Fig. 1. Concept and simulation results of the masing-enhanced quantum sensing.

(A) Stimulated emission of radiation (downward arrows) occurs when spins with population inversion in a resonator interact coherently with injected microwave photons (left-hand side arrow). The amount of detected microwave photons (right-hand side arrow) is substantially increased, so-called masing, if the inverted spins N is greater than the masing threshold (N_threshold). (B) Schematic illustration of the masing effect on ensemble spin resonance. An ensemble spin resonance spectrum (blue curve) constitutes numerous subensembles (white) with different resonant frequencies. The signal associated with specific subensembles where the amount of inverted spins N is greater than N_threshold can be enhanced by maser action (purple packets). The observed linewidth is narrowed correspondingly (purple envelope). (C) Simulation of the threshold behavior with the predator-prey model. The number of microwave photons n in a resonator increases nonlinearly with the number of inverted spins N. The blue triangle (N = 2 × 10¹¹) and star (N = 6 × 10¹²) representing the typical values of N in the below- and above-threshold regimes are labeled with the associated tangent lines and slopes. (D) Simulation of the masing effect on measured ensemble spin resonance. The distribution of the inverted spins across the resonance N(ω) is set to be Lorentzian (blue dashed lines). On the basis of the correlation of n with N simulated in (C), by varying the amplitude of the distribution N_max [blue triangle and star from (C)], the measured spin ensemble resonance in the below- (top) and above-threshold (bottom) regimes is reflected by distinct distributions of the detected number of microwave photons n(ω) (purple solid lines) in terms of the amplitude and linewidth.