Transmon Qubit Modeling and Characterization for Dark Matter Search

This study presents the design, simulation, and experimental characterization of a superconducting transmon qubit circuit prototype for potential applications in dark matter detection experiments. We describe a planar circuit design featuring two noninteracting transmon qubits, one with fixed frequency and the other flux tunable. Finite-element simulations were employed to extract key Hamiltonian parameters and optimize component geometries. The qubit was fabricated and then characterized at 20 mK, allowing for a comparison between simulated and measured qubit parameters. Good agreement was found for transition frequencies and anharmonicities (within 1% and 10%, respectively) while coupling strengths exhibited larger discrepancies (30%). We discuss potential causes for measured coherence times falling below expectations (<inline-formula><tex-math notation="LaTeX">$T_{1}\sim \,$</tex-math></inline-formula>1&#x2013;2 <italic>&#x03BC;</italic>s) and propose strategies for future design improvements. Notably, we demonstrate the application of a hybrid 3D&#x2013;2D simulation approach for energy participation ratio evaluation, yielding a more accurate estimation of dielectric losses. This work represents an important first step in developing planar quantum nondemolition single-photon counters for dark matter searches, particularly for axion and dark photon detection schemes.