Quantum Radiation Pressure Research Articles

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.

Zigzag optical cavity for sensing and controlling torsional motion

Precision sensing and manipulation of milligram-scale mechanical oscillators has attracted growing interest in the fields of table-top explorations of gravity and tests of quantum mechanics at macroscopic scales. Torsional oscillators present an opportunity in this regard due to their remarked isolation from environmental noise. For torsional motion, an effective employment of optical cavities to enhance optomechanical interactions—as already established for linear oscillators—so far faced certain challenges. Here, we propose a concept for sensing and manipulating torsional motion, where exclusively the torsional rotations of a pendulum are mapped onto the path length of a single two-mirror optical cavity. The concept inherently alleviates many limitations of previous approaches. A proof-of-principle experiment is conducted with a rigidly controlled pendulum to explore the sensing aspects of the concept and to identify practical limitations in a potential state-of-the art setup. Based on this study, we anticipate development of precision torque sensors utilizing torsional pendulums that can support sensitivities below 10−19Nm/Hz, while the motion of the pendulums are dominated by quantum radiation pressure noise at sub-microwatts of incoming laser power. These developments will provide horizons for experiments at the interface of quantum mechanics and gravity. Published by the American Physical Society 2024

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 285m long, high-finesse, near-detuned optical resonator. With about 8.5dB of generated squeezing, up to 5.6dB 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 2dB. Frequency-dependent squeezing is produced with a rotation frequency stability of about 6Hz 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 4.5dB and 2dB, respectively.

Control scheme for polarization circulation speed meter using a dual-retardation waveplate

In interferometric gravitational wave detectors, quantum radiation pressure noise, which is a back action of the measurement, will limit their sensitivities at low frequencies. Speed meters are one of the solutions to reduce the back action noise and improve the sensitivities, and furthermore, they can surpass the standard quantum limit over a wide range of frequencies. The Polarization Circulation Speed Meter is the latest incarnation of the speed meter concept in the sense that it requires a slight modification in the conventional interferometer designs; however, its control scheme has not been developed. The main difficulty is the length and alignment control of the cavity formed by the polarization circulation mirror and the input test masses, whose round-trip phase shift should be kept to $\pi$. In this article, we propose a new control scheme using a dual-retardation waveplate, called Dual-Retardance Control (DRC). In addition, we compare the shot noise level of the DRC to another simpler scheme by dithering. Finally, we design the experimental setup for the demonstration of the DRC and show the expected results through the transfer function measurement.

Angular trapping of a linear-cavity mirror with an optical torsional spring

Optomechanical systems have attracted intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over a milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it and imposes a limitation on the sensitivity. Here, we show that the optical radiation pressure can be used to trap the rotational motion of the suspended mirror without additional active feedback control when the $g$ factors of the cavity are negative and one mirror is much heavier than the other one. Furthermore, we demonstrate experimentally the validity of the trapping. We measured the rotational stiffness of a suspended tiny mirror with various intracavity power. The result indicates that the radiation pressure of the laser beam inside the cavity actually works as a positive restoring torque. Moreover, we discuss the feasibility of observing quantum radiation pressure fluctuation with our experimental setup as an application of our trapping configuration.

Probing squeezing for gravitational-wave detectors with an audio-band field

Squeezed vacuum states are now employed in gravitational-wave interferometric detectors, enhancing their sensitivity and thus enabling richer astrophysical observations. In future observing runs, the detectors will incorporate a filter cavity to suppress quantum radiation pressure noise using frequency-dependent squeezing. Interferometers employing internal and external cavities decohere and degrade squeezing in complex new ways, which must be studied to achieve increasingly ambitious noise goals. This paper introduces an audio diagnostic field (ADF) to quickly and accurately characterize the frequency-dependent response and the transient perturbations of resonant optical systems to squeezed states. This analysis enables audio field injections to become a powerful tool to witness and optimize interactions such as inter-cavity mode matching within gravitational-wave instruments. To demonstrate, we present experimental results from using the audio field to characterize a 16 m prototype filter cavity.

LIGO’s quantum response to squeezed states

Gravitational Wave interferometers achieve their profound sensitivity by combining a Michelson interferometer with optical cavities, suspended masses, and now, squeezed quantum states of light. These states modify the measurement process of the LIGO, VIRGO and GEO600 interferometers to reduce the quantum noise that masks astrophysical signals; thus, improvements to squeezing are essential to further expand our gravitational view of the universe. Further reducing quantum noise will require both lowering decoherence from losses as well more sophisticated manipulations to counter the quantum back-action from radiation pressure. Both tasks require fully understanding the physical interactions between squeezed light and the many components of km-scale interferometers. To this end, data from both LIGO observatories in observing run three are expressed using frequency-dependent metrics to analyze each detector's quantum response to squeezed states. The response metrics are derived and used to concisely describe physical mechanisms behind squeezing's simultaneous interaction with transverse-mode selective optical cavities and the quantum radiation pressure noise of suspended mirrors. These metrics and related analysis are broadly applicable for cavity-enhanced optomechanics experiments that incorporate external squeezing, and -- for the first time -- give physical descriptions of every feature so far observed in the quantum noise of the LIGO detectors.

Quantum optomechanics without the radiation pressure force noise.

This Letter proposes a new method to eliminate the quantum radiation pressure force noise in optomechanics at frequencies much smaller than the resonance frequency of the optomechanical mirror. With no radiation pressure force noise, the shot noise and thermal noise together determine the total noise in the system. The force sensitivity of the optomechanical cavity is improved beyond standard quantum limit at frequencies much smaller than the resonance frequency of the mechanical oscillator. Finally, optimum optomechanical cavity design parameters for attaining the best sensitivity are discussed.

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

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

Demonstration of an amplitude filter cavity at gravitational-wave frequencies

Quantum vacuum fluctuations fundamentally limit the precision of optical measurements, such as those in gravitational-wave detectors. Injection of conventional squeezed vacuum can be used to reduce quantum noise in the readout quadrature, but this reduction is at the cost of increasing noise in the orthogonal quadrature. For detectors near the limits imposed by quantum radiation pressure noise (QRPN), both quadratures impact the measurement, and the benefits of conventional squeezing are limited. In this paper, we demonstrate the use of a critically-coupled 16m optical cavity to diminish anti-squeezing at frequencies below 90Hz where it exacerbates QRPN, while preserving beneficial squeezing at higher frequencies. This is called an amplitude filter cavity, and it is useful for avoiding degradation of detector sensitivity at low frequencies. The attenuation from the cavity also provides technical advantages such as mitigating backscatter.

Thermal noise study of a radiation pressure noise limited optical cavity with fused silica mirror suspensions

In this work we study the thermal noise of two monolithically suspended mirrors in a tabletop high-finesse optical cavity. We show that, given suitable seismic filters, such a cavity can be designed to be sensitive to quantum radiation pressure fluctuations in the audio band of gravitational wave interferometric detectors below 1 kHz. Indeed, the thermal noise of the suspensions and of the coatings constitutes the main limit to the observation of quantum radiation pressure fluctuations. This limit can be overcome with an adequate choice of mirror suspension and coating parameters. Finally, we propose to combine two optical cavities, like those modeled in this work, to obtain a tabletop quantum radiation pressure-limited interferometer.Graphical abstract

Quantum Backaction on kg-Scale Mirrors: Observation of Radiation Pressure Noise in the Advanced Virgo Detector.

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise.

Frequency-Dependent Squeezing for Advanced LIGO.

The first detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in 2015 launched the era of gravitational-wave astronomy. The quest for gravitational-wave signals from objects that are fainter or farther away impels technological advances to realize ever more sensitive detectors. Since 2019, one advanced technique, the injection of squeezed states of light, is being used to improve the shot-noise limit to the sensitivity of the Advanced LIGO detectors, at frequencies above ∼50 Hz. Below this frequency, quantum backaction, in the form of radiation pressure induced motion of the mirrors, degrades the sensitivity. To simultaneously reduce shot noise at high frequencies and quantum radiation pressure noise at low frequencies requires a quantum noise filter cavity with low optical losses to rotate the squeezed quadrature as a function of frequency. We report on the observation of frequency-dependent squeezed quadrature rotation with rotation frequency of 30Hz, using a 16-m-long filter cavity. Anovel control scheme is developed for this frequency-dependent squeezed vacuum source, and the results presented here demonstrate that a low-loss filter cavity can achieve the squeezed quadrature rotation necessary for the next planned upgrade to Advanced LIGO, known as "A+."

Broadband reduction of quantum radiation pressure noise via squeezed light injection

The Heisenberg uncertainty principle states that the position of an object cannot be known with infinite precision, as the momentum of the object would then be totally uncertain. This momentum uncertainty then leads to position uncertainty in future measurements. When continuously measuring the position of an object, this quantum effect, known as back-action, limits the achievable precision1,2. In audio-band, interferometer-type gravitational-wave detectors, this back-action effect manifests as quantum radiation pressure noise (QRPN) and will ultimately (but does not yet) limit sensitivity3. Here, we present the use of a quantum engineered state of light to directly manipulate this quantum back-action in a system where it dominates the sensitivity in the 10–50 kHz range. We observe a reduction of 1.2 dB in the quantum back-action noise. This experiment is a crucial step in realizing QRPN reduction for future interferometric gravitational-wave detectors and improving their sensitivity. An amplitude squeezed light source that operates down to 1 kHz frequencies—the lowest squeezing frequency—is generated in nonlinear crystal-based systems. By injecting the squeezed light into a microresonator, the quantum radiation pressure noise is reduced by 1.2 dB.

Measurement of quantum back action in the audio band at room temperature.

Quantum mechanics places a fundamental limit on the precision of continuous measurements. The Heisenberg uncertainty principle dictates that as the precision of a measurement of an observable (for example, position) increases, back action creates increased uncertainty in the conjugate variable (for example, momentum). In interferometric gravitational-wave detectors, higher laser powers reduce the position uncertainty created by shot noise(the photon-counting error caused by the quantum nature of the laser) but necessarily do so at the expense of back action in the form of quantum radiation pressure noise (QRPN)1. Once at design sensitivity, the gravitational-wave detectors Advanced LIGO2, VIRGO3 and KAGRA4 will be limited by QRPN at frequencies between 10hertz and 100hertz. There exist several proposals to improve the sensitivity of gravitational-wave detectors by mitigating QRPN5-10, but until now no platform has allowed for experimental tests of these ideas. Here we present a broadband measurement of QRPN at room temperature at frequencies relevant to gravitational-wave detectors. The noise spectrum obtained shows effects due to QRPN between about 2kilohertz and 100kilohertz, and the measured magnitude of QRPN agrees with our model. We now have a testbed for studying techniques with which to mitigate quantum back action, such as variational readout and squeezed light injection7, with the aim of improving the sensitivity of future gravitational-wave detectors.

Gravitational wave detection using laser interferometry beyond the standard quantum limit.

Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources-photon shot noise and quantum radiation pressure noise-which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates.This article is part of a discussion meeting issue 'The promises of gravitational-wave astronomy'.

Demonstration of a switchable damping system to allow low-noise operation of high- Q low-mass suspension systems

Low mass suspension systems with high-Q pendulum stages are used to enable quantum radiation pressure noise limited experiments. Utilising multiple pendulum stages with vertical blade springs and materials with high quality factors provides attenuation of seismic and thermal noise, however damping of these high-Q pendulum systems in multiple degrees of freedom is essential for practical implementation. Viscous damping such as eddy-current damping can be employed but introduces displacement noise from force noise due to thermal fluctuations in the damping system. In this paper we demonstrate a passive damping system with adjustable damping strength as a solution for this problem that can be used for low mass suspension systems without adding additional displacement noise in science mode. We show a reduction of the damping factor by a factor of 8 on a test suspension and provide a general optimisation for this system.

Optical absorption of silicon nitride membranes at 1064 nm and at 1550 nm

Because of a low mechanical loss, thin films made of silicon nitride (${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$) are interesting for fundamental research and development in the field of gravitational-wave detection. ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ membranes allow for the characterization of quantum radiation pressure noise (RPN), which will be a limiting noise source in gravitational-wave detectors of the second and third generations. Furthermore, ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ is an interesting material for possible thermal noise reduction in highly reflective mirror coatings. For both applications, the optical absorption of ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ needs to be low. This paper presents absorption measurements on low-stress ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ membranes showing an absorption a factor of 7 lower at 1550 nm than at 1064 nm resulting in an estimated 2 times higher sensitivity in RPN experiments at the higher wavelength and making ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ an interesting material for highly reflective multimaterial mirror coatings at 1550 nm.

Quantum correlation measurements in interferometric gravitational-wave detectors

Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational wave detectors, such as the Advanced Laser Interferometer Gravitational wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer for the first time.

Towards thermal noise free optomechanics

Thermal noise generally greatly exceeds quantum noise in optomechanical devices unless the mechanical frequency is very high or the thermodynamic temperature is very low. This paper addresses the design concept for a novel optomechanical device capable of ultrahigh quality factors in the audio frequency band with negligible thermal noise. The proposed system consists of a minimally supported millimeter scale pendulum mounted in a double end-mirror sloshing cavity that is topologically equivalent to a membrane-in-the-middle cavity. The radiation pressure inside the high-finesse cavity allows for high optical stiffness, cancellation of terms which lead to unwanted negative damping and suppression of quantum radiation pressure noise. We solve the optical spring dynamics of the system using the Hamiltonian, find the noise spectral density and show that stable optical trapping is possible. We also assess various loss mechanisms, one of the most important being the acceleration loss due to the optical spring. We show that practical devices, starting from a centre-of-mass pendulum frequency of 0.1 Hz, could achieve a maximum quality factor of (1014) with optical spring stiffened frequency 1–10 kHz. Small resonators of mass 1 g or less could achieve a Q-factor of (1011) at a frequency of 100 kHz. Applications for such devices include white light cavities for improvement of gravitational wave detectors, or sensors able to operate near the quantum limit.