Cavity quantum electrodynamics (CQED) effects, such as Rabi splitting, Rabi oscillations, and superradiance, have been demonstrated with nitrogen vacancy (NV) center spins in diamond coupled to microwave resonators at cryogenic temperature. In this Letter, we explore the possibility to realize strong collective coupling and CQED effects with ensembles of NV spins at room temperature. Our calculations show that thermal excitation of the individual NV spins leads to population of collective Dicke states with low symmetry and a reduced collective coupling to the microwave resonators. Optical pumping can be applied to counteract the thermal excitation of the NV centers and to prepare the spin ensemble in Dicke states with high symmetry. The resulting strong coupling with high-quality resonators enables the study of intriguing CQED effects across the weak-to-strong coupling regime, and may have applications in quantum sensing and quantum information processing.

Cavity Quantum Electrodynamics Effects with Nitrogen Vacancy Center Spins Coupled to Room Temperature Microwave Resonators.

We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to sustain a coherent light-field. In particular, our model applies to solids within a two-band approximation, in which the electrons act as Schwinger fermions. We propose to use this Floquet-assisted superradiant phase to obtain controllable optical gain for a laser-like operation. 

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Floquet engineering of non-equilibrium superradiance

Abstract Recent experimental and theoretical studies demonstrated microwave mode cooling and cavity quantum electrodynamics (C-QED) effects at room temperature by using optically cooled nitrogen-vacancy (NV) spins. In this article, we consider improvements of these effects by exploring parameters in recent diamond maser experiments with a high frequency microwave resonator. By accounting for the rich electronic and spin levels, we provide a more complete treatment of optical pumping and dissipation in NV centers, and study the dependence of system performance on laser power. We predict the reduction of microwave photon number down to 261 (equivalent to a temperature of 116 K), about five times lower than the values reported recently. We also predict the laser-power controlled C-QED effects across weak-to-strong coupling regimes, and observe saturation of these effects under strong laser pumping. Our model can be modified straightforwardly to investigate similar effects with other solid-state spins and possible C-QED effects in maser operation. 

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Microwave mode cooling and cavity quantum electrodynamics effects at room temperature with optically cooled nitrogen-vacancy center spins

Recent experiments have demonstrated Rabi-oscillations, superradiant pulses and stimulated emission from negatively-charged nitrogen-vacancy (NV−) center spins in microwave resonators. These phenomena witness the kind of collective and strong coupling which has been the prerequisite for observation of superradiant lasing in the optical frequency regime. In this article, we investigate the possibility to employ coherence, present in both the collective NV− spin ensemble and the microwave field, to achieve a superradiant maser. Our calculations show that a superradiant maser with a linewidth below millihertz can be achieved with moderate kilohertz incoherent pumping of over 1014 spins at room temperature. We show that the superradiant masing prevails in the presence of inhomogeneous broadening, and we present numerical and analytical studies of the dependence of the phenomenon on the various physical parameters.

A superradiant maser with nitrogen-vacancy center spins

Recent experiments have demonstrated Rabi-oscillations, superradiant pulses and stimulated emission from negatively-charged nitrogen-vacancy ($\mathrm{NV}^{-}$) center spins in microwave resonators. These phenomena witness the kind of collective and strong coupling which has been prerequisite for observation of superradiant lasing in the optical frequency regime. In this article, we investigate the possibility to employ coherence, present in both the collective $\mathrm{NV}^{-}$ spin ensemble and the microwave field, to achieve a superradiant maser. Our calculations show that a superradiant maser with a linewidth below millihertz can be achieved with moderate kilohertz incoherent pumping of over $10^{14}$ spins kept at low temperature. We show that the superradiant masing prevails in the presence of inhomogeneous broadening, and we present numerical and analytical studies of the dependence of the phenomenon on the various physical parameters.

A Superradiant Maser with Nitrogen-Vacancy Center Spins

Cavity quantum electrodynamics (C-QED) effects, such as Rabi splitting, Rabi oscillations and superradiance, have been demonstrated with nitrogen vacancy center spins in diamond in microwave resonators at cryogenic temperature. In this article we explore the possibility to realize strong collective coupling and the resulting C-QED effects with ensembles of spins at room temperature. Thermal excitation of the individual spins by the hot environment leads to population of collective Dicke states with low symmetry and a reduced collective spin-microwave field coupling. However, we show with simulations that the thermal excitation can be compensated by spin-cooling via optical pumping. The resulting population of Dicke states with higher symmetry implies strong coupling with currently available high-quality resonators and enables C-QED effects at room temperature with potential applications in quantum sensing and quantum information processing.

Qilong Wu

Papers

A superradiant maser with nitrogen-vacancy center spins

A Superradiant Maser with Nitrogen-Vacancy Center Spins

Cavity Quantum Electrodynamics Effects with Nitrogen Vacancy Center Spins in Diamond and Microwave Resonators at Room Temperature