Advanced Virgo during the LIGO-Virgo-KAGRA fourth observing run

Technical Summary: Advanced Virgo during the LIGO-Virgo-KAGRA Fourth Observing Run

Problem and Context
This paper details the performance, commissioning challenges, and operational configuration of the Advanced Virgo detector during the fourth observing run (O4) of the LIGO-Virgo-KAGRA (LVK) network, spanning from April 10, 2024, to November 18, 2025. The primary technical challenge addressed is the operation of a nearly unstable dual-recycled optical configuration. Unlike the power-recycled configuration used in the third observing run (O3), Advanced Virgo was upgraded to a dual-recycled Fabry-Perot Michelson interferometer by installing a Signal Recycling (SR) mirror. This configuration, combined with the installation of a 285 m filter cavity for frequency-dependent squeezing, brought the recycling cavity stability $g$-factor to approximately 0.999988. While theoretically optimal for bandwidth, this "nearly unstable" state renders the system highly sensitive to thermal lensing, wavefront distortions, and Higher-Order Modes (HOMs), leading to significant control and noise challenges that limited the detector's sensitivity.

Methodology and Operational Strategies
The paper describes the specific methodologies employed to acquire lock, maintain stability, and mitigate noise in this complex optical environment:

• Lock Acquisition: The standard "variable finesse" strategy used in O3 was abandoned due to the increased degrees of freedom (five longitudinal). Instead, an Auxiliary Laser System (ALS) was utilized to decouple the arm cavities from the central interferometer. By locking the arms with the auxiliary laser and introducing a Common Arm Motion (CARM) offset, the central degrees of freedom (PRCL, MICH, SRCL) could be locked independently before the arms were brought back to resonance.
• Thermal Compensation: To manage the thermal lensing induced by circulating power in the nearly unstable cavities, a distributed Thermal Compensation System (TCS) was employed. This included Ring Heaters (RH), Central Heating Radius of Curvature Correction (CHRoCC), and CO$_2$ laser projectors acting on Compensation Plates (CPs). A specific strategy involved using a "Central Heating" (CH) actuator to mimic the thermal load of the main beam during lock acquisition, preventing thermal transients that would destabilize the recycling cavities.
• Alignment Control: Due to the coupling of the SR mirror alignment with HOMs, standard alignment signals were insufficient. The team utilized double mechanical dithering techniques. For the Signal Recycling (SR) mirror, the alignment was controlled by monitoring the detector bandwidth via the Differential Arm (DARM) signal response to mechanical dithers, intentionally misaligning the SR mirror to a specific point to minimize excess noise.
• Noise Mitigation: A dominant broadband excess noise was identified in the 50–200 Hz range. Investigations revealed this noise originated from the coupling of carrier HOMs to the fundamental mode at the output, amplified by the nearly unstable Signal Recycling Cavity (SRC). The primary mitigation strategy was the intentional misalignment of the SR mirror (by $\sim$2 $\mu$rad), which reduced the SRC gain for HOMs and the detector bandwidth from $\sim$430 Hz to $\sim$190 Hz. Additionally, scattered light was mitigated through the installation of new diaphragms and beam dumps on optical benches (SDB1, SNEB, SWEB) and the replacement of the West End (WE) mirror to remove a point absorber.

Key Contributions and Upgrades
The paper documents several instrumental upgrades and their specific outcomes:

• High Finesse Output Mode Cleaner (OMC): Replaced a two-cavity system with a single high-finesse ($\sim$1000) cavity to reduce losses and improve filtering of the 6 MHz sideband.
• Quantum Noise Reduction: A 285 m filter cavity was commissioned. However, due to the necessity of SR misalignment to mitigate excess noise, frequency-independent squeezing was used instead of frequency-dependent squeezing, as the latter's benefits were negated by the increased optical losses in the misaligned SRC.
• Input Mode Cleaner (IMC) Payload: The IMC end mirror payload was redesigned to improve pitch stiffness and remove a gearbox resonance, allowing stable operation at higher laser powers.
• Calibration: A new Newtonian calibrator (using spinning rotors) was deployed to provide an absolute reference for calibration, reducing uncertainty to 0.17% compared to the photon calibrator.
• Scattered Light Control: Significant improvements were made to optical bench baffling and the installation of beam dumps to reduce back-scattered light noise, particularly from the SDB1 bench.

Results and Performance

• Duty Cycle: Advanced Virgo achieved a 68.9% duty cycle during O4b and O4c. This was lower than the $\sim$75% achieved in O3, largely due to the complexity of the lock acquisition procedure (median locking time increased to 45 minutes) and the sensitivity of the nearly unstable configuration to environmental glitches.
• Astrophysical Range: The angle-averaged median range to Binary Neutron Star (BNS) mergers was 53 Mpc. This represents a modest improvement of 10–15% over O3 but was significantly limited by the excess noise.
• Noise Budget: The detector sensitivity was dominated by a broadband excess noise in the 50–200 Hz range, scaling as $f^{-0.67}$. This noise was traced to HOMs resonating in the SRC. While the intentional SR misalignment reduced this noise, it simultaneously degraded the high-frequency sensitivity and rendered the frequency-dependent squeezing injection ineffective.
• Network Performance: The LVK network duty cycle (all three detectors observing simultaneously) was 33%, lower than O3, due to the synchronization of downtimes to maximize joint observing time.

Significance and Future Prospects
The paper concludes that while the nearly unstable dual-recycled configuration was successfully commissioned and operated, its inherent sensitivity to thermal deformations and HOMs masked the benefits of other upgrades (such as the high-finesse OMC and squeezing system). The authors state that the experience gained during O4 commissioning has led to a proposal for a major future upgrade: replacing the current nearly unstable recycling cavities with stable recycling cavities using a three-mirror telescope topology. This change is expected to reduce sensitivity to thermal lensing, eliminate the need for SR misalignment, and significantly improve the BNS range to 90–130 Mpc in the next phase of detector operation. The paper serves as a comprehensive technical record of the challenges encountered in operating near the stability limit of optical cavities and the trade-offs required to maintain detector operation.