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

Dhruva Ganapathy, Victoria Xu, Wenxuan Jia, Chris Whittle, Maggie Tse, Lisa Barsotti, Matthew Evans, and Lee McCuller

Phys. Rev. D 105, 122005 – Published 21 June 2022

Abstract

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 intercavity 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.

Received 9 March 2022
Accepted 23 May 2022

DOI:https://doi.org/10.1103/PhysRevD.105.122005

Physics Subject Headings (PhySH)

Gravitational wave detectors

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Dhruva Ganapathy ^*, Victoria Xu , Wenxuan Jia , Chris Whittle , Maggie Tse , Lisa Barsotti , Matthew Evans , and Lee McCuller

Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*dhruva96@mit.edu

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Vol. 105, Iss. 12 — 15 June 2022

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Images

Figure 1
Experimental layout of a squeezer system with an audio diagnostic field. The output of the 1064 nm laser is split into two paths, one of which is upconverted to 532 nm by second harmonic generation, and used to pump the optical parametric oscillator (OPO). The other path of the 1064 nm laser is passed through a series of two acousto-optic modulators, AOM1 and AOM2, which generate both the ADF at a frequency $\pm f$ , and the CLF at $f_{CLF}$ ; the CLF actuates on the AOM1 frequency $f_{CLF}$ to stabilize the squeezing angle. The OPO is a doubly resonant bowtie cavity with mirrors $M_{1}$ , $M_{2}$ , $M_{3}$ , $M_{4}$ . The 532 nm OPO pump field is injected via $M_{1}$ , while the 1064 nm CLF and ADF tones are injected into the OPO via $M_{2}$ . The audio diagnostic, coherent locking, and squeezed vacuum fields all exit the OPO via transmission through mirror $M_{1}$ , and subsequently copropagate through an optical system before homodyne detection with a local oscillator (LO) field. The homodyne signal detected at the readout photodetector is demodulated at the audio frequency $f$ to obtain the real (I) and imaginary (Q) quadratures of the ADF-LO beatnote.
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Figure 2
Demodulation space spanned by the ADF-LO signal $e^{↑}$ for various squeezing levels. In both plots, the different colors correspond to different levels of generated external squeezing [expressed in dB of noise reduction; see Eq. (15)] by an OPO with a reflectivity $r_{1}$ of 0.935. The upper plot shows the real ( $ℜ$ ) and imaginary parts ( $ℑ$ ) of the signal as a function of squeezing angle $ϕ$ in degrees. The crosses correspond to squeezing ( $ϕ = 0$ ) while the dots correspond to antisqueezing ( $ϕ = π / 2$ ). The lower shows a parametric plot of the real and imaginary quadratures of demodulated ADF-LO beatnote signal. Here, the dot and cross markers also correspond to the respective major and minor axes of the ellipse. Their ratio can be used to compute the external squeezing level generated by the OPO [Eq. (14)]. The units of $e^{↑}$ have been chosen to normalize the case of no squeezing, $z = 0$ , to a unit circle.
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Figure 3
Characterization of a 16-m filter cavity using a sweep of the audio diagnostic field. Quadrature observables $m_{p}$ and $m_{q}$ are calculated from measurements of the normalized ADF-LO beatnote ${\bar{e}}^{↑ ↓}$ at two different squeezing angles, squeezing ( $ϕ = 0$ , blue) and antisqueezing ( $ϕ = π / 2$ , red), using Eqs. (37) and (38). The normalized beatnote data is compared to the filter cavity model from Eq. (43). The plot presents the experimental data, demodulated into real (solid) and imaginary (dashed) parts, along with the model curves fit to the data. The generated squeezing level measured by demodulating the ADF after the filter cavity [Eq. (39)] was verified against the squeezing level measured by demodulating the ADF directly after the squeezer [Eq. (14)]. The fit parameters are given in Table 1.
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Figure 4
Filter cavity loss, rotation, and dephasing calculated from $m_{p}$ and $m_{q}$ (from Fig. 3) using Eqs. (25)–(27) plotted along with model curves (solid). The top plot corresponds to the squeezing efficiency $η$ multiplied by the noise gain $Γ$ which is 1 for the filter cavity. The middle plot shows the squeezing rotation $θ$ in degrees. The bottom plot contains the square root of the frequency-dependent dephasing $Ξ$ . $\sqrt{Ξ}$ has a similar effect on squeezing as phase noise $Δ ϕ$ with the same RMS value, and therefore it has been represented in units of radians. Blue corresponds to squeezing while red corresponds to antisqueezing.
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Figure 5
Simulation of quadrature observables and squeezing degradation metrics for an ideal interferometer with (blue) and without (red) a filter cavity. The left curves correspond to the rotation $θ$ and dephasing $Ξ$ ( $\sqrt{Ξ}$ has been represented as equivalent RMS phase noise in radians) of the two configurations. The center plots contain the squeezing efficiency $η$ along with the optomechanical gain from the interferometer $Γ$ . For an interferometer with losses, the efficiency and gain cannot be measured independently. However, models of the frequency dependence of these effects would allow us to discriminate between and make independent estimates of the two quantities. Following this, we can also back out the loss of the interferometer-filter cavity combination by normalizing to the gain, $Γ$ , fit from the measured interferometer. The right plots show the quadrature observables $m_{p}$ , $m_{q}$ which have been generated using Eq. (49). Equations (25)–(27) are used to convert the quadrature observables into squeezing metrics. It is assumed that the interferometer reaches the standard quantum limit at a frequency of $Ω_{SQL} = 2 π \cdot 60 Hz$ . Simulation parameters, representing design specifications for frequency-dependent squeezing in LIGO [26], assume round trip filter cavity losses of 60 ppm, input mirror transmissivity of 1200 ppm, cavity detuning of 43 Hz, and mode matching efficiency of 0.99.
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Figure 6
Alternate OPO configurations. (a) Alternate bowtie, (b) Linear cavity.
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