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arXiv:2004.10503 · Physical review. D/Physical review. D.

Quantum squeezing schemes for heterodyne readout

Teng Zhang, Д. В. Мартынов, A. Freise, Haixing Miao

Published Jun 25, 2020• 7 citations
arXivHTMLPDF

Abstract

Advanced gravitational-wave detectors are limited by quantum noise in their most sensitive frequency band. Quantum noise suppression techniques, such as the application of the quantum squeezed state of light, have been actively studied in the context of homodyne readouts. In this paper, we consider quantum squeezing schemes for the heterodyne readouts. This is motivated by a successful suppression of the higher-order-mode content by stable recycling cavities in advanced detectors. The heterodyne readout scheme requires precise tuning of the interferometer parameters and a broadband squeezing source, but is conceptually simple and elegant. We further show that it is compatible with the frequency-dependent squeezing, which reduces both the shot noise and the radiation-pressure noise. We propose a test of the heterodyne readout with squeezing in Advanced LIGO. This can serve as a pathfinder not only for the implementation in future detectors, such as the Einstein Telescope and Cosmic Explorer, but also for general high-precision optical measurements.

DOI
10.1103/physrevd.101.124052

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Advanced gravitational-wave detectors are limited by quantum noise in their most sensitive frequency band. Quantum noise suppression techniques, such as the application of the quantum squeezed state of light, have been actively studied in the context of homodyne readouts. In this paper, we consider quantum squeezing schemes for the heterodyne readouts. This is motivated by a successful suppression of the higher-order-mode content by stable recycling cavities in advanced detectors. The heterodyne readout scheme requires precise tuning of the interferometer parameters and a broadband squeezing source, but is conceptually simple and elegant. We further show that it is compatible with the frequency-dependent squeezing, which reduces both the shot noise and the radiation-pressure noise. We propose a test of the heterodyne readout with squeezing in Advanced LIGO. This can serve as a pathfinder not only for the implementation in future detectors, such as the Einstein Telescope and Cosmic Explorer, but also for general high-precision optical measurements.
Quantum noise is one of the limiting factors in laser-interferometric gravitational-wave (GW) detectors. The application of squeezed states in these interferometers allows the reduction of quantum noise in one quadrature. Due to opto-mechanical coupling in a GW detector the squeezed quadrature needs to be rotated within the spectrum to achieve a broadband noise reduction. So far, the implementation of additional filter cavities is considered that allow for the optimal, frequency-dependent rotation of the squeezed quadrature. However, these cavities need to have low loss, a length in the order of \unit[100]{m} and must be situated in the vacuum system, making them cost-intensive. In 2017, Ma and coworkers proposed a scheme for the broadband quantum-noise reduction without the need of additional filter cavities. It was shown by Brown et al. that a similar scheme can be used to broadband-enhance interferometers with a detuned signal-recycling cavity. Here, we performed a proof-of-principle experiment of the proposal on a table-top-scale. Squeezed states were produced detuned to the carrier field of a \unit[2.5]{m}-linear cavity and read out in a bichromatic homodyne detection. The frequencies of the lower and upper local oscillator were at entangled sidebands of the squeezed field. Depending on the relations between the involved frequencies, we can address both variants of the proposal. We show, that the frequency-dependences of the resulting noise spectra fit to a theoretical model we derived from the theory used by Ma et al. With this work we set the path towards an implementation of these schemes in a GW-detector prototype, where the compatibility of the approach with a low-frequency suspended interferometer can be tested. Moreover, we used the same setup to show nonclassical interferometer enhancement at low frequencies by high-frequency squeezed states. Here, a heterodyne readout scheme was implemented to avoid limiting noises at low frequencies. The application of squeezed states centered around the local oscillator frequency yielded an improvement in signal-to-noise ratio of $\unit[3.4]{dB}\pm\unit[0.3]{dB}$. Additionally, I designed, built and characterized a compact source of squeezed vacuum-states at \unit[1064]{nm} with a footprint of just $\unit[0.8]{m^2}$. I show measurements of squeezed states from this source with a reduction of quantum noise of $\unit[10.7]{dB}\pm\unit[0.2]{dB}$ below the vacuum noise and present a noise reduction in the frequency range from \unit[70]{kHz} to \unit[65]{MHz}.
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 30 Hz, using a 16-m-long filter cavity. A novel 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+."
Precision measurements using traditional heterodyne readout suffer a 3dB quantum noise penalty compared with homodyne readout. The extra noise is caused by the quantum fluctuations in the image vacuum. We propose a two-carrier gravitational-wave detector design that evades the 3dB quantum penalty in heterodyne readout. Such a heterodyne readout scheme can reduce technical complexity and technical noise couplings compared to homodyne readout. We further propose a new way of frequency-dependent squeezing utilizing two-mode squeezing in our scheme. It naturally achieves more precise audio frequency signal measurements with radio frequency squeezing which avoids the classical noise at audio frequency. In addition, the detector is also compatible with other quantum non-demolition techniques.
Direct detection of gravitational waves will require earth based detectors to measure strains of the order 10−21, at frequencies of 100 Hz, a sensitivity that has been accomplished with the initial generation of LIGO interferometric gravitational wave detectors. A new generation of detectors currently under construction is designed improve on the sensitivity of the initial detectors by about a factor of 10. The quantum nature of light will limit the sensitivity of these Advanced LIGO interferometers at most frequencies; new approaches to reducing the quantum noise will be needed to improve the sensitivity further. This quantum noise originates from the vacuum fluctuations that enter the unused port of the interferometer and interfere with the laser light. Vacuum fluctuations have the minimum noise allowed by Heisenberg’s uncertainty principle, ∆X1∆X2 ≥ 1, where the two quadratures X1 and X2 are non-commuting observables responsible for the two forms of quantum noise, shot noise and radiation pressure noise. By replacing the vacuum fluctuations entering the interferometer with squeezed states, which have lower noise in one quadrature than the vacuum state, we have reduced the shot noise of a LIGO interferometer. The sensitivity to gravitational waves measured during this experiment represents the best sensitivity achieved to date at frequencies above 200 Hz, and possibly the first time that squeezing has been measured in an interferometer at frequencies below 700 Hz. The possibility that injection of squeezed states could introduce environmental noise couplings that would degrade the crucial but fragile low frequency sensitivity of a LIGO interferometer has been a major concern in planning to implement squeezing as part of baseline interferometer operations. These results demonstrate that squeezing is compatible with the low frequency sensitivity of a full scale gravitational wave interferometer. We also investigated the limits to the level of squeezing observed, including optical losses and fluctuations of the squeezing angle. The lessons learned should allow for responsible planning to implement squeezing in Advanced LIGO, either as an alternative to high power operation or an early upgrade to improve the sensitivity. This thesis is available at DSpace@MIT and has LIGO document number P1300006. Thesis Supervisor: Nergis Mavalvala Title: Professor of Physics
Quantum noise imposes a fundamental limitation on the sensitivity of interferometric gravitationalwave detectors like LIGO, manifesting as shot noise and quantum radiation pressure noise.Here, we present the first realization of frequency-dependent squeezing in full-scale gravitational-wave detectors, resulting in the reduction of both shot noise and quantum radiation pressure noise, with broadband detector enhancement from tens of hertz to several kilohertz.In the LIGO Hanford detector, squeezing reduced the detector noise amplitude by a factor of 1.6 (4.0 dB) near 1 kHz; in the Livingston detector, the noise reduction was a factor of 1.9 (5.8 dB).These improvements directly impact LIGO's scientific output for high-frequency sources (e.g., binary neutron star postmerger physics).The improved lowfrequency sensitivity, which boosted the detector range by 15%-18% with respect to no squeezing, corresponds to an increase in the astrophysical detection rate of up to 65%.Frequency-dependent squeezing was enabled by the addition of a 300-meter-long filter cavity to each detector as part of the LIGO Aþ upgrade.
Precision measurements using a traditional heterodyne readout suffer a 3 dB quantum noise penalty compared with a homodyne readout. The extra noise is caused by the quantum fluctuations in the image vacuum. We propose a two-carrier gravitational-wave detector design that evades the 3 dB quantum penalty of the heterodyne readout. We further propose a new way of realizing frequency-dependent squeezing utilizing two-mode squeezing in our scheme. It naturally achieves more precise audio frequency signal measurements with radio frequency squeezing. In addition, the detector is compatible with other quantum nondemolition techniques.