High-precision cavity spectroscopy using high-frequency squeezed light

In this article, we present a novel spectroscopy technique that improves the signal-to-shot-noise ratio without the need to increase the laser power. Detrimental effects by technical noise sources are avoided by frequency-modulation techniques (frequency up-shifting). Superimposing the signal on non-classical states of light leads to a reduced quantum noise floor. Our method reveals in a proof-of-concept experiment small signals at Hz to kHz frequencies even below the shot noise limit. Our theoretical calculations fully support our experimental findings. The proposed technique is interesting for applications such as high-precision cavity spectroscopy, e.g., for explosive trace gas detection where the specific gas might set an upper limit for the laser power employed.

The Squeezed Light Source for the Advanced Virgo Detector in the Observation Run O3

From 1 April 2019 to 27 March 2020, the Advanced Virgo detector, together with the two Advanced LIGO detectors, conducted the third joint scientific observation run O3, aiming for further detections of gravitational wave signals from astrophysical sources. One of the upgrades to the Virgo detector for O3 was the implementation of the squeezed light technology to improve the detector sensitivity beyond its classical quantum shot noise limit. In this paper, we present a detailed description of the optical setup and performance of the employed squeezed light source. The squeezer was constructed as an independent, stand-alone sub-system operated in air. The generated squeezed states are tailored to exhibit high purity at intermediate squeezing levels in order to significantly reduce the interferometer shot noise level while keeping the correlated enhancement of quantum radiation pressure noise just below the actual remaining technical noise in the Advanced Virgo detector.

Near-Degenerate Quadrature-Squeezed Vacuum Generation on a Silicon-Nitride Chip

Squeezed states are a primary resource for continuous-variable (CV) quantum information processing. To implement CV protocols in a scalable and robust way, it is desirable to generate and manipulate squeezed states using an integrated photonics platform. In this Letter, we demonstrate the generation of quadrature-phase squeezed states in the radio-frequency carrier sideband using a small-footprint silicon-nitride microresonator with a dual-pumped four-wave-mixing process. We record a squeezed noise level of 1.34 dB (±0.16  dB) below the photocurrent shot noise, which corresponds to 3.09 dB (±0.49  dB) of quadrature squeezing on chip. We also show that it is critical to account for the nonlinear behavior of the pump fields to properly predict the squeezing that can be generated in this system. This technology represents a significant step toward creating and manipulating large-scale CV cluster states that can be used for quantum information applications, including universal quantum computing.

Observation of a comb of squeezed states with a strong squeezing factor by a bichromatic local oscillator

We demonstrate the experimental detection of an optical squeezing covering several higher resonances of the optical parametric amplifier (OPA) by adopting a bichromatic local oscillator (BLO). The BLO is generated from a waveguide electro-optic phase modulator (WGM) and subsequent optical mode cleaner (OMC), without the need of additional power balance and phase control. The WGM is used for generating the frequency-shifted sideband beams with equal power and certain phase difference, and the OMC is used for filtering the unwanted optical modes. Among a measurement frequency range from 0 to 16.64 GHz, the maximum squeezing factors are superior to 10 dB below the shot noise limit for the first three discrete odd-order resonances of the OPA.

Laser Intensity Noise Suppression for Preparing Audio-Frequency Squeezed Vacuum State of Light

Laser intensity noise suppression has essential effects on preparation and characterization of the audio-frequency squeezed vacuum state of light based on a sub-threshold optical parametric oscillator (OPO). We have implemented two feedback loops by using relevant acousto-optical modulators (AOM) to stabilize the intensity of 795-nm near infrared (NIR) fundamental laser and 397.5-nm ultraviolet (UV) laser generated by cavity-enhanced frequency doubling. Typical peak-to-peak laser intensity fluctuation with a bandwidth of ~10 kHz in a half hour has been improved from ±7.45% to ±0.06% for 795-nm NIR laser beam, and from ±9.04% to ±0.05% for 397.5-nm UV laser beam, respectively. The squeezing level of the squeezed vacuum state at 795 nm prepared by the sub-threshold OPO with a PPKTP crystal has been improved from −3.3 to −4.0 dB around 3~9 kHz of analysis frequency range.

Increasing the Astrophysical Reach of the Advanced Virgo Detector via the Application of Squeezed Vacuum States of Light

Current interferometric gravitational-wave detectors are limited by quantum noise over a wide range of their measurement bandwidth. One method to overcome the quantum limit is the injection of squeezed vacuum states of light into the interferometer's dark port. Here, we report on the successful application of this quantum technology to improve the shot noise limited sensitivity of the Advanced Virgo gravitational-wave detector. A sensitivity enhancement of up to 3.2±0.1  dB beyond the shot noise limit is achieved. This nonclassical improvement corresponds to a 5%-8% increase of the binary neutron star horizon. The squeezing injection was fully automated and over the first 5 months of the third joint LIGO-Virgo observation run O3 squeezing was applied for more than 99% of the science time. During this period several gravitational-wave candidates have been recorded.

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.

Twin-beam intensity-difference squeezing below 10 Hz

We report the generation of strong, bright-beam intensity-difference squeezing down to measurement frequencies below 10 Hz. We generate two-mode squeezing in a four-wave mixing (4WM) process in Rb vapor, where the single-pass-gain nonlinear process does not require cavity locking and only relies on passive stability. We use diode laser technology and several techniques, including dual seeding, to remove the noise introduced by seeding the 4WM process as well as the background noise. Twin-beam intensity-difference squeezing down to frequencies limited only by the mechanical and atmospheric stability of the lab is achieved. These results should enable important low-frequency applications such as direct intensity-difference imaging with bright beams on integrating detectors.

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.

Quantum communication based on two-mode entangled state with quantum noise locking method

The two-mode entangled state is an important basic non-classical state and it has been used in many quantum communication projects. We propose a new quantum communication scheme with a two-mode entangled state which can transmit signals encoded by a thermal-state light field. Also, instead of locking several phases in the whole process, we use only one locking servo system at the final stage. The locking error signal comes from the measured quantum variances by using the quantum noise locking method. A proof-of-principle derivation shows that it is very convenient to achieve the secure condition against individual attacks. It would be utilized in practical quantum information process.

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.

Dependence of measured audio-band squeezing level on local oscillator intensity noise

We investigate the dependence of the measured squeezing level on the local oscillator (LO) intensity noise. The theoretical results indicate that it produces a large measurement error with the increase of the LO intensity noise, but the measurement error has immunity to the product P of the common mode rejection ratio (CMRR) with the LO intensity noise. According to the investigation results and the LO intensity noise, we employ a detector with the CMRR of 67 dB to detect the quantum noise at audio frequencies, the product P of the CMRR with the LO intensity noise is 20 dB below the shot noise limit (SNL), which can induce the measurement error of 0.1 dB for 10 dB of squeezing. Finally, the squeezing level measured at 15.2 kHz is 9.9 ± 0.2 dB. The influence of the intensity noise of the LO, and the electronic noise of the detector is subtracted, the inferred squeezing level is approximately 10.2 ± 0.2 dB. It is extremely important to quantify the requirements of the CMRR of the detector for measuring the squeezing at audio frequency and inferring the real squeezing level.

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.

Audio-Band Frequency-Dependent Squeezing for Gravitational-Wave Detectors

Quantum vacuum fluctuations impose strict limits on precision displacement measurements, those of interferometric gravitational-wave detectors among them. Introducing squeezed states into an interferometer's readout port can improve the sensitivity of the instrument, leading to richer astrophysical observations. However, optomechanical interactions dictate that the vacuum's squeezed quadrature must rotate by 90° around 50 Hz. Here we use a 2-m-long, high-finesse optical resonator to produce frequency-dependent rotation around 1.2 kHz. This demonstration of audio-band frequency-dependent squeezing uses technology and methods that are scalable to the required rotation frequency and validates previously developed theoretical models, heralding application of the technique in future gravitational-wave detectors.

Enhancing the Bandwidth of Gravitational-Wave Detectors with Unstable Optomechanical Filters

Advanced interferometric gravitational-wave detectors use optical cavities to resonantly enhance their shot-noise-limited sensitivity. Because of positive dispersion of these cavities-signals at different frequencies pick up different phases, there is a tradeoff between the detector bandwidth and peak sensitivity, which is a universal feature for quantum measurement devices having resonant cavities. We consider embedding an active unstable filter inside the interferometer to compensate the phase, and using feedback control to stabilize the entire system. We show that this scheme in principle can enhance the bandwidth without sacrificing the peak sensitivity. However, the unstable filter under our current consideration is a cavity-assisted optomechanical device operating in the instability regime, and the thermal fluctuation of the mechanical oscillator puts a very stringent requirement on the environmental temperature and the mechanical quality factor.

Scheme for efficient extraction of low-frequency signal beyond the quantum limit by frequency-shift detection

Low-frequency (Hz~kHz) squeezing is very important in many schemes of quantum precision measurement. But it is more difficult than that at megahertz-frequency because of the introduction of laser low-frequency technical noise. In this paper, we propose a scheme to obtain a low-frequency signal beyond the quantum limit from the frequency comb in a non-degenerate frequency and degenerate polarization optical parametric amplifier (NOPA) operating below threshold with type I phase matching by frequency-shift detection. Low-frequency squeezing immune to laser technical noise is obtained by a detection system with a local beam of two-frequency intense laser. Furthermore, the low-frequency squeezing can be used for phase measurement in Mach-Zehnder interferometer, and the signal-to-noise ratio (SNR) can be enhanced greatly.

Squeezed light for advanced gravitational wave detectors and beyond

Recent experiments have demonstrated that squeezed vacuum states can be injected into gravitational wave detectors to improve their sensitivity at detection frequencies where they are quantum noise limited. Squeezed states could be employed in the next generation of more sensitive advanced detectors currently under construction, such as Advanced LIGO, to further push the limits of the observable gravitational wave Universe. To maximize the benefit from squeezing, environmentally induced disturbances such as back scattering and angular jitter need to be mitigated. We discuss the limitations of current squeezed vacuum sources in relation to the requirements imposed by future gravitational wave detectors, and show a design for squeezed light injection which overcomes these limitations.

Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light

Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.

High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity

We report the generation of squeezed vacuum states of light at 1550 nm with a broadband quantum noise reduction of up to 4.8 dB ranging from 5 MHz to 1.2 GHz sideband frequency. We used a custom-designed 2.6 mm long biconvex periodically-poled potassium titanyl phosphate (PPKTP) crystal. It featured reflectively coated end surfaces, 2.26 GHz of linewidth and generated the squeezing via optical parametric amplification. Two homodyne detectors with different quantum efficiencies and bandwidths were used to characterize the non-classical noise suppression. We measured squeezing values of up to 4.8 dB from 5 to 100 MHz and up to 3 dB from 100 MHz to 1.2 GHz. The squeezed vacuum measurements were limited by detection loss. We propose an improved detection scheme to measure up to 10 dB squeezing over 1 GHz. Our results of GHz bandwidth squeezed light generation provide new prospects for high-speed quantum key distribution.

First long-term application of squeezed states of light in a gravitational-wave observatory

We report on the first long-term application of squeezed vacuum states of light to improve the shot-noise-limited sensitivity of a gravitational-wave observatory. In particular, squeezed vacuum was applied to the German-British detector GEO 600 during a period of three months from June to August 2011, when GEO 600 was performing an observational run together with the French-Italian Virgo detector. In a second period, the squeezing application continued for about 11 months from November 2011 to October 2012. During this time, squeezed vacuum was applied for 90.2% (205.2 days total) of the time that science-quality data were acquired with GEO 600. A sensitivity increase from squeezed vacuum application was observed broadband above 400 Hz. The time average of gain in sensitivity was 26% (2.0 dB), determined in the frequency band from 3.7 to 4.0 kHz. This corresponds to a factor of 2 increase in the observed volume of the Universe for sources in the kHz region (e.g., supernovae, magnetars). We introduce three new techniques to enable the long-term application of squeezed light, and show that the glitch rate of the detector did not increase from squeezing application. Squeezed vacuum states of light have arrived as a permanent application, capable of increasing the astrophysical reach of gravitational-wave detectors.

Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor

Using a nondegenerate four-wave mixing process in hot rubidium vapor, we demonstrate a compact diode-laser-pumped system for the generation of intensity-difference squeezing down to 8 kHz with a maximum squeezing of -7 dB. To the best of our knowledge, this is the first demonstration of kilohertz-level intensity-difference squeezing using a semiconductor laser as the pump source. This scheme is of interest for experiments involving atomic ensembles, quantum communications, and precision measurements. The diode-laser-pumped system would extend the range of possible applications for squeezing due to its low cost, ease of operation, and ease of integration.

Quantum Measurement Theory in Gravitational-Wave Detectors

The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.

Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB

Continuous-wave squeezed states of light at the wavelength of 1550 nm have recently been demonstrated, but so far the obtained factors of noise suppression still lag behind today's best squeezing values demonstrated at 1064 nm. Here we report on the realization of a half-monolithic nonlinear resonator based on periodically-poled potassium titanyl phosphate which enabled the direct detection of up to 12.3 dB of squeezing at 5 MHz. Squeezing was observed down to a frequency of 2 kHz which is well within the detection band of gravitational wave interferometers. Our results suggest that a long-term stable 1550 nm squeezed light source can be realized with strong squeezing covering the entire detection band of a 3rd generation gravitational-wave detector such as the Einstein Telescope.

Backscatter tolerant squeezed light source for advanced gravitational-wave detectors

We report on the performance of a dual-wavelength resonant, traveling-wave optical parametric oscillator to generate squeezed light for application in advanced gravitational-wave interferometers. Shot noise suppression of 8.6±0.8 dB was measured across the detection band of interest to Advanced LIGO, and controlled squeezing measured over 5900 s. Our results also demonstrate that the traveling-wave design has excellent intracavity backscattered light suppression of 47 dB and incident backscattered light suppression of 41 dB, which is a crucial design issue for application in advanced interferometers.

Invited review article: Interferometric gravity wave detectors

A direct detection of gravitational waves is still lacking today. A network of several earthbound interferometric detectors is currently operating with a continuously improving sensitivity. The window of interest for observation has a lower cut off in the frequency domain below some tens of hertz, determined by the effect of seismic motion. For larger frequencies, the sensitivity is limited by thermal effects below few hundreds of hertz and by the quantum nature of light above that value. Each of these sources of noise pose a big technological challenge to experimentalists, and there are big expectations for the next generation of detectors. A reduction of thermal effects by at least one order of magnitude will be obtained with new and carefully designed materials. At that point the quantum nature of light will become an issue, and the use of quantum non-demolition techniques will become mandatory. In this review, we discuss interferometric detection of gravitational waves from an instrumental point of view. We try to address conceptually important issues with an audience of non-experts in mind. A particular emphasis is given to the description of the current limitations and to the perspectives of beating them.

Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor

We experimentally demonstrate the creation of two correlated beams generated by a nondegenerate four-wave-mixing amplifier at λ=795 nm in hot rubidium vapor. We achieve intensity difference squeezing at frequencies as low as 1.5 kHz which is so far the lowest frequency to observe squeezing in an atomic system. The squeezing spans from 5.5 to 16.5 MHz with a maximum squeezing of -5 dB at 1 MHz. We can control the squeezing bandwidth by changing the pump power. Both low frequency and controllable bandwidth squeezing show great potential in sensitivity detection and precise control of the atom optics measurement.

Noise suppression, linewidth narrowing of a master oscillator power amplifier at 1.56 microm and the second harmonic generation output at 780 nm

We have demonstrated a 2 W cw single frequency 1.56 microm laser using a diode laser seeded Erbium doped fiber power amplifier, and a 715 mW cw single-frequency 780 nm laser by an external cavity enhanced second-harmonic-generation. The performance of the system was improved greatly by the seed diode laser optical locked to the resonant frequency of confocal F-P cavity. The linewidth of the 1.56 microm laser was narrowed from 2 MHz to 200 kHz, meanwhile, the intensity and phase noises were suppressed by 10 dB and 12 dB, respectively. The linewidth of the 780 nm laser was narrowed from 2 MHz to 300 kHz, meanwhile, the intensity and phase noises were suppressed by 11 dB and 13 dB, respectively.

Observation of entanglement between two light beams spanning an octave in optical frequency

We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.

Delay of squeezing and entanglement using electromagnetically induced transparency in a vapour cell

We demonstrate experimentally the delay of squeezed light and entanglement using Electromagnetically Induced Transparency (EIT) in a rubidium vapour cell. We perform quadrature amplitude measurements of the probe field and find no appreciable excess noise from the EIT process. From input squeezing of 3.2+/-0.5 dB at low sideband frequencies, we observed the survival of 2.0+/-0.5 dB of squeezing at the EIT output. By splitting the squeezed light on a beam-splitter, we generated biased entanglement between two beams. We transmit one of the entangled beams through the EIT cell and correlate the quantum statistics of this beam with its entangled counterpart. We experimentally observed a 2.2+/-0.5 micros delay of the biased entanglement and obtained a preserved degree of wavefunction inseparability of 0.71+/-0.01, below the unity value for separable states.

Observation of squeezed light with 10-dB quantum-noise reduction

Squeezing of light's quantum noise requires temporal rearranging of photons. This again corresponds to creation of quantum correlations between individual photons. Squeezed light is a nonclassical manifestation of light with great potential in high-precision quantum measurements, for example, in the detection of gravitational waves [C. M. Caves, Phys. Rev. D 23, 1693 (1981)10.1103/PhysRevD.23.1693]. Equally promising applications have been proposed in quantum communication [H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory 24, 657 (1978)10.1109/TIT.1978.1055958]. However, after 20 years of intensive research doubts arose whether strong squeezing can ever be realized as required for eminent applications. Here we show experimentally that strong squeezing of light's quantum noise is possible. We reached a benchmark squeezing factor of 10 in power (10 dB). Thorough analysis reveals that even higher squeezing factors will be feasible in our setup.

Tools for multimode quantum information: modulation, detection, and spatial quantum correlations

We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear chi(2) material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.

Coherent control of vacuum squeezing in the gravitational-wave detection band

We propose and demonstrate a coherent control scheme for stable phase locking of squeezed vacuum fields. We focus on sideband fields at frequencies from 10 Hz to 10 kHz, which is a frequency regime of particular interest in gravitational-wave detection and for which conventional control schemes have failed so far. A vacuum field with broadband squeezing covering this entire band was produced using optical parametric oscillation and characterized with balanced homodyne detection. The system was stably controlled over long periods utilizing two coherent but frequency shifted control fields. In order to demonstrate the performance of our setup the squeezed field was used for a nonclassical sensitivity improvement of a Michelson interferometer at audio frequencies.

Generating controllable atom-light entanglement with a Raman atom laser system

We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a Bose-Einstein condensate via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field and show that, with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.