# Squeezing in Gravitational Wave Detectors

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## Abstract

**:**

## 1. Introduction

#### 1.1. Introduction to Quantum Noise in Gravitational Wave Detectors

#### 1.2. Theoretical Description of Quantum Light, Squeezing

#### 1.3. Squeezing in Gravitational Wave Detectors

## 2. Frequency Dependent Squeezing

## 3. Generating Squeezed States of Light

## 4. Results and History in GEO600, LIGO, Virgo

## 5. Integration of Squeezing in Gravitational-Wave Detectors

#### 5.1. Loss and Phase Noise

#### 5.2. Backscatter, Technical Noise Introduced by Squeezer

#### 5.3. Controls

#### 5.4. Filter Cavity

#### 5.5. Mode Matching and Frequency Dependence of Interferometer Response

## 6. Conclusions and Future Plans

#### 6.1. Plans for Upgrading Existing Detectors

#### 6.2. Plans for Next Generation Detectors

#### 6.3. Summary and Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | Note, our definition of phase and amplitude quadrature operators is specifically by choosing a basis of the quadrature operators suitable to describe their respective first-order modulations of a reference classical field. This in contrast to conceptual operators defined to uniquely represent phase and amplitude measurements at all orders (e.g., the Susskind–Glogower or Pegg–Barnett phase operators). |

2 | In interferometers with either arm or signal extraction cavities, the effect is reversed. |

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**Figure 1.**Quantum noise, given in terms of equivalent gravitational-wave detector sensitivity, in the Advanced LIGO design configuration (other noises not shown), calculated using [17]. Gravitational-wave detectors are sensitive to strain, change in arm length over the total arm length. At frequencies above 200 Hz, shot noise is the dominant quantum noise while radiation pressure dominates below 50 Hz. The addition of frequency independent squeezing can reduce one type of quantum noise while increasing the other (see Section 2). Once other noise sources are reduced enough that radiation pressure dominates the low frequency sensitivity of an interferometer, injecting frequency independent squeezing will degrade the sensitivity at some frequencies. Reflecting the squeezed field off of a filter cavity can rotate and filter the squeezing in a frequency dependent way to achieve a broadband sensitivity improvement. The parameters of the injected squeezing, losses, and filter cavity are chosen here so that there is 6 dB of shot noise reduction, and 8 dB of increase in quantum radiation pressure without a filter cavity, and 6 dB improvement in quantum radiation pressure noise with a filter cavity.

**Figure 2.**Ball-and-stick diagrams for a coherent state of light (

**left**), a squeezed state of light (

**center**), and squeezed vacuum (

**right**). The red line is a phasor: the amplitude of the state is represented by the length of the line, while the phase is represented by the angle of the line relative to the two quadrature axes—X${}_{1}$ and X${}_{2}$. The uncertainty of the state is represented by a fuzzy ball at the end of the stick. The squeezed vacuum field is oriented with angle $\theta $ to the quadrature axes.

**Figure 3.**Simplified optical layout of a dual-recycled Fabry–Perot Michelson interferometer (grey box), with frequency-dependent squeezing injected at the output port, as is planned the aLIGO and AdVirgo detectors in Observing Run 4. The squeezed vacuum source generates frequency-independent squeezed light. The squeezed beam (dashed red line) is reflected off the filter cavity, passes back through one or more squeezer Faraday isolators, and is injected into the main interferometer through the output Faraday isolator.

**Figure 4.**Simplified schematic for squeezed light generation. Red lines indicate 1064 nm beams, green lines are 532 nm, dashed line is squeezed light. The squeezer laser pumps a second harmonic generator which creates the 532 nm light which in turn pumps an optical parametric oscillator.

**Figure 5.**(

**Top**) Improved sensitivity of the LIGO Livingston detector in the 3rd observing run, reproduced from [9]. The black trace shows the sensitivity without squeezing injected, while the green trace shows the 2.7 ± 0.1 dB shot noise reduction with squeezing injected. The dashed magenta line shows a model of quantum noise in the detector without squeezing injected, while the gray trace is an estimate of the other noises. (

**Bottom**) Improved sensitivity of the Virgo interferometer in the 3rd observing run, reproduced from [10]. The black trace shows the sensitivity without squeezing injected, the red trace shows the 3.2 ± 0.1 dB shot noise reduction with squeezing injected, and blue shows the 8.5 ± 0.1 dB increase in shot noise when the squeezing quadrature is rotated by 90 degrees.

**Figure 6.**(

**Left**) Levels of loss and phase noise in a squeezing measurement can be characterized by measuring the level of squeezing as the parametric gain is varied by changing the OPO pump power. Expressions used to make this plot are explained in [55,56]. The 20% and 7% loss levels are expected requirements for reaching 6 dB and 10 dB of observed squeezing in current and future interferometers. (

**Right**) Observable squeezing level with parametric gain optimized for high squeezing [48,52]. This figure shows that to improve from 3 dB to 6 dB of squeezing requires mostly loss reduction, but to reach the 10 dB level of squeezing will also require low phase noise.

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Dwyer, S.E.; Mansell, G.L.; McCuller, L.
Squeezing in Gravitational Wave Detectors. *Galaxies* **2022**, *10*, 46.
https://doi.org/10.3390/galaxies10020046

**AMA Style**

Dwyer SE, Mansell GL, McCuller L.
Squeezing in Gravitational Wave Detectors. *Galaxies*. 2022; 10(2):46.
https://doi.org/10.3390/galaxies10020046

**Chicago/Turabian Style**

Dwyer, Sheila E., Georgia L. Mansell, and Lee McCuller.
2022. "Squeezing in Gravitational Wave Detectors" *Galaxies* 10, no. 2: 46.
https://doi.org/10.3390/galaxies10020046