Determine the device-specific pair-response kernel

Determine the gravitational-wave pair-response kernel $R_n^{\rm pair}$ for a specified SQUID-terminated superconducting cavity using a detector model beyond the one-dimensional circuit description, so that the gravitational-wave-induced photon-pair-production response can be quantified.

Background

The paper distinguishes the ordinary frequency-response kernel RnωR_n^{\omega} from the pair-response kernel RnpairR_n^{\rm pair}. The former governs resonance-frequency modulation, whereas the latter determines the coefficient of the photon-pair-production interaction an†2+an2a_n^{\dagger 2}+a_n^2. These kernels coincide only under the restricted approximation that the perturbation does not modify the modal normalization or effective modal capacitance.

The authors state that the one-dimensional circuit model does not contain sufficient information to determine the pair-response kernel. A device-specific calculation would therefore need to incorporate the mechanical and electromagnetic response of the actual cavity, including modal normalization and overlap effects, in order to convert the conditional photon-production formulas into a quantitative prediction.

References

This result should be understood conditionally, since the gravitational-wave strain enters through the pair-response kernel $R_n{\rm pair}$, whose value cannot be determined from the one-dimensional circuit model alone.

— High-Frequency Gravitational-Wave Transduction in a SQUID-Terminated Superconducting Cavity  (2609.01054 - Hadil et al., 1 Sep 2026) in Section 4, subsection “Quantum Hamiltonian and Photon-Pair Generation,” paragraph following Eq. (\ref{eq:photon_number_short_time_quantum_section})