Cyclic-Quadrature Intracavity Signal Amplification for Gravitational-Wave Detectors
The high-frequency sensitivity of laser-interferometric gravitational-wave detectors is limited by quantum shot noise. Increasing the circulating optical power reduces shot noise, but is constrained by thermal effects and optomechanical instabilities. We propose cyclic-quadrature intracavity signal amplification, in which an optical parametric amplifier (OPA) inside a detuned signal-recycling cavity is used as a phase-sensitive amplifier of the gravitational-wave signal quadrature. By detuning the signal-recycling cavity for $π$/4, the optical quadratures rotate by $π$/2 on each round trip, so a signal generated in the phase quadrature appears in the readout phase quadrature only after odd-numbered passes through the OPA. Successive contributions to the readout phase quadrature, which are separated by two round trips, have alternating signs, making this two-round-trip evolution anti-resonant. During each two-round-trip cycle, however, the same field experiences one amplification and one deamplification, so neither vacuum squeezing nor parametric gain accumulates. Despite the destructive interference between signal contributions separated by two round trips, the OPA increases the signal component extracted through the output coupler, thereby improving the signal-to-noise ratio. When the OPA gain is sufficiently large, the response approaches that of an interferometer with an effective power enhancement of $1/τ^2$, where $τ$ is the amplitude transmissivity of the quadrature-rotation mirror that forms the amplifier cavity. We apply the proposed scheme to a current gravitational-wave detector with a near-future upgrade and show that it improves the quantum-noise-limited sensitivity over a broad frequency range extending into the kilohertz band.