Resonant Loop Interferometers for High-Frequency Gravitational Waves

TL;DR

This work introduces closed-loop interferometers as a novel method to probe high-frequency gravitational-wave backgrounds, exploiting geometric resonances that yield sharp, comb-like sensitivity at discrete frequencies set by loop geometry. By circulating light in square or triangular loops and aligning the TT GW projections, the GW-induced phase shifts add coherently over $n$ round trips, producing a detectable signal with minimal cross-correlation requirements. With a realistic ET-inspired baseline (a $10\ \mathrm{km}$ loop and finesse $\mathcal{F}=500$), the approach can reach below the BBN bound up to tens of kilohertz after one year, scaling as $h_{\min} \propto n^{-1} T^{-1/2}$ and exhibiting a universal $\Omega_{\rm GW} h^2 \propto f^5$ envelope at high frequencies. This resonant, self-identifying signature provides a distinctive, practical pathway to explore high-frequency stochastic gravitational-wave backgrounds and early-Universe physics at temperatures well above the CMB epoch, without relying on cross-correlation.

Abstract

Gravitational waves at kilohertz and higher frequencies offer a unique probe of the early Universe at temperatures well beyond the reach of the cosmic microwave background, corresponding to energy scales $\gtrsim 10^9$ GeV. Existing detector concepts fall many orders of magnitude short of the big-bang nucleosynthesis (BBN) bound on the stochastic background in this regime. We propose a new interferometric architecture based on closed optical loops, in which the gravitational-wave-induced phase shift accumulates coherently over many traversals. This produces sharp, narrowband resonances whose predictable comb structure provides a distinct experimental signature. For square or triangular loops with parameters compatible with the Einstein Telescope infrastructure, and finesse values of order 500, we project sensitivity that approaches and even surpasses the BBN bound up to tens of kilohertz after one year of integration. Such loop interferometers thus open a realistic and distinctive path toward exploring high-frequency stochastic gravitational-wave backgrounds.

Figures (3)

• Figure 1: Illustration of the detection principle for a square-loop resonator under a normally incident GW with $\lambda_{\rm GW}=2L$. Top: two cycles of the GW strain $h(t)$. Bottom: four snapshots over one round trip showing the quadrupolar deformation of the loop; blue/red arrows indicate CW and CCW propagation. Alternating stretches and squeezes yield four $\pi$-shifted projections that add coherently at the resonance condition.
• Figure 2: Schematic of the loop interferometer realizations. (a) Square configuration with four mirrors, operated with CW and CCW beams for differential readout. (b) Triangular configuration with three mirrors, typically operated with a single circulating beam. In both cases, the input laser (left) is coupled into the resonator and the output field is interfered with a local oscillator at the detector (right).
• Figure 3: Projected sensitivity of loop interferometers. Blue: triangular $10$ km setup with finesse $\mathcal{F}=500$ ($n\simeq160$), showing both the instantaneous response $S_h^{1/2}(f)$ (light blue, inset) and the one-year integrated sensitivity (dark blue). Orange: square setup with identical parameters. Green dot-dashed: ET-HF design sensitivity Kaiser:2020tlg; gray dotted: ET power-law–integrated (PLIS) curve Schmitz:2020syl for reference. The red dashed curve denotes the cosmological upper bound from BBN and Planck data Caprini:2018mtuYeh:2022heq. Loop interferometers exhibit sharp geometric resonances where the reach can approach or exceed the BBN bound.