Frequency-Dependent Squeezed Vacuum Source for the Advanced Virgo Gravitational-Wave Detector

In this Letter, we present the design and performance of the frequency-dependent squeezed vacuum source that will be used for the broadband quantum noise reduction of the Advanced Virgo Plus gravitational-wave detector in the upcoming observation run. The frequency-dependent squeezed field is generated by a phase rotation of a frequency-independent squeezed state through a 285 m long, high-finesse, near-detuned optical resonator. With about 8.5 dB of generated squeezing, up to 5.6 dB of quantum noise suppression has been measured at high frequency while close to the filter cavity resonance frequency, the intracavity losses limit this value to about 2 dB. Frequency-dependent squeezing is produced with a rotation frequency stability of about 6 Hz rms, which is maintained over the long term. The achieved results fulfill the frequency dependent squeezed vacuum source requirements for Advanced Virgo Plus. With the current squeezing source, considering also the estimated squeezing degradation induced by the interferometer, we expect a reduction of the quantum shot noise and radiation pressure noise of up to 4.5 dB and 2 dB, respectively.

Introduction.-Interferometricgravitational-wave detectors, such as LIGO and Virgo, have so far observed around 100 gravitational-wave candidate sources, which have already provided several results spanning astrophysics, fundamental physics, and cosmology [1].These detectors are limited by quantum noise in a large fraction of their operating spectrum.In these modified Michelson interferometers with kilometer-long arms and test masses suspended from pendulums in a cascade, quantum noise manifests itself in two ways: a high-frequency (> 100 Hz) readout noise, so-called shot noise, and a noise that physically displaces the mirrors, the radiation pressure noise (< 100 Hz).The origin of these noises is found in the quantum vacuum fluctuations that enter the detector from the "antisymmetric port," i.e., the point at which the two beams recombine [2].In a coherent vacuum state, fluctuations of the phase and amplitude (known as coherent quadratures) are equal.However, one can produce, through optical parametric oscillator-based devices, squeezed vacuum states with fluctuations increased on the amplitude quadrature and reduced on the phase quadrature, which also contains the gravitational-wave signal and is effectively detected.[3].These "squeezed" states were produced and injected into the interferometers during the last (O3) datataking period (2019-2020).They allowed for a highfrequency sensitivity improvement of 3 dB, which led the detector network to have a significant increase in the number of detected gravitational-wave candidates [4][5][6].This "frequency-independent squeezing" (FIS) has the disadvantage, however, of increasing the radiation pressure noise resulting in a potential low-frequency sensitivity degradation as indeed observed by LIGO and Virgo during O3 [7,8].The reason for this increase is an optomechanically driven and frequency-dependent rotation of the two squeezed vacuum quadratures inside the interferometer, so that at low frequency the gravitational signal is aligned with the quadrature that has larger fluctuations.To reduce the quantum noise in the whole detection bandwidth, a highfinesse optical cavity with suspended mirrors-the "filter cavity" (FC)-can be used to prerotate the produced squeezing quadratures as a function of frequency, allowing the smaller fluctuations quadrature to always be aligned with the gravitational-wave signal [9].This technique, demonstrated in many prototypes [10][11][12][13][14], has now been developed for Advanced Virgo Plus (AdVþ).This article describes the design and performances of the frequency-dependent squeezing (FDS) AdVþ source, before its injection into the interferometer.The source is obtained by combining a frequency-independent squeezing source and a 285-m, high-finesse Fabry-Perot cavity.Assuming 20% of additional optical losses [15] from the interferometer, the present frequency-dependent squeezing source would make it possible to reduce quantum noise by 4.5 dB at high frequency and 2 dB at low frequency.This represents a relevant improvement in comparison to the FIS configuration used in O3.Considering the impact of other technical noises, this corresponds to an increase in the binary-neutron-star (BNS) and binary-black-hole detection range of up to 9%, with respect to the frequency-dependent squeezing case, which translates into an increase of 29% of the observable-Universe volume.At the same time the 4.5 dB highfrequency noise suppression results in an enhanced sensitivity when searching for higher-frequency sources, such as neutron star late inspirals [16] and postmerger [17] and supernova-core collapses [18].
Experimental setup.-Asshown in Fig. 1, the experimental setup is composed of the frequency-independent squeezed vacuum source, which is the same as that used in Virgo during the last observational run (O3) [19] with minor modifications [15], a 285 m long Fabry-Pérot resonator with suspended mirrors, which plays the role of the filter cavity, and two suspended optical benches to inject the squeezed vacuum into the filter cavity and the reflected beam into the interferometer from the antisymmetric port.The system is also equipped with a diagnostic homodyne detector (HD), which is used to characterize the frequency dependent squeezing without needing the interferometer.
Filter cavity: The filter cavity has been designed to have a linewidth of ≈25 Hz, which also corresponds to the desired detuning frequency.Such values have been chosen in order to produce the optimal rotation frequency of the squeezing ellipse, given the interferometer parameters for the forthcoming observing run (O4).Given that some of the squeezing degradation mechanism (e.g., the cavity round-trip losses) are inversely proportional to the cavity length [20], the choice of the cavity extension comes from a trade-off between the reduction of the squeezing degradation due to these effects and the advantage of a smaller infrastructure.The choice of a FC length of 285 m combined with the need of a linewidth of 25 Hz fixes its finesse to F IR ≈ 10 4 ; experimental measurements gave F IR ¼ 9695 AE 4. The other target parameters for the AdVþ FDS source are listed in Table I.A detailed analysis of the reasons that led to the choice of these parameters can be found in Ref. [15].The expanded area in the green frame contains the simplified optical layout, the description of which can be found in the text.The measurements reported in Figs. 2 and 3 are made with the half-wave plate HWP1, setting the IR beam polarization axis in order to maximize the polarizing beam splitter PS1 reflection toward the M5 mirror, and from there to the diagnostic homodyne detector.Prior to the measurements, the subcarrier beam is used to align the IR fields to the FC.It is subsequently blocked by the motorized shutter SH.This procedure is automatically repeated after each FC unlock.Alternatively, by rotating with HWP1 the beam's polarization by 90°, the IR beams are directed toward the interferometer for squeezing injection, which is part of the currently ongoing second phase of the project.The figure shows the beam paths for the two mutually exclusive cases.The relevant acronyms are as follows: AOM, acoustooptic modulator; HWP, half-wave plate; M, mirror; DM, dichroic mirror; SHG, second harmonic generator; OPA, optical parametric amplifier; HD, homodyne detector; QPD, rf quadrant photodiode; PD, photodiode; PLL, phase locked loop; SH, beam shutter; PS, polarizing beam splitter; DET, detection bench; FCIM and FCEM, filter cavity input and end mirror, respectively.
The cavity is installed inside the Virgo detector's north tunnel, parallel to one of the interferometer arms (see Fig. 1).It comprises two concave mirrors with 150 mm diameter.The radius of curvature (558 m) has been chosen in order to minimize the cavity round-trip losses due to degeneracy with higher order modes [21].If needed, the radius of curvature can be fine-tuned using ring heaters installed in vacuum around the mirrors [22].
Simulation with measured mirror surface roughness maps shows that this corresponds to a round-trip loss of ≃10 ppm.Scattering from higher-frequency defects has been measured to be 5.5 and 8 ppm for the input [23] and the end [24] mirrors, respectively.The end-mirror transmission is 3.2 ppm, while the coating absorption is below 1 ppm.The expected round-trip losses are therefore less than 30 ppm.A compact suspension system was designed and implemented for seismic isolation of the filter cavity mirrors.It is composed of a down-scaled version of the Virgo superattenuator inverted pendulum and a geometric antispring filter [25].The mirrors are then suspended using the standard Virgo "marionette" concept [26].
Auxiliary benches for squeezing injection: The squeezing source is hosted on a nonsuspended in-air optical bench (EQB1) where it is superposed to the auxiliary IR control beams (see below).On the same bench, an acoustooptic modulator is used to set the green beam frequency with respect to the squeezed beam, thus setting the initial detuning condition of the latter.
All these beams are then injected into the vacuum system on the first suspended bench (SQB1).At this level, the IR beams are superposed on the green auxiliary beam, after being reflected by the first polarizer of a double-stage Faraday isolator [27] and they are then sent toward a second suspended bench (SQB2) and to the FC input mirror (see Fig. 1).The IR beams reflected by the FC propagate back to SQB1 together with the green beam where, by selecting the polarization orientation with a half-wave plate (HWP1), it is possible to direct the IR beams either toward the interferometer or toward the diagnostic homodyne detector on EQB1, as in the case of the reported measurements.The green beam propagates back to EQB1, where the sensors for the green control of the FC are located.
In order to achieve the requirements on the residual seismic motion, the in-vacuum benches SQB1 and SQB2 are suspended using a multistage seismic attenuation system [25] that is already used for other auxiliary optical benches in AdVþ.
Cavity control strategy: In the configuration used to acquire the FDS measurements reported in this Letter, the FC was longitudinally and angularly controlled with a green (532 nm) beam.This auxiliary field is derived from a pickoff of the optical parametric amplifier (OPA) pump beam, produced by a second harmonic generator (SHG).The finesse of the filter cavity at this wavelength is approximately 100.This corresponds to a much larger bandwidth of the cavity optical resonance for the green, with respect to the IR, which makes the longitudinal control easier to acquire.The error signal for the FC longitudinal control is obtained from the green beam in reflection of the cavity with a Pound-Drever-Hall technique.The correction signals below 100 Hz are sent to the FC end mirror, while the higher-frequency corrections are sent to the laser frequency control.The resulting lock precision, of the order of 1 Hz rms, fulfills the AdVþ design requirement.
The automatic alignment loop that keeps the FC mirrors aligned on the green beam is based on the differential wavefront sensing technique [28] and the correction signal is additionally blended with the optical lever signals at a frequency of 50 mHz.An additional loop, based on the application of a mirror angular position modulation, is used to ensure that the FC optical axis passes through the mirror center.
The squeezing ellipse angle stabilization is obtained via the coherent control technique [29], which requires an auxiliary IR beam with a 4 MHz frequency offset from the squeezed beam.
For the injection of FDS into the interferometer, it is foreseen to control the whole system with IR beams.For this purpose, an auxiliary IR "subcarrier beam" (SC) is added [30].The SC laser source is phase-locked to the squeezer main laser frequency with a frequency offset Ω SC ¼ 1.262 GHz.To avoid disturbing the interferometer operation, such offset has been chosen to make the beam antiresonant in the signal recycling cavities and in the output mode cleaner.The SC beam is mode-matched into the OPA and its frequency is also set to be antiresonant for this cavity.As shown in Fig. 1, the beam is thus back-reflected from the OPA and it copropagates with the squeezed field.Misalignment of the SC beam with respect to the filter cavity is sensed by a 0.1% pickoff of the FC reflection, which propagates in the direction of the in-air bench EQB2, where the alignment rf-quadrant photodiodes are hosted.The same bench also hosts the photodiodes for the FC longitudinal control with IR.For the measurements considered in this Letter, the SC beam is only used to prepare the system for the FDS standalone measurement and is subsequently blocked.Experimental results.-Theperformance of frequencydependent squeezed vacuum is highly affected by any optical loss that may occur along the path between the generation of the quantum state inside the OPA and the final measurement at the HD.Therefore, prior to the analyses of FDS measurements and the long-term stability of our setup, an independent loss budget is performed in order to quantify the degradation.
Loss budget: The parameters that degrade the FDS are obtained with independent measurements and are summarized in Table I.The resulting propagation loss between EQB1 to FC, net of the readout losses, is ð10 AE 1Þ% and the squeezing ellipse angular noise ð31 AE 21Þ mrad.These parameters have been estimated using the model developed in [31] by comparing squeezing and antisqueezing for various pump powers.
Since the SC beam is 99.8% mode matched to the OPA cavity, it can be used to estimate the mode matching between the squeezed beam and the FC, which is determined to be about 98.5% with long-term fluctuations lower than 1%.
The FC round-trip losses are determined with three different methods [32,33].The results are distributed over the interval (50-90) ppm, which is higher than the expected value considering only the mirror roughness.The physical origin of this discrepancy has not yet been understood, but it leads to a worsening of the O4 calculated BNS merger horizon of less than 1%.
The readout losses are estimated by taking the measured HD contrast ð98 AE 1Þ%, the dark noise clearance (1%), and the expected photodiodes quantum efficiency (99%) [19] into account.It is worth noting that, in the case of FDS injection into the interferometer, the readout losses are expected to be different, since a distinct detection system will be used.
Table I summarizes the measured parameters presented in this Letter versus the maximum target values for O4.Except for the FC losses discussed above, the target values have been achieved.Nevertheless, since FDS has not yet been injected into the interferometer, additional contributions from the latter are expected in terms of injection losses and squeezing phase noise.
Frequency-dependent squeezing: In the AdVþ baseline design [15] the bright SC beam is expected to be rejected by the output mode cleaner and can therefore be used for the longitudinal and angular control of the FC without affecting the detection sensitivity.This configuration cannot be used for the squeezing measurements performed with the diagnostic homodyne detector, because the relatively high power of the copropagating SC beam induces saturation and excess technical noise on each homodyne photodiode.Therefore, all of the FDS measurements presented in this Letter are performed with the FC controlled with the green only and the SC beam blocked, relying on the assumption that, during the measurement, the IR alignment and locking to the FC are preserved.
During the commissioning phase of the AdVþ FDS source, several squeezing measurements, with different FC detuning down to a frequency of 25 Hz, have been acquired with the homodyne detector.At frequencies below 20-25 Hz the measurements were often degraded by a nonstationary noise generated by the scattered light produced in the local oscillator (LO) path, which then recombined with the squeezed field [34].Therefore, the systematic FDS measurements campaign has been done at slightly higher detuning frequencies.It is worth noticing that this detrimental effect is not expected to be relevant when the squeezed field will be injected into the interferometer, since the HD LO will be blocked, while the contribution of the interferometer LO is predicted to be limited, by the Faraday isolators inserted into the squeezed path (see Fig. 1) [15].
A typical set of measurements made at various homodyne angles is shown in Fig. 2, where the level of noise on the HD (in dB) is normalized to the shot noise.The FC detuning Δω fc is set at 45 Hz before starting the measurements.The squeezing ellipse angle ϕ HD as seen by the HD is changed by tuning the path length of the LO beam.Using the theoretical model described in [20], the detuning frequency and homodyne angle were fitted, while the loss budget parameters in Table I were kept within the experimental uncertainty ranges.Over time, the fitted detunings, as seen by the squeezed state, show a drift of around 10 Hz, the origin of which is investigated below.At frequencies close to Δω fc , the squeezing level is degraded by the FC round-trip losses.Nevertheless, even in this frequency range, a shot-noise suppression of at least 2 dB has been observed.At higher frequencies, where the squeezed field is antiresonant to the FC, squeezing levels of down to 5.6 dB are obtained with about 8.5 dB of produced FIG. 2. Relative squeezing level to shot noise in dB (positive is antisqueezing, negative is squeezing) measured at the homodyne detector, for different values of the coherent control phase, and for (44-55) Hz detuning of the FC resonance.The experimental data (solid lines) are fitted using an analytic model of squeezing degradation (dashed lines).The squeezing source generates (8.0-8.5)dB of squeezing.Note that below 20 Hz, all experimental curves increase in noise due to scattered light coupled to low-frequency seismic motion.squeezing.To our knowledge, these results far exceed the reference values obtained in previous publications [13,14] and constitute the state of the art for FDS sources implemented for injection in gravitational-wave interferometric detectors.
Long-term stability: The long-term operation of the FDS system requires additional care in the system controls in order to compensate the daily motion between all of the suspended benches.All these processes, as well as the controls of the squeezing source, are automated in a hierarchical locking procedure managed by a finite state machine [35].In this way the complete engagement of the FDS measurement after any system failure (for instance a filter cavity unlock) is automatically achieved in less than 4 min.
Figure 3 shows the time frequency plot of the FDS level for a homodyne angle of 90°over a time period of about 48 h.Squeezed light is continuously produced, even if a drift in the squeezing properties is observed.In particular, both the detuning frequency and the squeezing dip amplitude slowly change over time, with an excursion of about 10 Hz and 1 dB, respectively.The antisqueezing value above 1 kHz also changes, reaching a maximum of 8.5 dB with a variation of 1 dB not attributable to variations in the produced antisqueezing level, but rather to the worsening of the infrared alignment to the filter cavity.This behavior is related to the fact that, during the measurement, the FC is fully controlled with the green beam, while the IR fields are not actively locked and aligned to it.
The detuning stability can be affected by several issues when the cavity is operated with a bichromatic control [36], e.g., by the temperature drifts of the cavity mirrors.In fact, the phase acquired after a reflection from the FC mirrors shows a different temperature dependence for green and infrared and this produces IR detuning drifts in the presence of a temperature change when the cavity is locked with the green.This behavior was observed and shown in Fig. 4, reporting a 24-h data acquisition period, in which the temperature of the end mirror was not optimally stabilized.The detuning frequency and the end mirror temperature, approximated by the temperature detected by a thermometer placed on the mirror ring heater, time delayed by 60 min, appear correlated with a scaling factor of ð114 AE 1Þ Hz=K.The slope is in agreement with the results obtained with an analytical model [37].The applied time lags are justified by the mirror's suspension thermal resistance, which manifests with a time delay in responding to a change in the ring heater temperature.After this observation, the temperature of the mirrors was controlled to better than 30 mK rms, producing the results of Fig. 3.
Although the achieved level of detuning stability would impact less than 1.5% in the best theoretical estimate of the O4 BNS horizon, a lower detuning drift is expected when using the SC-IR beam for filter cavity control.To verify this statement, we locked the OPA to a bright beam derived from the squeezer main laser.Then the OPA output and the SC beams were directed toward the FC and the transmitted IR field was observed while scanning the FC resonance frequency acting on the green acousto-optic modulator.The relative detuning of the two infrared beams, initially set to about 1 kHz, was preserved within 4 Hz over 1 d of acquisition time.
Conclusion.-The frequency-dependent squeezed vacuum source for the broadband quantum noise reduction of the AdVþ detector has been built and characterized at the observatory site.The demonstrated performances in terms of squeezing level and long-term detuning stability FIG. 3. Power spectral density (PSD) of the diagnostic homodyne detector output normalized to the shot-noise level versus the time of data acquisition.Every 3 min a power spectral density similar to that of Fig. 2 (blue line) with a homodyne angle of 90°i s estimated.In correspondence with the acquisition time, the PSD is drawn in the plot with the frequency in the ordinate and the amplitude with a color scale, the calibration of which in dB of squeezing, is represented by the vertical bar on the right.The homodyne angle was chosen to maximize the contrast with which the detuning frequency is observed.The detuning frequency, initially set to be equal to 80 Hz, where the quantum noise suppression is at its maximum, is represented by the yellow curve, which fluctuates in time by about 10 Hz peak to peak.The sudden increase in the antisqueezing level occurring after about 6 h results from an optimization of the infrared alignment.are the best so far reported in the literature.While almost all of the degradation parameters are kept within their designed ranges, the unforeseen value for the FC round-trip loss may reduce the sensitivity for BNS by less than 1%.The actual sensitivity of Advanced Virgo Plus will depend on the squeezing degradation sources and on the residual technical noise of the interferometer.In the design report [15] the interferometer losses were quoted at about 20% [15].This would produce a high-frequency sensitivity enhancement of about 4.5 dB and with respect to the FIS injection, an increment in the BNS coalescence detection rate of 29%.However, the actual impact of the interferometer losses will be evaluated in the second part of the project, which foresees the injection of the FDS field into the interferometer antisymmetric port.

FIG. 1 .
FIG. 1. Experimental setup (not to scale) for the FDS generation installed at the Virgo site.The interferometer arms and the filter cavity are 3 km and 285 m long, respectively, while the SQB1-SQB2 and SQB2-FCIM vacuum tanks are 10 m and 40 m apart, respectively.The expanded area in the green frame contains the simplified optical layout, the description of which can be found in the text.The measurements reported in Figs.2 and 3are made with the half-wave plate HWP1, setting the IR beam polarization axis in order to maximize the polarizing beam splitter PS1 reflection toward the M5 mirror, and from there to the diagnostic homodyne detector.Prior to the measurements, the subcarrier beam is used to align the IR fields to the FC.It is subsequently blocked by the motorized shutter SH.This procedure is automatically repeated after each FC unlock.Alternatively, by rotating with HWP1 the beam's polarization by 90°, the IR beams are directed toward the interferometer for squeezing injection, which is part of the currently ongoing second phase of the project.The figure shows the beam paths for the two mutually exclusive cases.The relevant acronyms are as follows: AOM, acoustooptic modulator; HWP, half-wave plate; M, mirror; DM, dichroic mirror; SHG, second harmonic generator; OPA, optical parametric amplifier; HD, homodyne detector; QPD, rf quadrant photodiode; PD, photodiode; PLL, phase locked loop; SH, beam shutter; PS, polarizing beam splitter; DET, detection bench; FCIM and FCEM, filter cavity input and end mirror, respectively.

FIG. 4 .
FIG. 4. Filter cavity detuning frequency versus the end mirror ring heater temperature.Each point corresponds to a pair of values measured every 3 min within 24 h.The maximum correlation is obtained assuming that the temperature of the mirror lags behind that of the ring heater by about 60 min.

TABLE I .
Measurements and O4 target parameters.The measured injection losses and phase noise parameters do not include the interferometer contribution, which is instead included in the target parameter column.