We demonstrate the generation of broad-band continuous-wave optical squeezing down to 200Hz using a below threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise and detuning fluctuations, present in optical parametric amplifiers have negligible effect on squeezing produced by a below threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational wave detectors.
A 2.8-dB polarization squeezing of the Stokes operator S2 for the rubidium D1 line (795 nm) is achieved, with the lowest squeezing band at an audio frequency of 2.6 kHz. Two methods are applied for improving the squeezing towards low frequencies: an orthogonal-polarized locking beam that precludes residual unwanted interference and quantum noise locking method that stabilizes the relative phase between the squeezed vacuum and the local oscillator. The squeezing level is limited by absorption-induced losses at short wavelengths, here is 397.5 nm. The generated polarization squeezed light can be…
Quantum vacuum fluctuations impose strict limits on precision displacement measurements, those of interferometric gravitational-wave detectors among them. Introducing squeezed states into an interferometer's readout port can improve the sensitivity of the instrument, leading to richer astrophysical observations. However, optomechanical interactions dictate that the vacuum's squeezed quadrature must rotate by 90 degrees around 50Hz. Here we use a 2-m-long, high-finesse optical resonator to produce frequency-dependent rotation around 1.2kHz. This demonstration of audio-band frequency-dependent s…
Generation of quantum light source is a promising technique to overcome the standard quantum limit in precision measurement. Here, we demonstrate an experimental generation of quadrature squeezing resonating on the cesium D2 line down to 10 Hz for the first time. The maximum squeezing in audio frequency band is 5.57 dB. Moreover, we have presented a single-photon modulation locking to control the squeezing angle, while effectively suppressing the influence of laser noise on low-frequency squeezing. The whole system operates steadily for hours. The generated low-frequency quantum light source c…
The detection of kilohertz-band gravitational waves promises discoveries in astrophysics, exotic matter, and cosmology. To improve the kilohertz quantum noise-limited sensitivity of interferometric gravitational-wave detectors, we investigate nondegenerate internal squeezing: optical parametric oscillation inside the signal-recycling cavity with distinct signal-mode and idler-mode frequencies. We use an analytic Hamiltonian model to show that this stable, all-optical technique is tolerant to decoherence from optical detection loss and that it, with its optimal readout scheme, is feasible for b…
Broadband quantum noise reduction can be achieved in gravitational wave detectors by injecting frequency dependent squeezed light into the the dark port of the interferometer. This frequency dependent squeezing can be generated by combining squeezed light with external filter cavities. However, in future long baseline interferometers (LBIs), the filter cavity required to achieve the broadband squeezing has a low bandwidth -- necessitating a very long cavity to mitigate the issue from optical loss. It has been shown recently that by taking advantage of Einstein-Podolsky-Rosen (EPR) entanglement…
Using a nondegenerate four-wave mixing (FWM) process based on a double-Λ scheme in hot cesium vapor, we demonstrate a compact diode-laser-pumped quantum light source for the generation of quantum correlated twin beams with a maximum squeezing of 6.5 dB. The squeezing is observed at a Fourier frequency in the audio band down to 0.7 kHz which, to the best of our knowledge, is the first observation of sub-kilohertz intensity-difference squeezing in an atomic system so far. A phase-matching condition is also investigated in our system, which confirms the spatial-multi-mode characteristics of the F…
Continuous-wave squeezed states of light at the wavelength of 1550 nm have recently been demonstrated, but so far the obtained factors of noise suppression still lag behind today's best squeezing values demonstrated at 1064 nm. Here we report on the realization of a half-monolithic nonlinear resonator based on periodically-poled potassium titanyl phosphate which enabled the direct detection of up to 12.3 dB of squeezing at 5 MHz. Squeezing was observed down to a frequency of 2 kHz which is well within the detection band of gravitational wave interferometers. Our results suggest that a long-ter…
We investigate the squeezing of primordial gravitational waves (PGWs) in terms of quantum discord. We construct a classical state of PGWs without quantum discord and compare it with the Bunch-Davies vacuum. Then it is shown that the oscillatory behavior of the angular-power spectrum of the cosmic microwave background (CMB) fluctuations induced by PGWs can be the signature of the quantum discord of PGWs. In addition, we discuss the effect of quantum decoherence on the entanglement and the quantum discord of PGWs for super-horizon modes. For the state of PGWs with decoherence effect, we examine …
Squeezed states of light have been recently used to improve the sensitivity of laser interferometric gravitational-wave detectors beyond the quantum limit. To completely establish quantum engineering as a realistic option for the next generation of detectors, it is crucial to study and quantify the noise coupling mechanisms which injection of squeezed states could potentially introduce. We present a direct measurement of the impact of backscattered light from a squeezed-light source deployed on one of the 4 km long detectors of the Laser Interferometric Gravitational Wave Observatory (LIGO). W…
Squeezed Quasinormal Modes from Nonlinear Gravitational Effects
Nordita, Stockholm University and KTH Royal Institute of Technology（诺尔迪塔，斯德哥尔摩大学与皇家理工学院）；Tata Institute of Fundamental Research Hyderabad（泰姬玛哈巴德基础研究所）；Department of Physics, Stockholm University（斯德哥尔摩大学物理系）；Department of Physics and Origins Project, Arizona State University（亚利桑那州立大学物理系与起源项目）；T. D. Lee Institute（李政道研究所）；Wilczek Quantum Center, Department of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院费曼量子中心）；Center for Theoretical Physics, Massachusetts Institute of Technology（麻省理工学院理论物理中心）
Quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. In the past 30 years, techniques for squeezing the quantum uncertainty as well as for enhancing the gravitational-wave signal with optical resonators were invented. Resonators, however, have finite linewidths; and the high signal frequencies that are produced during the scientifically highly interesting ring-down of astrophysical compact-binary mergers cannot be resolved today. Here, we propose an optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one…
Axion-like particles (ALPs) are promising dark matter candidates. They are typically described by a classical field, motivated by large phase space occupation numbers. Here we show that such a description is accompanied by a quantum effect: squeezing due to gravitational self-interactions. For a typical QCD axion today, the onset of squeezing is reached on $\mathrm{μs}$-scales and grows over millennia. Thus within the usual models based on the classical Schrödinger-Poisson equation, a type of Gross-Pitaevskii equation, any viable ALP is nonclassical. We also show that squeezing may be relevant…
We discuss the quantum mechanical description of a gravitational wave interacting with a cavity electromagnetic field. Quantum fluctuations of the gravitational vacuum induce squeezing in the optical field. Moreover, this squeezing experiences revivals, a purely quantum effect. Measuring these gravitationally induced revivals, although out of reach from experiments, would provide evidence on the quantum nature of gravity. We also discuss the quantum mechanical treatment of the interaction between coherent and squeezed gravitational wave states and a gravity wave detector. In the case of a cohe…
Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or …
The ongoing global effort to detect gravitational waves continues to push the limits of precision measurement while aiming to provide a new tool for understanding both astrophysics and fundamental physics. Squeezed states of light offer a proven means of increasing the sensitivity of gravitational wave detectors, potentially increasing the rate at which astrophysical sources are detected by more than an order of magnitude. Since radiation pressure noise plays an important role in advanced detectors, frequency dependent squeezing will be required. In this paper we propose a practical approach t…
Ponderomotive squeezing of the output light of an optical cavity has been recently observed in the MHz range in two different cavity optomechanical devices. Quadrature squeezing becomes particularly useful at lower spectral frequencies, for example in gravitational wave interferometers, despite being more sensitive to excess phase and frequency noise. Here we show a phase/frequency noise cancellation mechanism due to destructive interference which can facilitate the production of ponderomotive squeezing in the kHz range and we demonstrate it experimentally in an optomechanical system formed by…
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 optomecha…
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 in…
Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard technique, the production of squeezed states of the collective excitations in gases of ultracold atoms, the phonons of a Bose-Einstein condensate (BEC), is a comparably recent problem. This task is continuously gaining relevance with a growing number of proposals for BEC-based quantum metrological devices and the possibility to apply them in the detection of grav…
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 s…
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum is injected into the usually unused input port. It is investigated under which conditions the gravitational wave signal may be amplified without increasing counting noise concurrently. Such a possibility was suggested as a consequence of the entanglement of the two output ports of a beam splitter. We find that amplification without concurrent increase of noise is not possible for reasonable squeezing parameters. Photon distributions for various…
Multi-level quantum protocols may potentially supersede standard quantum optical polarization-encoded protocols in terms of amount of information transmission and security. However, for free space telecomunications, we do not have tools for limiting loss due to diffraction and perturbations, as for example turbulence in air. Here we study propagation invariant quantum X-waves with angular momentum; this representation expresses the electromagnetic field as a quantum gas of weakly interacting bosons. The resulting spatio-temporal quantized light pulses are not subject to diffraction and dispers…
The Standard Quantum Limit (SQL) in interferometric displacement measurement imposes a restriction on the precision of the measurement due to its quantum back-action noise. This limit can be surpassed over a broad frequency band by injecting squeezed vacuum states with a frequency dependent (FD) quadrature angle into the measurement system. Here, we demonstrate the generation of FD squeezed vacuum states by utilizing Einstein-Podolsky-Rosen (EPR) entangled states. The frequency dependence of the squeezed state can be tuned by conditionally filtering the measurement once the two entangled field…
Laser intensity noise suppression has essential effects on preparation and characterization of the audio-frequency squeezed vacuum state of light based on a sub-threshold optical parametric oscillator (OPO).We have implemented two feedback loops by using relevant acousto-optical modulators (AOM) to stabilize the intensity of 795-nm near infrared (NIR) fundamental laser and 397.5-nm ultraviolet (UV) laser generated by cavity-enhanced frequency doubling.Typical peak-to-peak laser intensity fluctuation with a bandwidth of $\sim10$ kHz in a half hour has been improved from $\pm7.45$$\%$ to $\pm0.0…
Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing…
The precise estimation of the gravitational acceleration is important for various disciplines. We consider making such an estimation using quantum optics. A Mach-Zehnder interferometer in an "optical fountain" type arrangement is considered and used to define a standard quantum limit for estimating the gravitational acceleration. We use an approach based on quantum field theory on a curved, Schwarzschild metric background to calculate the coupling between the gravitational field and the optical signal. The analysis is extended to include the injection of a squeezed vacuum to the Mach-Zehnder a…
The detectors of the international gravitational-wave (GW) observatory network are currently taking data with sensitivities improved via squeezing the photon counting noise of the laser light used. Several GW candidate events, such as black-hole mergers, are already in the pipeline to be analyzed in detail. While the brand-new field of GW astronomy relies on squeezed light for reaching higher sensitivities, the physical understanding of such light, although being well-described by quantum theory, is still under discussion. Here, I present a description of why squeezed light, as now being explo…
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 $μ$m region. Our work aims for reusing the existing high-performance lasers at 1064 nm. Here, we report the real…
Currently, the German/British gravitational wave detector GEO600 is being upgraded in course of the GEO-HF program. One part of this upgrade consists of the integration of a squeezed light laser to nonclassically improve the detection sensitivity at frequencies where the instrument is limited by shot noise. This has been achieved recently [1]. The permanent employment of squeezed light in gravitational wave observatories requires a long-term stability of the generated squeezed state. In this paper, we discuss an unwanted mechanism that can lead to a varying squeezing factor along with a changi…
The universe is believed to be originated from a quantum state. However, defining measurable quantities for the quantum properties in the present universe has gained interest recently. In this submission, we propose a quantum Poincare sphere as an observable quantity that can hint at the quantumness of primordial gravitational waves and large-scale magnetic fields. The Poincare sphere is defined in terms of quantum stokes operators associated with the polarization of those fields, which can be measured directly. We have further studied the effects of the initial non-BD vacuum on the power spec…
Only a few years ago, it was realized that the zero-area Sagnac interferometer topology is able to perform quantum nondemolition measurements of position changes of a mechanical oscillator. Here, we experimentally show that such an interferometer can also be efficiently enhanced by squeezed light. We achieved a nonclassical sensitivity improvement of up to 8.2 dB, limited by optical loss inside our interferometer. Measurements performed directly on our squeezed-light laser output revealed squeezing of 12.7 dB. We show that the sensitivity of a squeezed-light enhanced Sagnac interferometer can …
Frequency dependent squeezing is the main upgrade for achieving broadband quantum noise reduction in upcoming observation runs of gravitational wave detectors. The proper frequency dependence of the squeezed quadrature is obtained by reflecting squeezed vacuum from a Fabry-Perot filter cavity detuned by half of its linewidth. However, since the squeezed vacuum contains no classical amplitude, co-propagating auxiliary control beams are required to achieve the filter cavity's length, alignment, and incident beam pointing stability. In our frequency dependent squeezing experiment at the National …
One of the noise sources that currently limits gravitational wave (GW) detectors comes from the quantum nature of the light causing uncertain amplitude and phase. Phase uncertainty limits the precision of an interferometric measurement. This measurement is also subject to quantum back-action, caused by the radiation pressure force fluctuations produced by the amplitude uncertainty (QRPN). In order to lower this quantum noise, GW detectors plan to use squeezed light injection. In this thesis, I focus on using radiation-pressure-mediated optomechanical (OM) interaction to generate squeezed light…
Narrow-band intensity-difference squeezing beams have important applications in quantum metrology and gravitational wave detection. The best way to generate narrow-band intensity-difference squeezing is to employ parametrically-amplified four-wave mixing process in high-gain atomic media. Such IDS can be further enhanced by cascading multiple parametrically-amplified four-wave mixing processes in separate atomic media. The complicated experimental setup, added losses and required high-power pump laser with the increase of number of stages can limit the wide uses of such scheme in practical app…
The Standard Quantum Limit in continuous monitoring of a system is given by the trade-off of shot noise and back-action noise. In gravitational-wave detectors, such as Advanced LIGO, both contributions can simultaneously be squeezed in a broad frequency band by injecting a spectrum of squeezed vacuum states with a frequency-dependent squeeze angle. This approach requires setting up an additional long base-line, low-loss filter cavity in a vacuum system at the detector's site. Here, we show that the need for such a filter cavity can be eliminated, by exploiting EPR-entangled signal and idler be…
We investigate a Bose-Einstein condensate (BEC) as a gravitational wave detector, and study its sensitivity by optimizing the properties of the condensate and the measurement duration. We show that detecting kilohertz gravitational waves is limited by current experimental techniques in squeezing BEC phonons. Future improvements in technology to squeeze BEC states can make them competitive detectors for gravitational waves of astrophysical and/or cosmological origin.
Gravitational wave detectors (GWDs), which have brought about a new era in astronomy, have reached such a level of maturity that further improvement necessitates quantum-noise-evading techniques. Numerous proposals to this end have been discussed in the literature, e.g., invoking frequency-dependent squeezing or replacing the current Michelson interferometer topology by that of the quantum speedmeter. Recently, a proposal based on the linking of a standard interferometer to a negative-mass spin system via entangled light has offered an unintrusive and small-scale new approach to quantum noise …
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of …
Cross-correlation heterodyne detectors exhibit the potential for suppression of the detection quantum noise below shot noise without use of optical squeezing for capturing weak optical signals in low frequency bands. To understand the underlying mechanism, we develop a quantum theory to describe the noise performance of cross-correlation heterodyne detectors. By calculating the cross spectral density (CSD) of the photocurrent fluctuations from a cross-correlation heterodyne detector, we prove that its noise performance can break the shot noise limit and exceed that of a regular heterodyne dete…
