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

Pushing the boundaries of gravitational wave detection

Broadband reduction of quantum noise should accelerate discovery.

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.

Experimental observation of Earth's rotation with quantum entanglement

Precision interferometry with quantum states has emerged as an essential tool for experimentally answering fundamental questions in physics. Optical quantum interferometers are of particular interest because of mature methods for generating and manipulating quantum states of light. Their increased sensitivity promises to enable tests of quantum phenomena, such as entanglement, in regimes where tiny gravitational effects come into play. However, this requires long and decoherence-free processing of quantum entanglement, which, for large interferometric areas, remains unexplored territory. Here, we present a table-top experiment using maximally path-entangled quantum states of light in a large-scale interferometer sensitive enough to measure the rotation rate of Earth. The achieved sensitivity of 5 μrad s-1 constitutes the highest rotation resolution ever reached with optical quantum interferometers. Further improvements to our methodology will enable measurements of general-relativistic effects on entangled photons, allowing the exploration of the interplay between quantum mechanics and general relativity, along with tests for fundamental physics.

A Bi-CMOS electronic photonic integrated circuit quantum light detector

Complimentary metal-oxide semiconductor (CMOS) integration of quantum technology provides a route to manufacture at volume, simplify assembly, reduce footprint, and increase performance. Quantum noise-limited homodyne detectors have applications across quantum technologies, and they comprise photonics and electronics. Here, we report a quantum noise-limited monolithic electronic-photonic integrated homodyne detector, with a footprint of 80 micrometers by 220 micrometers, fabricated in a 250-nanometer lithography bipolar CMOS process. We measure a 15.3-gigahertz 3-decibel bandwidth with a maximum shot noise clearance of 12 decibels and shot noise clearance out to 26.5 gigahertz, when measured with a 9-decibel-milliwatt power local oscillator. This performance is enabled by monolithic electronic-photonic integration, which goes below the capacitance limits of devices made up of separate integrated chips or discrete components. It exceeds the bandwidth of quantum detectors with macroscopic electronic interconnects, including wire and flip chip bonding. This demonstrates electronic-photonic integration enhancing quantum photonic device performance.

First Results of the Laser-Interferometric Detector for Axions (LIDA)

We present the operating principle and the first observing run of a novel kind of direct detector for axions and axionlike particles in the galactic halo. Sensitive to the polarisation rotation of linearly polarised laser light induced by an axion field, our experiment is the first detector of its kind collecting scientific data. We discuss our peak sensitivity of 1.51×10^{-10}  GeV^{-1} (95% confidence level) to the axion-photon coupling strength in the axion mass range of 1.97-2.01 neV which is, for instance, motivated by supersymmetric grand-unified theories. We also report on effects that arise in our high-finesse in-vacuum cavity at an unprecedented optical continuous-wave intensity of 4.7  MW/cm^{2}. Our detector already belongs to the most sensitive direct searches within its measurement band, and our results pave the way towards surpassing the current sensitivity limits even of astrophysical observations in the mass range from 10^{-8} down to 10^{-16}  eV via quantum-enhanced laser interferometry, especially with the potential of scaling our detector up to kilometer length.

A High-Finesse Suspended Interferometric Sensor for Macroscopic Quantum Mechanics with Femtometre Sensitivity

We present an interferometric sensor for investigating macroscopic quantum mechanics on a table-top scale. The sensor consists of a pair of suspended optical cavities with finesse over 350,000 comprising 10 g fused silica mirrors. The interferometer is suspended by a four-stage, light, in-vacuum suspension with three common stages, which allows for us to suppress common-mode motion at low frequency. The seismic noise is further suppressed by an active isolation scheme, which reduces the input motion to the suspension point by up to an order of magnitude starting from 0.7 Hz. In the current room-temperature operation, we achieve a peak sensitivity of 0.5 fm/Hz in the acoustic frequency band, limited by a combination of readout noise and suspension thermal noise. Additional improvements of the readout electronics and suspension parameters will enable us to reach the quantum radiation pressure noise. Such a sensor can eventually be utilized for demonstrating macroscopic entanglement and for testing semi-classical and quantum gravity models.

Kerr-Enhanced Optical Spring

We propose and experimentally demonstrate the generation of enhanced optical springs using the optical Kerr effect. A nonlinear optical crystal is inserted into a Fabry-Perot cavity with a movable mirror, and a chain of second-order nonlinear optical effects in the phase-mismatched condition induces the Kerr effect. The optical spring constant is enhanced by a factor of 1.6±0.1 over linear theory. To our knowledge, this is the first realization of optomechanical coupling enhancement using a nonlinear optical effect, which has been theoretically investigated to overcome the performance limitations of linear optomechanical systems. The tunable nonlinearity of demonstrated system has a wide range of potential applications, from observing gravitational waves emitted by binary neutron star postmerger remnants to cooling macroscopic oscillators to their quantum ground state.

Pinpointing gravitational waves via astrometric gravitational wave antennas

The direct detection of gravitational waves by ground-based optical interferometers has opened a new window in astronomy. Besides, the sensitivity of these linear detectors to the direction of arrival of an incoming gravitational wave is limited compared to current prospects of high-precision, space-based, astrometry. Indeed, advanced methods of differential relativistic astrometry offer a unique opportunity to overcome that situation. Here, we present a novel concept for a gravitational wave antenna that uses angles between close pairs of point-like sources as natural (angular) "arms" to characterise the very tiny variations in angular separations induced by a passing gravitational wave. The proposed new astrometric gravitational wave observable proves to be a powerful tool to substantially enhance the effect of gravitational waves of different strengths by exploiting optical resolution to the fullest. Then, by optically multiplexing three (or more) of such astrometric "arms", it would be also possible to pinpoint source directions to unprecedented levels.

10-dB squeeze laser tuneable over half a nanometer around 1550 nm

Lasers for generating monochromatic light beams with sideband spectra in strongly squeezed vacuum states are the basis for aspired optical continuous-variable quantum computers. We have developed a "squeeze laser" that produces 10 dB squeezed vacuum states at a wavelength of 1550 nm, the latter being tunable by 0.5 nm without losing the high squeeze factor. Several identical squeeze lasers can thus be combined to realise wavelength-division multiplexing. Our squeeze laser uses the mature technology of parametric down-conversion in a periodically poled KTP crystal placed in a cavity that resonates both the squeezed field and the second harmonic pump field. Unlike previous realisations, we achieve the double resonance and phase matching by individually optimising and controlling the temperatures of two sections of the crystal body. The wavelength range is currently limited by the tuneability of the 1550 nm master laser.

Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality

Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection.

Tomography of a Number-Resolving Detector by Reconstruction of an Atomic Many-Body Quantum State

The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.

Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here, we show a novel type of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the noninteracting harmonic oscillator. By driving the system, we generate squeezing which has the unique property of time-independent uncertainties and squeezed dynamics. Such squeezing might find applications in continuous backaction evading measurements and should already be observable in optomechanical systems and Coulomb crystals.

Characterization and evasion of backscattered light in the squeezed-light enhanced gravitational wave interferometer GEO 600

Squeezed light is injected into the dark port of gravitational wave interferometers, in order to reduce the quantum noise. A fraction of the interferometer output light can reach the OPO due to sub-optimal isolation of the squeezing injection path. This backscattered light interacts with squeezed light generation process, introducing additional measurement noise. We present a theoretical description of the noise coupling mechanism and we prove the model with experimental results. We propose a control scheme to achieve a de-amplification of the backscattered light inside the OPO with a consequent reduction of the noise caused by it. The scheme was implemented at the GEO 600 detector and has proven to be crucial in maintaining a good level of quantum noise reduction of the interferometer for high parametric gain of the OPO. In particular, the mitigation of the backscattered light noise helped in reaching 6 dB of quantum noise reduction [Phys. Rev. Lett.126, 041102 (2021)10.1103/PhysRevLett.126.041102]. We show that the impact of backscattered-light-induced noise on the squeezing performance is phenomenologically equivalent to increased phase noise of the squeezing angle control. The results discussed in this paper provide a way for a more accurate estimation of the residual phase noise of the squeezed light field. Finally, the knowledge of the backscattered light noise coupling mechanism is a useful tool to inform the design of the squeezing injection path in terms of path stability and optical isolation.

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.

Single and coupled cavity mode sensing schemes using a diagnostic field

Precise optical mode matching is of critical importance in experiments using squeezed-vacuum states. Automatic spatial-mode matching schemes have the potential to reduce losses and improve loss stability. However, in quantum-enhanced coupled-cavity experiments, such as gravitational-wave detectors, one must also ensure that the sub-cavities are also mode matched. We propose what we believe to be a new mode sensing scheme, which works for simple and coupled cavities. The scheme requires no moving parts, nor tuning of Gouy phases. Instead a diagnostic field tuned to the HG20/LG10 mode frequency is used. The error signals are derived to be proportional to the difference in waist position, and difference in Rayleigh ranges, between the sub-cavity eigenmodes. The two error signals are separable by 90 degrees of demodulation phase. We demonstrate reasonable error signals for a simplified Einstein Telescope optical design. This work will facilitate routine use of extremely high levels of squeezing in current and future gravitational-wave detectors.

Mitigating Quantum Decoherence in Force Sensors by Internal Squeezing

The most efficient approach to laser interferometric force sensing to date uses monochromatic carrier light with its signal sideband spectrum in a squeezed vacuum state. Quantum decoherence, i.e., mixing with an ordinary vacuum state due to optical losses, is the main sensitivity limit. In this Letter, we present both theoretical and experimental evidence that quantum decoherence in high-precision laser interferometric force sensors enhanced with optical cavities and squeezed light injection can be mitigated by a quantum squeeze operation inside the sensor's cavity. Our experiment shows an enhanced measurement sensitivity that is independent of the optical readout loss in a wide range. Our results pave the way for quantum improvements in scenarios where high decoherence previously precluded the use of squeezed light. Our results hold significant potential for advancing the field of quantum sensors and enabling new experimental approaches in high-precision measurement technology.

Quantum-Enhanced Magnetometry at Optimal Number Density

We study the use of squeezed probe light and evasion of measurement backaction to enhance the sensitivity and measurement bandwidth of an optically pumped magnetometer (OPM) at sensitivity-optimal atom number density. By experimental observation, and in agreement with quantum noise modeling, a spin-exchange-limited OPM probed with off-resonance laser light is shown to have an optimal sensitivity determined by density-dependent quantum noise contributions. Application of squeezed probe light boosts the OPM sensitivity beyond this laser-light optimum, allowing the OPM to achieve sensitivities that it cannot reach with coherent-state probing at any density. The observed quantum sensitivity enhancement at optimal number density is enabled by measurement backaction evasion.

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.

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.

Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramér-Rao to Barankin

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramér-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.

Unification of Thermal and Quantum Noises in Gravitational-Wave Detectors

Contemporary gravitational-wave detectors are fundamentally limited by thermal noise-due to dissipation in the mechanical elements of the test mass-and quantum noise-from the vacuum fluctuations of the optical field used to probe the test-mass position. Two other fundamental noises can in principle also limit sensitivity: test-mass quantization noise due to the zero-point fluctuation of its mechanical modes and thermal excitation of the optical field. We use the quantum fluctuation-dissipation theorem to unify all four noises. This unified picture shows precisely when test-mass quantization noise and optical thermal noise can be ignored.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

Protection of Noise Squeezing in a Quantum Interferometer with Optimal Resource Allocation

Interferometers are crucial for precision measurements, including gravitational waves, laser ranging, radar, and imaging. The phase sensitivity, the core parameter, can be quantum-enhanced to break the standard quantum limit (SQL) using quantum states. However, quantum states are highly fragile and quickly degrade with losses. We design and demonstrate a quantum interferometer utilizing a beam splitter with a variable splitting ratio to protect the quantum resource against environmental impacts. The optimal phase sensitivity can reach the quantum Cramér-Rao bound of the system. This quantum interferometer can greatly reduce the quantum source requirements in quantum measurements. In theory, with a 66.6% loss rate, the sensitivity can break the SQL using only a 6.0 dB squeezed quantum resource with the current interferometer rather than a 24 dB squeezed quantum resource with a conventional squeezing-vacuum-injected Mach-Zehnder interferometer. In experiments, when using a 2.0 dB squeezed vacuum state, the sensitivity enhancement remains at ∼1.6  dB via optimizing the first splitting ratio when the loss rate changes from 0% to 90%, indicating that the quantum resource is excellently protected with the existence of losses in practical applications. This strategy could open a way to retain quantum advantages for quantum information processing and quantum precision measurement in lossy environments.

Unconditional and Robust Quantum Metrological Advantage beyond N00N States

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multiphoton entangled N00N states can in principle beat the shot-noise limit and reach the Heisenberg limit, high N00N states are difficult to prepare and fragile to photon loss which hinders them from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for the photonic quantum computer Jiuzhang, to propose and realize a new scheme that achieves a scalable, unconditional, and robust quantum metrological advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in the Fisher information extracted per photon, without discounting for photon loss and imperfections, which outperforms ideal 5-N00N states. The Heisenberg-limited scaling, the robustness to external photon loss, and the ease-of-use of our method make it applicable in practical quantum metrology at a low photon flux regime.

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

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

12.6 dB squeezed light at 1550 nm from a bow-tie cavity for long-term high duty cycle operation

Squeezed states are an interesting class of quantum states that have numerous applications. This work presents the design, characterization, and operation of a bow-tie optical parametric amplifier (OPA) for squeezed vacuum generation. We report the high duty cycle operation and long-term stability of the system that makes it suitable for post-selection based continuous-variable quantum information protocols, cluster-state quantum computing, quantum metrology, and potentially gravitational wave detectors. Over a 50 hour continuous operation, the measured squeezing levels were greater than 10 dB with a duty cycle of 96.6%. Alternatively, in a different mode of operation, the squeezer can also operate 10 dB below the quantum noise limit over a 12 hour period with no relocks, with an average squeezing of 11.9 dB. We also measured a maximum squeezing level of 12.6 dB at 1550 nm. This represents one of the best reported squeezing results at 1550 nm to date for a bow-tie cavity. We discuss the design aspects of the experiment that contribute to the overall stability, reliability, and longevity of the OPA, along with the automated locking schemes and different modes of operation.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Squeezed States of Light for Future Gravitational Wave Detectors at a Wavelength of 1550 nm

The generation of strongly squeezed vacuum states of light is a key technology for future ground-based gravitational wave detectors (GWDs) to reach sensitivities beyond their quantum noise limit. For some proposed observatory designs, an operating laser wavelength of 1550 nm or around 2  μm is required to enable the use of cryogenically cooled silicon test masses for thermal noise reduction. Here, we present for the first time the direct measurement of up to 11.5 dB squeezing at 1550 nm over the complete detection bandwidth of future ground-based GWDs ranging from 10 kHz down to below 1 Hz. Furthermore, we directly observe a quantum shot-noise reduction of up to (13.5±0.1)  dB at megahertz frequencies. This allows us to derive a precise constraint on the absolute quantum efficiency of the photodiode used for balanced homodyne detection. These results hold important insight regarding the quantum noise reduction efficiency in future GWDs, as well as for quantum information and cryptography, where low decoherence of nonclassical states of light is also of high relevance.

Thermally controlled optical resonator for vacuum squeezed states separation

Future gravitational-wave detectors will use frequency-dependent squeezed vacuum states to obtain broadband reduction of quantum noise. Quantum noise is one of the major limitations to the sensitivity of these detectors. Advanced LIGO+, Advanced Virgo+, and KAGRA plan to generate frequency-dependent squeezed states by coupling a frequency-independent squeezed light state with a filter cavity. An alternative technique is under consideration, based on conditional squeezing with quantum entanglement: Einstein-Podolsky-Rosen (EPR) squeezing. In the EPR scheme, two vacuum entangled states, the signal field at ω₀ and the idler field at ω₀+Δ, must be spatially separated with an optical resonator and sent to two separate homodyne detectors. In this framework, we have designed and tested a solid Fabry-Perot etalon, to be used in an EPR table-top experiment prototype, thermally controlled without the use of a control probe optical beam. This device can also be used in optical experiments where the use of a bright beam to control an optical resonator is not possible, or where a simpler optical device is preferred.

Enhancing vacuum squeezing via magnetic field optimization

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

Research Facilities for Europe’s Next Generation Gravitational-Wave Detector Einstein Telescope

The Einstein Telescope is Europe’s next generation gravitational-wave detector. To develop all necessary technology, four research facilities have emerged across Europe: The Amaldi Research Center (ARC) in Rome (Italy), ETpathfinder in Maastricht (The Netherlands), SarGrav in the Sos Enattos mines on Sardinia (Italy) and E-TEST in Liége (Belgium) and its surroundings. The ARC pursues the investigation of a large cryostat, equipped with dedicated low-vibration cooling lines, to test full-scale cryogenic payloads. The installation will be gradual and interlaced with the payload development. ETpathfinder aims to provide a low-noise facility that allows the testing of full interferometer configurations and the interplay of their subsystems in an ET-like environment. ETpathfinder will focus amongst others on cryogenic technologies, silicon mirrors, lasers and optics at 1550 and 2090 nm and advanced quantum noise reduction schemes. The SarGrav laboratory has a surface lab and an underground operation. On the surface, the Archimedes experiment investigates the interaction of vacuum fluctuations with gravity and is developing (tilt) sensor technology for the Einstein Telescope. In an underground laboratory, seismic characterisation campaigns are undertaken for the Sardinian site characterisation. Lastly, the Einstein Telecope Euregio meuse-rhine Site & Technology (E-TEST) is a single cryogenic suspension of an ET-sized silicon mirror. Additionally, E-TEST investigates the Belgian–Dutch–German border region that is the other candidate site for Einstein Telescope using boreholes and seismic arrays and hydrogeological characterisation. In this article, we describe the Einstein Telescope, the low-frequency part of its science case and the four research facilities.

The Current Status and Future Prospects of KAGRA, the Large-Scale Cryogenic Gravitational Wave Telescope Built in the Kamioka Underground

KAGRA is a gravitational-wave (GW) detector constructed in Japan with two unique key features: It was constructed underground, and the test-mass mirrors are cooled to cryogenic temperatures. These features are not included in other kilometer-scale detectors but will be adopted in future detectors such as the Einstein Telescope. KAGRA performed its first joint observation run with GEO600 in 2020. In this observation, the sensitivity of KAGRA to GWs was inferior to that of other kilometer-scale detectors such as LIGO and Virgo. However, further upgrades to the detector are ongoing to reach the sensitivity for detecting GWs in the next observation run, which is scheduled for 2022. In this article, the current situation, sensitivity, and future perspectives are reviewed.

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.

Extract the Degradation Information in Squeezed States with Machine Learning

In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine-learning architecture with a convolutional neural network, we illustrate a fast, robust, and precise quantum state tomography for continuous variables, through the experimentally measured data generated from the balanced homodyne detectors. Compared with the maximum likelihood estimation method, which suffers from time-consuming and overfitting problems, a well-trained machine fed with squeezed vacuum and squeezed thermal states can complete the task of reconstruction of the density matrix in less than one second. Moreover, the resulting fidelity remains as high as 0.99 even when the antisqueezing level is higher than 20 dB. Compared with the phase noise and loss mechanisms coupled from the environment and surrounding vacuum, experimentally, the degradation information is unveiled with machine learning for low and high noisy scenarios, i.e., with the antisqueezing levels at 12 dB and 18 dB, respectively. Our neural network enhanced quantum state tomography provides the metrics to give physical descriptions of every feature observed in the quantum state with a single scan measurement just by varying the local oscillator phase from 0 to 2π and paves a way of exploring large-scale quantum systems in real time.

Detecting Gravitational Waves with Advanced Virgo

Advanced Virgo is the European gravitational-wave detector that, along with the American ones, is part of the global network of detectors that have been pinpointing gravitational waves since 2015. These kilometer-scale laser interferometers, measuring the distance between quasi-free-falling mirrors, represent the suitable detectors to explore the Universe through gravitational radiation. The initial Virgo experiment completed several runs of scientific data between 2007 and 2011, establishing the upper limits on the gravitational-wave rate expected for several astrophysical sources. The Advanced Virgo project led this instrument to unprecedented sensitivities making gravitational wave detections a routine occurrence. In this review, the basic techniques to build gravitational-waves interferometers and the upgrades needed to boost their sensitivities, even beyond the classical limit, are presented. The particular case of Advanced Virgo will be described hinting at its future developments, as well.

SU(2)-in-SU(1,1) Nested Interferometer for High Sensitivity, Loss-Tolerant Quantum Metrology

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.

Squeezed light at 2128 nm for future gravitational-wave observatories

All gravitational-wave observatories (GWOs) have been using the laser wavelength of 1064 nm. Ultra-stable laser devices are at the sites of GEO 600, Kagra, LIGO, and Virgo. Since 2019, not only GEO 600, but also LIGO and Virgo have been using separate devices for squeezing the uncertainty of the light, so-called squeeze lasers. The sensitivities of future GWOs will strongly gain from reducing the thermal noise of the suspended mirrors, which involves shifting the wavelength into the 2 µm region. This Letter aims to reuse the existing high-performance lasers at 1064 nm. Here we report the realization of a squeeze laser at 2128 nm that uses pump light at 1064 nm. We achieve the direct observation of 7.2 dB of squeezing as the first step at megahertz sideband frequencies. The squeeze factor achieved is mainly limited by the photodiode's quantum efficiency, which we estimated to (92±3)%. Reaching larger squeeze factors seems feasible also in the required audio and sub-audio sideband, provided photo diodes with sufficiently low dark noise will be available. Our result promotes 2128 nm as the new, to the best of our knowledge, cost-efficient wavelength of GWOs.

Quantum Enhanced Cavity QED Interferometer with Partially Delocalized Atoms in Lattices

We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states is combined with the subsequent application of a compound pulse sequence that allows us to separate atoms by several lattice sites. This, together with the capability to load small atomic clouds in the lattice at micrometric distances from a surface, make our setup ideal for sensing short-range forces. We show that for arrays of 10^{4} atoms, our protocol can reduce the required averaging time by a factor of 10 compared to unentangled lattice-based interferometers after accounting for primary sources of decoherence.

Augmenting the Sensing Performance of Entangled Photon Pairs through Asymmetry

We analyze theoretically and experimentally cases of asymmetric detection, stimulation, and loss within a quantum nonlinear interferometer of entangled pairs. We show that the visibility of the SU(1,1) interference directly discerns between loss on the measured mode (signal) and the conjugated mode (idler). This asymmetry also affects the phase sensitivity of the interferometer, where coherent seeding is shown to mitigate losses that are suffered by the conjugated mode; therefore increasing the maximum threshold of loss that permits sub-shot-noise phase detection. Our findings can improve the performance of setups that rely on direct detection of entangled pairs, such as quantum interferometry and imaging with undetected photons.

Scaling Laws for the Sensitivity Enhancement of Non-Gaussian Spin States

We identify the large-N scaling of the metrological quantum gain offered by over-squeezed spin states that are accessible by one-axis twisting, as a function of the preparation time. We further determine how the scaling is modified by relevant decoherence processes and predict a discontinuous change of the quantum gain at a critical preparation time that depends on the noise. Our analytical results provide recipes for optimal and feasible implementations of quantum enhancements with non-Gaussian spin states in existing experiments, well beyond the reach of spin squeezing.

Robust squeezed light against mode mismatch using a self imaging optical parametric oscillator

We present squeezed light that is robust against spatial mode mismatch (beam displacement, tilt, and beam-size difference), which is generated from a self-imaging optical parametric oscillator below the threshold. We investigate the quantum properties of the generated light when the oscillator is detuned from the ideal self-imaging condition for stable operation. We find that the generated light is more robust to mode mismatch than single-mode squeezed light having the same squeezing level, and it even outperforms the single-mode infinitely squeezed light as the strength of mode mismatch increases.

Advanced Virgo: Status of the Detector, Latest Results and Future Prospects

The Virgo detector, based at the EGO (European Gravitational Observatory) and located in Cascina (Pisa), played a significant role in the development of the gravitational-wave astronomy. From its first scientific run in 2007, the Virgo detector has constantly been upgraded over the years; since 2017, with the Advanced Virgo project, the detector reached a high sensitivity that allowed the detection of several classes of sources and to investigate new physics. This work reports the main hardware upgrades of the detector and the main astrophysical results from the latest five years; future prospects for the Virgo detector are also presented.

Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals

Fully controllable ultracold atomic systems are creating opportunities for quantum sensing, yet demonstrating a quantum advantage in useful applications by harnessing entanglement remains a challenging task. Here, we realize a many-body quantum-enhanced sensor to detect displacements and electric fields using a crystal of ~150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high-Q mechanical oscillator, and the collective electronic spin serves as the measurement device. By entangling the oscillator and collective spin and controlling the coherent dynamics via a many-body echo, a displacement is mapped into a spin rotation while avoiding quantum back-action and thermal noise. We achieve a sensitivity to displacements of 8.8 ± 0.4 decibels below the standard quantum limit and a sensitivity for measuring electric fields of 240 ± 10 nanovolts per meter in 1 second. Feasible improvements should enable the use of trapped ions in searches for dark matter.

Revealing optical loss from modal frequency degeneracy in a long optical cavity

Optical loss plays a significant role in optical experiments involving optical cavities such as recycling cavities and filter cavities in laser interferometer gravitational-wave detectors. For those cavities, modal frequency degeneracy, where the fundamental and a higher order mode resonate inside the cavity simultaneously, is a potential mechanism which may bring extra optical loss to the cavity thus degrade detection sensitivity. In this paper, we report observation of modal frequency degeneracy in a large-scale suspended Fabry-Pérot cavity. The cavity g-factor is tuned by a CO₂ laser heating one test mass, and the cavity finesse is obtained from a ring-down measurement of the transmitted light. We demonstrate that the modal frequency degeneracy can cause a reduction of the cavity finesse by up to ∼30%, corresponding to a ∼2-fold increase in total optical loss. To minimize optical loss in gravitational-wave detectors, the effect of modal frequency degeneracy needs to be taken into account in the design and operation of the detector.

The first 5 years of gravitational-wave astrophysics

Gravitational waves are ripples in spacetime generated by the acceleration of astrophysical objects; a direct consequence of general relativity, they were first directly observed in 2015. Here, I review the first 5 years of gravitational-wave detections. More than 50 gravitational-wave events have been found, emitted by pairs of merging compact objects such as neutron stars and black holes. These signals yield insights into the formation of compact objects and their progenitor stars, enable stringent tests of general relativity, and constrain the behavior of matter at densities higher than that of an atomic nucleus. Mergers that emit both gravitational and electromagnetic waves probe the formation of short gamma-ray bursts and the nucleosynthesis of heavy elements, and they measure the local expansion rate of the Universe.

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.

Quantum Plasmonic Sensors

The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.