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Squeezed mechanical states are a valuable tool for quantum sensing and error correction in quantum computing, and a pivotal platform for tests of fundamental physics. Recently, solid state mechanical oscillators have been prepared in squeezed states using parametric interactions in both the microwave and optical regimes. It has long been predicted that a fast measurement rate comparable to the mechanical resonance frequency can prepare the oscillator under measurement into a quantum squeezed state. Despite decades of effort, this straightforward protocol is yet to be demonstrated in the quantum regime. Here, we use post-processing techniques to demonstrate preparation of a 50 ng GaAs cantilever in a conditional classical squeezed state with a minimum uncertainty (0.28 plus/minus 0.18) dB above (1.07 plus/minus 0.04 times) the zero point fluctuations, 3 orders of magnitude closer to the quantum regime in variance than the previous record. This paves the way to real-time measurement-based preparation of macroscopic oscillators in quantum squeezed states, and can be adapted to mechanical systems as large as the kg-scale test masses of the Laser Interferometer Gravitational-Wave Observatory (LIGO).

Modern interferometers such as LIGO have achieved sensitivities limited by quantum noise, comprised of radiation pressure and shot noise. To mitigate this noise, a static system is employed that minimizes the quantum noise within the measurement band. However, since gravitational wave inspiral signals are a single frequency changing over time, only noise at the chirp frequency needs to be minimized. Here we demonstrate dynamically tracking a target signal using an optical spring, resulting in an increased signal to noise ratio (SNR). We report on a SNR increase by up to a factor of 40 when compared to a static configuration.

The development of manufacturable and scalable integrated nonlinear photonic materials is driving key technologies in diverse areas such as high-speed communications, signal processing, sensing, and quantum information. Here, we demonstrate a novel nonlinear platform -- InGaP-on-insulator -- optimized for visible-to-telecommunication wavelength $\chi^{\left(2\right)}$ nonlinear optical processes. In this work, we detail our 100-mm wafer-scale InGaP-on-insulator fabrication process realized via wafer bonding, optical lithography, and dry-etching techniques. The resulting wafers yield 1000s of components in each fabrication cycle, with initial designs that include chip-to-fiber couplers, 12.5-cm-long nested spiral waveguides, and arrays of microring resonators with free-spectral ranges spanning 400-900 GHz. We demonstrate intrinsic resonator quality factors as high as 324,000 (440,000) for single-resonance (split-resonance) modes near 1550 nm corresponding to 1.56 dB cm$^{-1}$ (1.22 dB cm$^{-1}$) propagation loss. We analyze the loss versus waveguide width and resonator radius to establish the operating regime for optimal 775-to-1550 nm phase matching. By combining the high $\chi^{\left(2\right)}$ and $\chi^{\left(3\right)}$ optical nonlinearity of InGaP with wafer-scale fabrication and low propagation loss, these results open promising possibilities for entangled-photon, multi-photon, and squeezed light generation.

We present a robust, precise, and accurate method to simultaneously measure the refractive indices of two transparent materials within an interference coating. This is achieved by measuring both a photometrically accurate transmittance spectrum and the as-grown individual layer thicknesses of a thin-film multilayer structure. These measurements are used for a TMM-based curve-fitting routine which extracts the refractive indices and their measurement uncertainties via a Monte-Carlo-type error propagation. We demonstrate the performance of this approach by experimentally measuring the refractive indices of both, GaAs and Al$_{0.929}$Ga$_{0.071}$As, as present in an epitaxial distributed Bragg reflector. A variety of devices can be used to obtain the transmittance spectrum (e.g., FTIR, grating-based spectrophotometer) and layer thicknesses (e.g., SEM, TEM, AFM), the discussed approach is readily adaptable to virtually any wavelength region and many transparent material combinations of interest. The subsequent model-fitting approach yields refractive index values with $10^{-4}$-level uncertainty for both materials., Comment: 13 pages, 3 figures, submitted to PRL

We present our results for simultaneous measurement of the refractive indices of gallium arsenide (GaAs) and aluminum gallium arsenide (Al$_\mathrm{x}$Ga$_\mathrm{1-x}$As) from $2.0$ to $7.1\,\mathrm{\mu m}$ ($5000$ to $1400\,\mathrm{cm^{-1}}$). We obtain these values from a monocrystalline superlattice Bragg mirror of excellent purity (background doping $\leq 1 \times 10^{-14}\,\mathrm{cm^{-3}}$), grown via molecular beam epitaxy. To recover the refractive indices over such a broad wavelength range, we fit a dispersion model for each material. In a novel combination of well-established methods, we measure both a photometrically accurate transmittance spectrum of the Bragg mirror via Fourier-transform infrared spectrometry and the individual physical layer thicknesses of the structure via scanning electron microscopy. To infer the uncertainty of the refractive index values, we estimate relevant measurement uncertainties and propagate them via a Monte-Carlo method. This highly-adaptable approach conclusively yields propagated relative uncertainties on the order of $10^{-4}$ over the measured spectral range for both GaAs and Al$_{0.929}$Ga$_{0.071}$As. The fitted model can also approximate the refractive index for MBE-grown Al$_\mathrm{x}$Ga$_\mathrm{1-x}$As for $0\leq x \leq 1$. Both these updated values and the measurement approach will be essential in the design, fabrication, and characterization of next-generation active and passive optical devices in a spectral region that is of high interest in many fields, e.g., laser design and cavity-enhanced spectroscopy in the mid-infrared spectral region., Comment: 21 pages, 6 figures, transferred to PRResearch

Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by $\textbf{2.8}$ dB, corresponding to a reduction in the noise power by $\textbf{72}\pm\textbf{5.1}$ \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe., Comment: 10 pages, 4 figures

Thermal noise in high-reflectivity mirror coatings is a limiting factor in ground-based gravitational wave detectors. Reducing this coating thermal noise improves the sensitivity of detectors and enriches the scientific outcome of observing runs. Crystalline gallium arsenide and aluminum-alloyed gallium arsenide (referred to as AlGaAs) coatings are promising coating candidates for future upgrades of gravitational wave detectors because of their low coating thermal noise. However, AlGaAs-based crystalline coatings may be susceptible to an electro-optic noise induced by fluctuations in an electric field. We investigated the electro-optic effect in an AlGaAs coating by using a Fabry-Perot cavity, and concluded that the noise level is well below the sensitivity of current and planned gravitational-wave detectors.

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments. This will result in the development of novel quantum sensors and a means to probe the foundations of quantum physics at the interface with gravity. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. These new technologies will open up the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade., Comment: 9 pages, 2 figures, submitted as a Research Campaign Whitepaper for the BPS2023 Decadal Survey

We report on the cancellation of quantum back action noise in an optomechanical cavity. We perform two measurements of the displacement of the microresonator, one in reflection of the cavity, and one in transmission of the cavity. We show that measuring the amplitude quadrature of the light in transmission of the optomechanical cavity allows us to cancel the back action noise between 1 kHz and 50 kHz, and obtain a more sensitive measurement of the microresonator's position. To confirm that the back action is eliminated, we measure the noise in the transmission signal as a function of circulating power. By splitting the transmitted light onto two photodetectors and cross correlating the two signals, we remove the contributon from shot noise and measure a quantum noise free thermal noise spectrum. Eliminating the effects of back action in this frequency regime is an important demonstration of a technique that could be used to mitigate the effects of back action in interferometric gravitational wave detectors such as Advanced LIGO.

The radiation-pressure driven interaction of a coherent light field with a mechanical oscillator induces correlations between the amplitude and phase quadratures of the light. These correlations result in squeezed light -- light with quantum noise lower than shot noise in some quadratures, and higher in others. Due to this lower quantum uncertainty, squeezed light can be used to improve the sensitivity of precision measurements. In particular, squeezed light sources based on nonlinear optical crystals are being used to improve the sensitivity of gravitational wave (GW) detectors. For optomechanical squeezers, thermally driven fluctuations of the mechanical oscillator's position makes it difficult to observe the quantum correlations at room temperature, and at low frequencies. Here we present a measurement of optomechanically (OM) squeezed light, performed at room-temperature, in a broad band near audio-frequency regions relevant to GW detectors. We observe sub-poissonian quantum noise in a frequency band of 30 kHz to 70 kHz with a maximum reduction of 0.7 $\pm$ 0.1 dB below shot noise at 45 kHz. We present two independent methods of measuring this squeezing, one of which does not rely on calibration of shot noise., Comment: 5 pages, 4 figures in main text. 4 pages, 5 figures in supplemental information

We present the reduction and manipulation of quantum radiation pressure noise (QRPN) in an optomechanical cavity with the injection of squeezed light. The optomechanical system consists of a high-reflectivity single-crystal microresonator which serves as one mirror of a Fabry-Perot cavity. The experiment is performed at room temperature and is QRPN dominated between 10 kHz and 50 kHz, frequencies relevant to gravitational wave observatories. We observed a reduction of 1.2 dB in the measurement noise floor with the injection of amplitude squeezed light generated from a below-threshold degenerate optical parametric oscillator. This experiment is a crucial step in realizing the reduction of QRPN for future interferometric gravitational wave detectors and improving their sensitivity.

We investigated elastic loss in GaAs/AlGaAs multilayers to help determine the suitability of these coatings for future gravitational wave detectors. We measured large ($\approx 70$-mm diameter) substrate-transferred crystalline coating samples with an improved substrate polish and bonding method. The elastic loss, when decomposed into bulk and shear contributions, was shown to arise entirely from the bulk loss, $\phi_{\mathrm{Bulk}} = (5.33 \pm 0.03)\times 10^{-4}$, with $\phi_{\mathrm{Shear}} = (0.0 \pm 5.2) \times 10^{-7}$. These results predict the coating loss of an 8-mm diameter coating in a 35-mm long cavity with a 250-$\mu$m spot size (radius) to be $\phi_{\mathrm{coating}} = (4.78 \pm 0.05) \times 10^{-5}$, in agreement with the published result from direct thermal noise measurement of $\phi_{\mathrm{coating}} = (4 \pm 4) \times 10^{-5}$. Bonding defects were shown to have little impact on the overall elastic loss., Comment: Submitted to Journal of the Optical Society of America B, Feature: Fluctuation-Induced Phenomena in Photonic Systems

We present a method to calculate the power spectral density of Brownian noise in complex optomechanical systems using Levin's approach of virtual pressure and present first mechanical loss measurements for high-purity GaAs over a wide temperature range from 7 K to 250 K. The loss reveals three Debye loss peaks. Each peak corresponds to an Arrhenius-like relaxation process with activation energies of 17.9 meV, 65.4 meV and 123 meV respectively. Additional light induced damping was observed for photon energies below and above the fundamental gap of GaAs in contrast to observations by Okamoto et al.

We investigate the mechanical properties of freely suspended nanostrings fabricated from tensile-stressed, crystalline In$_{1-x}$Ga$_{x}$P. The intrinsic strain is a consequence of the epitaxial growth given by the lattice mismatch between the thin film and the substrate which is confirmed by x-ray diffraction measurements. The flexural eigenfrequencies of the nanomechanical string resonators reveal an orientation dependent stress with a maximum value of 650 MPa. The angular dependence is explained by a combination of anisotropic Young's modulus and a change of elastic properties caused by defects. As a function of the crystal orientation a stress variation of up to 50 % is observed. This enables fine tuning of the tensile stress for any given Ga content $x$, which implies interesting prospects for the study of high Q nanomechanical systems.

We report on the broadband measurement of quantum radiation pressure noise (QRPN) in an optomechanical cavity at room temperature over a broad range of frequencies relevant to gravitational-wave detectors. We show that QRPN drives the motion of a high-reflectivity single-crystal microresonator, which serves as one mirror of a Fabry-Perot cavity. In our measurements QRPN dominates over all other noise between 10 kHz and 50 kHz and scales as expected with the circulating power inside the cavity. The thermal noise of the microresonator, the largest noise source next to the QRPN, is measured and shown to agree with a structural damping model from 200 Hz to 30 kHz. By observing the effects of QRPN in the audio-band, we now have a testbed for studying techniques to mitigate back-action, such as variational readout and squeezed light injection, that could be used to improve the sensitivity of gravitational-wave detectors.

We present the experimental observation of an optical spring without the use of an optical cavity. The optical spring is produced by interference at a beamsplitter and, in principle, does not have the damping force associated with optical springs created in detuned cavities. The experiment consists of a Michelson-Sagnac interferometer (with no recycling cavities) with a partially reflective GaAs microresonator as the beamsplitter that produces the optical spring. Our experimental measurements at input powers of up to 360 mW show the shift of the optical spring frequency as a function of power and are in excellent agreement with theoretical predictions. In addition, we show that the optical spring is able to keep the interferometer stable and locked without the use of external feedback.

We describe and demonstrate a method to control a detuned movable-mirror Fabry-Perot cavity using radiation pressure in the presence of a strong optical spring. At frequencies below the optical spring resonance, self-locking of the cavity is achieved intrinsically by the optomechanical (OM) interaction between the cavity field and the movable end mirror. The OM interaction results in a high rigidity and reduced susceptibility of the mirror to external forces. However, due to a finite delay time in the cavity, this enhanced rigidity is accompanied by an anti-damping force, which destabilizes the cavity. The cavity is stabilized by applying external feedback in a frequency band around the optical spring resonance. The error signal is sensed in the amplitude quadrature of the transmitted beam with a photodetector. An amplitude modulator in the input path to the cavity modulates the light intensity to provide the stabilizing radiation pressure force.

The kinetics of the OH + CO reaction, fundamental to both atmospheric and combustion chemistry, are complex due to the formation of the HOCO intermediate. Despite extensive studies on this reaction, HOCO has not been observed at thermal reaction conditions. Exploiting the sensitive, broadband, and high-resolution capabilities of time-resolved cavity-enhanced direct frequency comb spectroscopy, we observe OD + CO reaction kinetics with the detection of stabilized trans-DOCO, the deuterated analogue of trans-HOCO, and its yield. By simultaneously measuring the time-dependent concentrations of both trans-DOCO and OD species, we observe unambiguous low-pressure termolecular dependence on the reaction rate coefficients for both N2 and CO bath gases. These results confirm the HOCO formation mechanism and quantify its yield., Comment: 39 pages, 14 figures

We report a stable double optical spring effect in an optical cavity pumped with a single optical field that arises as a result of birefringence. One end of the cavity is formed by a multilayer Al$_{0.92}$Ga$_{0.08}$As/GaAs stack supported by a microfabricated cantilever, with a natural mode frequency of $274$ Hz. The optical spring shifts the resonance to $21$ kHz, corresponding to a suppression of low frequency vibrations by a factor of more than $10^{4}$. The stable nature of the optical trap allows the cavity to be operated without any external feedback and with only a single optical field incident.

Substrate-transferred crystalline coatings have recently emerged as a groundbreaking new concept in optical interference coatings. Building upon our initial demonstration of this technology, we have now realized significant improvements in the limiting optical performance of these novel single-crystal $GaAs/Al_{x}Ga_{1-x}As$ multilayers. In the near-infrared (NIR), for coating center wavelengths spanning 1064 to 1560 nm, we have reduced the excess optical losses (scatter + absorption) to levels as low as 3 parts per million, enabling the realization of a cavity finesse exceeding $3\times 10^{5}$ at the telecom-relevant wavelength range near 1550 nm. Moreover, we demonstrate the direct measurement of sub-ppm optical absorption at 1064 nm. Concurrently, we investigate the mid-IR (MIR) properties of these coatings and observe exceptional performance for first attempts in this important wavelength region. Specifically, we verify excess losses at the hundred ppm level for wavelengths of 3300 and 3700 nm. Taken together, our NIR optical losses are now fully competitive with ion beam sputtered multilayer coatings, while our first prototype MIR optics have already reached state-of-the-art performance levels for reflectors covering this portion of the fingerprint region for optical gas sensing. Mirrors fabricated with our crystalline coating technique exhibit the lowest mechanical loss, and thus the lowest Brownian noise, the highest thermal conductivity, and, potentially, the widest spectral coverage of any "supermirror" technology in a single material platform. Looking ahead, we see a bright future for crystalline coatings in applications requiring the ultimate levels of optical, thermal, and optomechanical performance, Comment: 8 pages and 7 figures

Thermal noise is a limiting factor in many high-precision optical experiments. A search is underway for novel optical materials with reduced thermal noise. One such pair of materials, gallium arsenide and aluminum-alloyed gallium arsenide (collectively referred to as AlGaAs), shows promise for its low Brownian noise when compared to conventional materials such as silica and tantala. However, AlGaAs has the potential to produce a high level of thermo-optic noise. We have fabricated a set of AlGaAs crystalline coatings, transferred to fused silica substrates, whose layer structure has been optimized to reduce thermo-optic noise by inducing coherent cancellation of the thermoelastic and thermorefractive effects. By measuring the photothermal transfer function of these mirrors, we find evidence that this optimization has been successful., Comment: 10 pages, 7 figures

Indistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or even have entirely new features. Here, we introduce and experimentally demonstrate a quantum imaging concept that relies on the indistinguishability of the possible sources of a photon that remains undetected. Our experiment uses pair creation in two separate down-conversion crystals. While the photons passing through the object are never detected, we obtain images exclusively with the sister photons that do not interact with the object. Therefore the object to be imaged can be either opaque or invisible to the detected photons. Moreover, our technique allows the probe wavelength to be chosen in a range for which suitable sources and/or detectors are unavailable. Our experiment is a prototype in quantum information where knowledge can be extracted by and about a photon that is never detected., Comment: Comments welcome

Tapered optical fibers with a nanofiber waist are widely used tools for efficient coupling of light to photonic devices or quantum emitters via the nanofiber's evanescent field. In order to ensure well-controlled coupling, the phase and polarization of the nanofiber guided light field have to be stable. Here, we show that in typical tapered optical fibers these quantities exhibit high-frequency thermal fluctuations. They originate from high-Q torsional oscillations that opto-mechanically couple to the nanofiber-guided light. We present a simple ab-initio theoretical model that quantitatively explains the torsional mode spectrum and that can be used to design tapered optical fibers with tailored mechanical properties.

Thermally induced fluctuations impose a fundamental limit on precision measurement. In optical interferometry, the current bounds of stability and sensitivity are dictated by the excess mechanical damping of the high-reflectivity coatings that comprise the cavity end mirrors. Over the preceding decade, the mechanical loss of these amorphous multilayer reflectors has at best been reduced by a factor of two. Here we demonstrate a new paradigm in optical coating technology based on direct-bonded monocrystalline multilayers, which exhibit both intrinsically low mechanical loss and high optical quality. Employing these "crystalline coatings" as end mirrors in a Fabry-P\'erot cavity, we obtain a finesse of 150,000. More importantly, at room temperature, we observe a thermally-limited noise floor consistent with a tenfold reduction in mechanical damping when compared with the best dielectric multilayers. These results pave the way for the next generation of ultra-sensitive interferometers, as well as for new levels of laser stability.

Recent advances in micro- and nanofabrication techniques have led to corresponding improvement in the performance of optomechanical systems, which provide a promising avenue towards quantum-limited metrology and the study of quantum behavior in macroscopic mechanical objects. One major impediment to reaching the quantum regime is thermal excitation, which can be overcome for sufficiently high mechanical quality factor Q. Here, we propose a method for increasing the effective Q of a mechanical resonator by stiffening it via the optical spring effect exhibited by linear optomechanical systems, and show how the associated quantum radiation pressure noise can be evaded by sensing and feedback control. In a parameter regime that is attainable with current technology, this method allows for realistic quantum cavity optomechanics in a frequency band well below that which has been realized thus far., Comment: 11 pages (with appendix), 3 figures

Micro- and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavors. Their performance is in many cases limited by the deleterious effects of mechanical damping. Here, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the "phonon-tunneling" approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform the first rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunneling solver represents a major step towards accurate prediction of the mechanical quality factor., Comment: 12 pages, 4 figures

Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environment temperature (5 K versus 30 mK). Despite the large laser-added cooling factor of 4,000 and the cryogenic environment, our cooling performance is not limited by residual absorption effects. These results pave the way for the preparation of 100-um scale objects in the quantum regime. Possible applications range from quantum-limited optomechanical sensing devices to macroscopic tests of quantum physics., Comment: Published version

We present high-performance megahertz micromechanical oscillators based on freestanding epitaxial AlGaAs distributed Bragg reflectors. Compared with dielectric reflectors, the low mechanical loss of the monocrystalline heterostructure gives rise to significant improvements in the achievable mechanical quality factor Q while simultaneously exhibiting near unity reflectivity. Experimental characterization yields an optical reflectivity exceeding 99.98% and mechanical quality factors up to 20 000 at 4 K. This materials system is not only an interesting candidate for optical coatings with ultralow thermal noise, but also provides a promising path toward quantum optical control of massive micromechanical mirrors., Comment: 5 pages, 2 figures