Strain sensitivity enhancement in a Grover-Michelson interferometer

TL;DR

This work investigates strain sensitivity enhancement in gravitational-wave detectors by replacing the conventional central beam splitter of a Michelson with a four-port Grover coin, yielding the Grover-Michelson interferometer (GMI).The authors derive coupled-cavity field equations and introduce a nonlinear phase function $\gamma(\phi_N,\phi_E)$ that governs transmission, linking the GW transfer function $T_{GM}(\omega_{gw})$ to a cavity-field enhancement factor $\mathcal{G}$; they provide a shot-noise-limited NSR $\text{NSR}_{GM} = \sqrt{\frac{2\hbar}{\omega_0 P_0 \mathcal{G}}}\frac{\omega_{gw}}{\sin(\omega_{gw}\bar{L}/c)}\left[\frac{h}{\sqrt{Hz}}\right]$.The transfer function and NSR expressions are validated against finesse simulations, and the results show substantial sensitivity gains over a conventional Michelson, especially when the device operates on a bright-fringe condition and benefits from high recirculating power. Numerical comparisons with a simplified aLIGO baseline demonstrate that, in lossless scenarios, the GMI can exceed aLIGO performance by more than three orders of magnitude in certain bands, with gains moderated by realistic mirror losses; this performance is tunable via bias phases $\phi_N$ and $\phi_E$.By coupling the GMI to power, signal, or dual recycling configurations, the study shows strong low-frequency improvements (e.g., $<3\times10^{-23}$ h/√Hz from ~1–300 Hz for PR-GMI) and modest enhancements for SR- and DR-GMI, indicating configuration-dependent strategies for broadening the sensitive band.Practical deployment of a long-baseline GMI requires sub-picometer-level control of optical paths, careful mirror curvatures to minimize transverse-mode coupling, and coatings with losses near $10^{-8}$ to sustain high recirculating power without excessive thermal effects; squeezed-vacuum inputs were not considered but could offer further quantum-noise reductions.Achieving the predicted gains hinges on substantial reductions in out-of-loop laser frequency noise (roughly two orders of magnitude) and intensity noise (about a factor of six) beyond current aLIGO PSL performance, alongside CTN remaining subdominant at target frequencies.Overall, the work demonstrates that directionally unbiased multiport interferometers like the GMI can provide tunable, competitive enhancements to GW strain sensitivity, potentially rivaling traditional arm cavities as laser and coating technologies advance; future work should explore higher-frequency operation, alternative readout strategies, and further noise mitigation.

Abstract

The Michelson interferometric phase detection resolution can be enhanced by replacing conventional beam splitters with novel directionally unbiased four-port scatterers, such as Grover coins. We present a quantitative analysis of the noise-to-signal ratio of sideband frequencies generated by gravitational wave-induced phase perturbations in a Grover-Michelson interferometer (GMI). We discuss the principles of GMI signal enhancement and demonstrate how combining this configuration with additional light-recycling arrangements further enhances the performance.

Figures (10)

• Figure 1: Graphical representation of the actions of a dielectric beam splitter and a Grover coin. Their corresponding 4x4 unitary matrices are provided next to each graphic. The dielectric beam splitter routes incoming photons from one input to two output ports, with a relative phase determined by the orientation of the dielectric film. Due to Fresnel reflectance, the output amplitudes acquire a $\pi$-phase shift when incident on the film from air and no phase shift when incident through the bulk of the substrate. The Grover coin routes photons to all four output ports, regardless of the input port. Output amplitudes acquire a $\pi$-phase shift when reflected back to their input port.
• Figure 2: Abstract representation (left) and physical implementation (right) of a Grover-Michelson interferometer for gravitational wave detection. A Grover coin can be decomposed into a combination of balanced beam splitters and mirrors with relative phase shifts all set to 0 mod 2$\pi$. The end test masses (ETMs) in the interferometer arms are suspended, weighing 40kg each.
• Figure 3: Nonlinear phase function $\gamma(\phi_E,\phi_N)$ and transmission efficiency of a GMI vs. the scanning phase, which, here, is the roundtrip phase of the eastern arm, $\phi_E$. Each trace corresponds to a different bias point of the roundtrip phase in the northern interferometer arm, $\phi_N$. As the biasing phase is scanned, the $\gamma$ phase approaches a step function with respect to scanning phase, and the transmission exhibits narrowing peaks at $\phi_E=2\pi-\phi_N$.
• Figure 4: Normalized GMI transmission vs. eastern arm phase $\phi_E$ at various $\phi_N$ bias points in the (a) absence and (b) presence of loss in all of the mirrors. Mirror loss has the effect of reducing transmission at the bright fringe and broadening the peak with respect to the scanning phase.
• Figure 5: Optical layout diagram for the simplified aLIGO configuration evaluated in our numerical study. Power recycling mirror (PRM) and signal recycling mirror (SRM) have power transmittances of 3% and 20%, respectively. End test masses (ETMs) are set to a relative phase of $\pi-0.00025^\circ$ to bias at the dark fringe. The internal test masses (ITMs) have a power transmittance of 1.4%, and the interferometer arms are 4km long.