Nitrogen-vacancy (NV) centers in diamond are a prominent solid-state spin system with applications in sensing (magnetic, electric fields, strain, temperature) and quantum processing. Their properties—a spin-1 triplet ground state with long coherence time at room temperature, and optical spin state initialization and readout—are key. Optical pumping polarizes NV spins, a process shown to be equivalent to cooling a spin ensemble, capable of cooling a coupled microwave mode. Ng et al. demonstrated cooling a 2.87 GHz resonator from 293 K to 188 K. This benchtop, room-temperature cooling contrasts with conventional methods using bulky dilution refrigerators. A sufficiently cooled microwave mode could enable studies of quantum entanglement, quantum gate operations, quantum thermodynamics, and improve measurement sensitivity in spin resonance experiments. Inspired by C-QED effects with pentacene molecules at room temperature, the authors previously showed that optically cooled NV spins enable room-temperature C-QED effects (Rabi oscillations, splittings, stimulated superradiance). Microwave mode cooling using NV centers has been limited by weak spin-microwave coupling relative to spin dephasing and high ambient excitation of low-frequency modes. This article proposes a setup using a magnetic field to Zeeman-split NV spin levels, coupling the 9.22 GHz 0→+1 transition to a dielectric microwave resonator (9.22 GHz frequency, 1.88 MHz photon damping rate, as in Breeze et al.'s experiment). Unlike that experiment (which used the population-inverted 1→0 transition for continuous maser operation), this setup reduces thermal photons by a factor of three due to higher mode frequency, while the photon damping rate is three times smaller, reducing the thermalization rate by an order of magnitude. The energy transfer rate from the resonator to NV spins is three times larger due to its dependence on the square of the spin-resonator coupling. This setup enhances energy transfer and suppresses field thermalization, improving microwave mode cooling performance.

The introduction thoroughly reviews existing literature on NV centers in diamond, their applications in sensing and quantum computing, and the recent advancements in microwave mode cooling using optically cooled NV spins. It cites key publications demonstrating the feasibility of room-temperature cooling and C-QED effects with NV centers and other systems. The authors highlight the limitations of previous approaches and position their work as a significant advancement in this field, improving upon the efficiency of cooling and the strength of the coupling between the NV spins and the microwave resonator.

The authors employ a multi-level Jaynes-Cumming (JC) model to describe the coupled NV centers-microwave resonator system, accounting for the rich electronic and spin levels of NV centers (Figure 1b). This approach goes beyond the standard two-level model, providing a more accurate description of optical spin cooling and collective coupling. The model is solved using a mean-field approach to simulate a large number (trillions) of NV centers, incorporating spin-photon and spin-spin quantum correlations through a second-order mean-field approximation. The quantum master equation (Equation 1) describes the system dynamics, including terms for optical pumping, stimulated and spontaneous emission, inter-system crossing, spin-lattice relaxation, spin dephasing, and thermal photon emission/absorption. Various rates and the calculation of optical pumping rate from laser power are detailed in the Supplementary Information. The authors use the QuantumCumulant.jl package to solve the mean-field equations. To study optical spin cooling and microwave mode cooling, the model is applied to analyze system dynamics under pulsed and continuous laser excitation (Figures 2 and 3). Effective temperature is defined to quantify the resonator's non-equilibrium state. Rate equations are derived (Equation 2) to gain further insight, and these equations qualitatively reproduce the full model's dynamics. To investigate C-QED effects, the authors use the average of Dicke state numbers (J, M) to characterize the collective coupling of the NV spin ensemble to the microwave resonator (Figure 4a). They estimate these numbers using spin level populations and spin-spin correlations. Figures 4b and 4c show Rabi oscillations and splittings under pulsed and continuous-wave microwave field driving, respectively. The Supplementary Information provides further details on the model parameters, calculations, and additional analyses.

The multi-level JC model predicts a reduction in microwave photon number to 261 (equivalent to a temperature of 116 K), significantly lower than previously reported values. This improvement is attributed to the use of a high-frequency microwave resonator and a more complete treatment of the NV center dynamics. Spin-spin correlations are shown to contribute to a higher final temperature than predicted by simpler rate equations. The study reveals a laser-power-controlled C-QED effect, with the strength of the collective coupling increasing with laser power until saturation occurs at high laser powers. Rabi oscillations and splittings are observed, demonstrating strong coupling between the NV spin ensemble and the microwave mode. The results suggest that increasing the number of NV centers would enhance the C-QED effects. The analysis based on Dicke states indicates that the system is close to the strong coupling regime with the number of NV centers used in the diamond maser experiment and firmly in the strong coupling regime when the number of NV centers is increased by a factor of 10. The effect of optical heating is considered, and it is found that the heating can be mitigated by cooling the diamond sample with standard techniques.

The findings address the research question by demonstrating significantly improved microwave mode cooling and the realization of C-QED effects at room temperature using optically cooled NV centers. The use of a high-frequency microwave resonator and a more complete theoretical model are crucial for this achievement. The laser-power dependence of the cooling and C-QED effects provides valuable insights into the system's dynamics and opens up possibilities for controlling and optimizing these effects. The results are relevant to the field of quantum information science, paving the way for room-temperature implementations of quantum technologies. The model developed can be extended to study other solid-state spin systems and investigate other C-QED phenomena.

This study presents a significant advance in room-temperature microwave mode cooling and C-QED effects using optically cooled NV centers. A more complete theoretical model, coupled with the use of a high-frequency microwave resonator, led to a substantial reduction in microwave photon number and the observation of clear C-QED effects (Rabi oscillations and splittings). The laser power is shown to control the system's behavior, enabling the exploration of the weak-to-strong coupling regimes. Future research could focus on further optimizing the experimental setup to achieve even lower temperatures and stronger C-QED effects, and also exploring the potential of the model for studying other solid-state spin systems and C-QED phenomena, including pulsed and continuous-wave masing.

The study assumes homogeneous parameters (transition frequencies, coupling strengths, rates) for all NV centers. Inhomogeneities in the diamond sample could affect the results. While the effect of optical heating is considered, the model may not capture all possible heating mechanisms perfectly. The study focuses on a specific experimental setup; the results may not be directly generalizable to all NV center systems and microwave resonators.