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arXiv:2607.16885

Precision dynamics of resonantly enhanced optical parametric amplifiers

Evan D. Hall

quant-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations
arXivHTMLPDF

Abstract

Optical parametric amplification is a crucial technology for the production of continuous-wave squeezed vacuum, which is now applied to gravitational-wave interferometry and other highly sensitive measurements of optical phase. The amplifiers employed in gravitational-wave detection are resonantly enhanced with optical cavities, which introduces nontrivial dynamics to their operation and requires a frequency-domain model of the relations between optical fields. In this work, input-output relations between optical fields entering, circulating in, and exiting a model amplifier are solved directly to produce frequency-domain relations that fully incorporate the cavity dynamics. We also provide low-order zero-pole-gain expansions for these relations to facilitate their analysis from a feedback control perspective. In the limit of small cavity decay rates, our relations are shown to reduce to relations previously derived under a Hamiltonian formalism. Expressions for amplifier figures of merit and for squeezed quadrature variances are also analyzed. Along the way, we examine how information about the amplifier performance can be extracted from the frequency dependence of the input-output relations, providing characterization methods that are complementary to methods that examine the static amplifier behavior.

Comments
25 pages, 8 figures

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Optical parametric amplification is a crucial technology for the production of continuous-wave squeezed vacuum, which is now applied to gravitational-wave interferometry and other highly sensitive measurements of optical phase. The amplifiers employed in gravitational-wave detection are resonantly enhanced with optical cavities, which introduces nontrivial dynamics to their operation and requires a frequency-domain model of the relations between optical fields. In this work, input-output relations between optical fields entering, circulating in, and exiting a model amplifier are solved directly to produce frequency-domain relations that fully incorporate the cavity dynamics. We also provide low-order zero-pole-gain expansions for these relations to facilitate their analysis from a feedback control perspective. In the limit of small cavity decay rates, our relations are shown to reduce to relations previously derived under a Hamiltonian formalism. Expressions for amplifier figures of merit and for squeezed quadrature variances are also analyzed. Along the way, we examine how information about the amplifier performance can be extracted from the frequency dependence of the input-output relations, providing characterization methods that are complementary to methods that examine the static amplifier behavior.
With the recent detection of gravitational waves, non-classical light sources are likely to become an essential element of future detectors engaged in gravitational wave astronomy and cosmology. Operating a squeezed light source under high vacuum has the advantages of reducing optical losses and phase noise compared to techniques where the squeezed light is introduced from outside the vacuum. This will ultimately provide enhanced sensitivity for modern interferometric gravitational wave detectors that will soon become limited by quantum noise across much of the detection bandwidth. Here we describe the optomechanical design choices and construction techniques of a near monolithic glass optical parametric oscillator that has been operated under a vacuum of 10(-6) mbar. The optical parametric oscillator described here has been shown to produce 8.6 dB of quadrature squeezed light in the audio frequency band down to 10 Hz. This performance has been maintained for periods of around an hour and the system has been under vacuum continuously for several months without a degradation of this performance.
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Abstract The sensitivity of gravitational wave interferometric detectors is ultimately limited by the quantum noise, which arises from the quantum nature of light and it is driven by vacuum fluctuations of the optical field entering from the dark port of the interferometer. One way to improve the sensitivity of gravitational wave interferometers is to inject squeezed vacuum into the dark port. This has been already demonstrated for the main gravitational wave detectors (GEO, Advanced LIGO and Advanced VIRGO). We are studying tricks to produce a “frequency- dependent squeezing”: a standard method is to filter the squeezed optical field with one or more optical cavities (300 m long cavities). An alternative method using a pair of squeezed EPR (Einstein-Podolsky-Rosen) entangled beams to produce frequency-dependent squeezing by a non-degenerate OPO (Optical Parametric Oscillator) will be discussed in this paper. This method promises to achieve a frequency-dependent optimization of the injected squeezed light fields without the need for an external filter cavity.
The engineering of strongly squeezed vacuum states of light is a key technology for the reduction of quantum noise in gravitational wave detectors. We report on the observation of up to 12.0 dB squeezed vacuum states of light at the wavelength of 1064 nm in the frequency band from 10 Hz to 100 kHz. This is the strongest squeezing reported to date within this detection band. The squeezed states were generated in a half-monolithic, standing-wave cavity optical parametric amplifier, which was resonant for the fundamental and harmonic light fields. We chose appropriate reflectivities to obtain a significant reduction of the required pump power, which was 8.6 mW only. Our analysis revealed that the residual measurement phase noise was smaller than 3.5 mrad rms and that the squeezed light source provided up to 14 dB of squeezing for a downstream application. The experiment was electronically stabilized in all relevant degrees of freedom, demonstrating the applicability of the linear, doubly resonant cavity topology for current and future gravitational wave detectors.
A squeezed vacuum field can be amplified or deamplified when it is injected, as the signal beam, into a phase-sensitive optical parametric amplifier (OPA) inside an optical cavity. The spectral features of the reflected quantized signal field are controlled by the relative phase between the injected squeezed vacuum field and the pump field for the OPA. The experimental results demonstrate coherent phenomena of OPA in the quantum regime and show phase-sensitive manipulations of quantum fluctuations for quantum information processing.
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}.