Phase-Sensitive Optomechanical Amplifier (PSOMA)

Gravitational-wave detectors face a fundamental trade-off: reducing shot noise (by increasing laser power) increases radiation pressure noise, and vice versa. At any given frequency, the standard quantum limit (SQL) represents the best sensitivity achievable by balancing these two contributions. PSOMA — a phase-sensitive optomechanical amplifier — offers a way around this limit by amplifying the gravitational-wave signal before quantum noise contaminates the readout.

How it works

A phase-sensitive amplifier amplifies one quadrature of the optical field while deamplifying the orthogonal quadrature. If the amplified quadrature is aligned with the gravitational-wave signal, the signal-to-noise ratio improves — the signal grows while the noise in the measurement quadrature does not. This is distinct from phase-insensitive amplification, which amplifies both quadratures equally and adds at least half a quantum of noise.

In PSOMA, the amplification mechanism is optomechanical: the interaction between light and a mechanical resonator provides the parametric gain. The key insight from Bai, Venugopalan, Kuns, Wipf, Markowitz, Wade, Chen & Adhikari (2020) is that by engineering the optomechanical coupling and detuning, the interferometer’s own test masses can serve as the amplifier — no additional hardware is needed beyond modified control signals.

Target: the low-frequency band

PSOMA is most valuable at low frequencies (10–100 Hz), where radiation pressure noise currently dominates in Advanced LIGO. This is precisely the band where:

• Binary neutron star inspiral signals spend the most time, accumulating signal-to-noise ratio over minutes to hours before merger
• Intermediate-mass black hole mergers produce their peak gravitational-wave emission
• Stochastic gravitational-wave backgrounds from cosmological sources are expected

Reducing quantum noise in this band directly increases the time-volume of the universe accessible to LIGO, with a disproportionate impact on early-warning alerts for multi-messenger astronomy.

Comparison to other sub-SQL techniques

Several approaches exist for beating the standard quantum limit, each with different trade-offs:

• Frequency-dependent squeezing (currently deployed in LIGO): Rotates the squeeze angle as a function of frequency using a filter cavity, matching the squeezed quadrature to the signal quadrature at each frequency. Reduces noise but doesn’t amplify the signal. Requires a ~300 m filter cavity with very low optical loss.
• Variational readout: Changes the homodyne detection angle as a function of frequency to always measure the quadrature with the best signal-to-noise ratio. Equivalent to frequency-dependent squeezing in some configurations. Sensitive to optical losses.
• Speed meters: Interferometer topologies (Sagnac, zero-area Sagnac) that measure test mass velocity rather than displacement, naturally evading radiation pressure noise. Requires significantly different detector topology.
• PSOMA: Amplifies the signal quadrature directly, making the signal large compared to any downstream noise (including readout loss). More tolerant of optical losses than squeezing or variational readout, because the signal is amplified before the lossy elements.

PSOMA complements rather than replaces squeezed light injection. Squeezing reduces the noise floor; PSOMA amplifies the signal. In principle, both can be used simultaneously for a combined improvement that exceeds either technique alone. The connection to quantum control for metrology using non-Gaussian states is also relevant: optimal amplification protocols may benefit from non-classical state preparation, and the feedback control techniques developed for that project apply to PSOMA implementation.

Open questions

• Stability: Phase-sensitive operation requires precise control of the pump phase relative to the signal. In a km-scale interferometer with seismic noise, thermal drifts, and control loop interactions, how robust is this phase lock?
• Bandwidth: The optomechanical amplification bandwidth is set by the mechanical response of the test masses. Can the useful gain bandwidth be engineered to cover the full 10–100 Hz target band?
• Compatibility with squeezing: Theoretical proposals show PSOMA and squeezing can work together, but the combined control system complexity is significant. Has this been demonstrated even in tabletop experiments?
• Experimental demonstration: The concept is well-developed theoretically. What is the path to a proof-of-principle demonstration — at the Caltech 40m prototype, or in a dedicated tabletop experiment?