Genuine Tripartite Strong Coupling in a Superconducting-Spin Hybrid Quantum System

Abstract

We demonstrate genuine tripartite strong coupling in a solid-state hybrid quantum system comprising a superconducting transmon qubit, a fixed-frequency coplanar-waveguide resonator, and an ensemble of NV$^-$ centers in diamond. Frequency-domain spectroscopy reveals a characteristic three-mode avoided crossing, indicating that single excitations are coherently shared across all three subsystems. At higher probe powers, we observe nonlinear features including multiphoton transitions and signatures of transmon-${}^{14}\mathrm{N}$ nuclear-spin interactions, highlighting the accessibility of higher-excitation manifolds in this architecture. These results establish a new regime of hybrid cavity QED that integrates superconducting and spin degrees of freedom, providing a platform for exploring complex multicomponent dynamics and developing hybrid quantum interfaces.

Figures (4)

• Figure 1: (a) Schematic illustration of the setup, including control and measurement systems, and the hybrid quantum system. The chip is mounted in the mixing chamber of a dilution refrigerator operating at about $12$ mK. Input lines are equipped with cryogenic attenuators and filters to suppress thermal noise, while the output signal is routed through a circulator to cryogenic and then room temperature amplifier before detection by a vector network analyzer. A magnetic field is applied using a three-dimensional Helmholtz coil, and the transmon frequency is tuned by a DC bias line. (b) Circuit diagram of the hybrid quantum system. (c) Bus-transmon transmission spectra as DC bias is changed in the diamond-loaded case. (d) Bus-ensemble transmission spectra as the NV$^{-}$ ensemble is tuned into resonance with the bus mode via adjusting magnetic field tuning, when the transmon is decoupled. Additional weak peaks between the polaritons arise from the hyperfine structure of NV$^-$ centers associated with the intrinsic $^{14}\mathrm{N}$ nuclear spins.
• Figure 2: (a) Transmission spectroscopy of the hybrid system at a probe power of $-70$ dBm as the transmon frequency is swept across resonance with the bus and NV$^-$ ensemble. Red dotted lines: transition frequencies of the hybrid system under one-excitation approximation, with color shade indicating the proportion of photons in the resonator. (b-d) Transmission coefficients of three cuts in (a), highlighting the hybridized polaritonic modes in three resonance cases. Pale-blue lines: measured data. Green lines: processed data for guiding eyes. Red lines: theoretical simulations.
• Figure 3: Transmission spectra of the hybrid system at various probe powers when the transmon, bus resonator, and NV$^-$ ensemble are tuned into triple resonance. Pale blue lines: raw data. Green lines: processed data for guiding eyes. Red lines: positions of original polariton peaks. Orange lines: positions of additional spectura features.
• Figure 4: Full transmission spectrum of the hybrid system showing fine spectral features arising from the hyperfine structure of the NV$^-$ ensemble. Inset: Magnified view of the highlighted region.