Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer

Frequency-Dependent Squeezed Vacuum Source for the Advanced Virgo Gravitational-Wave Detector

In this Letter, we present the design and performance of the frequency-dependent squeezed vacuum source that will be used for the broadband quantum noise reduction of the Advanced Virgo Plus gravitational-wave detector in the upcoming observation run. The frequency-dependent squeezed field is generated by a phase rotation of a frequency-independent squeezed state through a 285 m long, high-finesse, near-detuned optical resonator. With about 8.5 dB of generated squeezing, up to 5.6 dB of quantum noise suppression has been measured at high frequency while close to the filter cavity resonance frequency, the intracavity losses limit this value to about 2 dB. Frequency-dependent squeezing is produced with a rotation frequency stability of about 6 Hz rms, which is maintained over the long term. The achieved results fulfill the frequency dependent squeezed vacuum source requirements for Advanced Virgo Plus. With the current squeezing source, considering also the estimated squeezing degradation induced by the interferometer, we expect a reduction of the quantum shot noise and radiation pressure noise of up to 4.5 dB and 2 dB, respectively.

Enhanced phase sensitivity in a Mach-Zehnder interferometer via photon recycling

We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of ∼9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramér-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift ϕ while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling.

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.

Ultrasensitive and long-range transverse displacement metrology with polarization-encoded metasurface

A long-range, high-precision, and compact transverse displacement metrology method is of crucial importance in many research areas. Recent schemes using optical antennas are limited in efficiency and the range of measurement due to the small size of the antenna. Here, we demonstrated the first prototype polarization-encoded metasurface for ultrasensitive long-range transverse displacement metrology. The transverse displacement of the metasurface is encoded into the polarization direction of the outgoing light via the Pancharatnam-Berry phase, which can be read out directly according to the Malus law. We experimentally demonstrate nanometer displacement resolution with the uncertainty on the order of 100 picometers for a large measurement range of 200 micrometers with the total area of the metasurface being within 900 micrometers by 900 micrometers. The measurement range can be extended further using a larger metasurface. Our work opens new avenues of applying metasurfaces in the field of ultrasensitive optical transverse displacement metrology.

Phase-sensitive manipulation of squeezed vacuum via a dual-recycled Michelson interferometer

The injection of squeezed vacuum state is an indispensable technology for the next generation gravitational wave observatory, which will open up a much larger window to the universe. After analyzing the absorption and dispersion properties of the reflected field of the dual-recycled Michelson interferometer (DRMI), we propose the phase-sensitive manipulation scheme of squeezed vacuum by utilizing the coupled-resonator-induced transparency in a dual-recycled Michelson interferometer (DRMI). In this way, the rotation frequency of squeezing ellipse can be finely tuned by the coupling strength, which overcome the limitation of the current solution (with a fixed rotation frequency) that employs a Fabry-Perot optical cavity as phase-sensitive manipulation element. This work will unleash the potential applications for quantum metrology beyond the shot noise limit.

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.

Long-term stable continuous variable entanglement generation in type-II non-degenerate optical parametric amplifier

Long-term stable entanglement is a crucial aspect in the implementation of reliable quantum information processes. However, long-term continuous variable entanglement generation, especially in type-II non-degenerate optical parametric amplifier, has yet to be reported on. Here, we derive the relationship between entanglement and temperature fluctuations in the crystal of a type-II non-degenerate optical parametric amplifier, and propose a novel method for long-term stable entanglement generation by locking the temperature of the crystal. In the experiment, we obtain a 5.4 dB entanglement lasting two hours. The method holds promise in the generation of a truly usable above 10 dB entanglement and brings us closer to continuous-variable quantum information processing.

Interference-Induced Quantum Squeezing Enhancement in a Two-beam Phase-Sensitive Amplifier

We experimentally demonstrate a method for realizing quantum squeezing enhancement which is induced by the interference in a two-beam phase-sensitive amplifier (PSA) based on a four-wave mixing process. Compared to the normal phase-insensitive amplifier with an intensity-difference squeezing (IDS) of 8.97±0.24  dB or 8.76±0.26  dB, the IDS of our two-beam PSA is enhanced to 10.13±0.21  dB under the same experimental situation. Furthermore, we study how various parameters influence the quantum squeezing enhancement of the PSA. These results clearly show that the physical mechanism inducing the IDS enhancement of the two-beam PSA is its intrinsic interference nature. Our results may find potential applications in improving the fidelity of quantum information processing and the precision of quantum metrology.

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.

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.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

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.

Length sensing and control of a Michelson interferometer with power recycling and twin signal recycling cavities

The techniques of power recycling and signal recycling have proven as key concepts to increase the sensitivity of large-scale gravitational wave detectors by independent resonant enhancement of light power and signal sidebands within the interferometer. Developing the latter concept further, twin signal recycling was proposed as an alternative to conventional detuned signal recycling. Twin signal recycling features the narrow-band sensitivity gain of conventional detuned signal recycling but furthermore facilitates the injection of squeezed states of light, increases the detector sensitivity over a wide frequency band and requires a less complex detection scheme for optimal signal readout. These benefits come at the expense of an additional recycling mirror, thus increasing the number of degrees of freedom in the interferometer which need to be controlled.In this article we describe the development of a length sensing and control scheme and its successful application to a tabletop-scale power recycled Michelson interferometer with twin signal recycling. We were able to lock the interferometer in all relevant longitudinal degrees of freedom and thus laid the foundation for further investigations of this interferometer configuration to evaluate its viability for the application in gravitational wave detectors.

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.

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.

A new method for locking the signal-field phase difference in a type-II optical parametric oscillator above threshold

We propose and demonstrate a new method for phaselocking the signal fields emitted above threshold by a nondegenerate, type-II optical parametric oscillator (OPO). This method is based on the observation that amplitude modulation of the pump beam produces a related modulation of the frequency difference of the OPO signals via the temperature-tuning of the index of refraction in the nonlinear crystal. We successfully use pump modulation as a correction for phase-difference locking of the OPO signals and observe a 1 kHz beat note stable over more than 10 s, both figures solely limited by the measurement time. This method eliminates the need for applying electronic phase-correction signals directly to the nonlinear crystal which caused crystal damage in a previous phaselocking technique.

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

Only a few years ago, it was realized that the zero-area Sagnac interferometer topology is able to perform quantum nondemolition measurements of position changes of a mechanical oscillator. Here, we experimentally show that such an interferometer can also be efficiently enhanced by squeezed light. We achieved a nonclassical sensitivity improvement of up to 8.2 dB, limited by optical loss inside our interferometer. Measurements performed directly on our squeezed-light laser output revealed squeezing of 12.7 dB. We show that the sensitivity of a squeezed-light enhanced Sagnac interferometer can surpass the standard quantum limit for a broad spectrum of signal frequencies without the need for filter cavities as required for Michelson interferometers. The Sagnac topology is therefore a powerful option for future gravitational-wave detectors, such as the Einstein Telescope, whose design is currently being studied.

Demonstration of a quantum-enhanced fiber Sagnac interferometer

The injection of squeezed light can be used to improve the sensitivity of an interferometer beyond the limit imposed by the zero-point fluctuation of the electromagnetic field. Here, we report on the realization of such a quantum-enhanced interferometer with a fiber-based Sagnac topology. Continuous wave squeezed states at 1550 nm with a noise reduction of 6.4 dB below shot noise were produced by type I optical parametric amplification and subsequently injected into the dark port of the interferometer. A reduction of the interferometer shot noise by 4.5 dB was observed, and the enhancement of the signal-to-noise ratio for a phase modulation signal generated within the interferometer could be demonstrated. We achieved a 95% fiber transmission for the squeezed states, which suggests that corresponding fiber-based quantum metrology and communication systems are feasible.

Parametric amplification of vacuum fluctuations in a spinor condensate

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 87Rb condensate. Interatomic interactions lead to correlated pair creation in the mF=±1 states from an initial mF=0 condensate, which acts as a vacuum for mF≠0. Although this pair creation from a pure mF=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial mF=±1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of nonclassical states of matter.

Broadband squeezing of quantum noise in a Michelson interferometer with Twin-Signal-Recycling

Twin-Signal-Recycling (TSR) builds on the resonance doublet of two optically coupled cavities and efficiently enhances the sensitivity of an interferometer at a dedicated signal frequency. We report on what we believe to be the first experimental realization of a TSR Michelson interferometer and also its broadband enhancement by squeezed light injection. The complete setup was stably locked, and a broadband quantum noise reduction of the interferometers shot noise by a factor of up to 4 dB was demonstrated. The system was characterized by measuring its quantum noise spectra for several tunings of the TSR cavities. We found good agreement between the experimental results and numerical simulations.

Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed-vacuum light

We show that the phase sensitivity Deltatheta of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit Deltatheta approximately 1/N(T), where N(T) is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, Deltatheta approximately 1/square root[|alpha|(2)e(2r)+sinh(2)r], can be saturated for arbitrary values of the squeezing parameter r and the amplitude of the coherent mode alpha by using a Bayesian phase inference protocol.

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.

Detuned Twin-Signal-Recycling for ultrahigh-precision interferometers

We propose a new interferometer technique for high-precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provide identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single-sideband recycling topologies of current and planned gravitational wave detectors. Furthermore, the application of squeezed states of light becomes less demanding.

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.

Experimental demonstration of continuous variable purification of squeezed States

We report on the first experimental demonstration of purification of nonclassical continuous variable states. The protocol uses two copies of phase-diffused states overlapped on a beam splitter and provides Gaussified, less mixed states with the degree of squeezing improved. The protocol uses only linear optical devices such as beam splitters and homodyne detection, thereby proving these optical elements can be used for successful purification of this type of state decoherence which occurs in optical transmission channels.

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.