Degenerate mirrorless lasing in thermal vapors

Theoretical predictions were made for the steady-state gain of an orthogonally polarized probe field in a degenerate two-level alkali atom system driven by a linearly polarized continuous-wave pump field in [Opt. Mem. Neural Networks 32 (Suppl 3), S443-S446 (2023)]. Employing linear response theory, we computed the probe absorption spectrum under conditions where the pump was detuned from resonance. The results revealed a sub-natural linewidth dispersive feature near the pump resonance, characterized by both gain and absorption. Furthermore, a distinct pure gain peak emerged at a sideband associated with a dressed-state transition. These phenomena are generally absent outside the ultracold regime due to inhomogeneous broadening, primarily from Doppler effects, which obscure the fine spectral structure. In this paper, it is demonstrated that the sideband gain peak is sustained in the warm vapor regime when both the pump Rabi frequency and detuning exceed the Doppler width, $\Omega_P > \Delta_P \gg \Delta_{Dop}$. Our results can enable degenerate mirrorless lasing in thermal alkali atom vapors, offering a significant enhancement in the signal-to-noise ratio for fluoroscopic remote magnetic sensing applications. The theoretical model studied in this paper is also a complete description of atomic vapors with isolated $J = 2 \to J' = 3$ transitions, such as atomic samarium.