Phase diagram of lasing under correlated pump from GPU-accelerated Truncated Wigner dynamics
Superradiant (SR) lasers store optical coherence in the atomic medium rather than the cavity field, but the incoherent drive that sustains inversion imposes a trade-off: local pumping yields coherent light at a rate that grows linearly with the atom number $N$, heating the medium through photon recoil, whereas fully collective pumping removes this scaling but limits the emission to partial coherence. We interpolate between these limits employing a spatially correlated pump on a chain of $N$ two-level atoms, with rates decaying with distance between atoms as a power law of exponent $α$. To study systems beyond the reach of exact solutions, we employ the Truncated Wigner Approximation (TWA), whose independent trajectories are ideally suited to GPU parallelism. Harnessing this, we perform a full scan of the steady-state observables for up to $10^4$ atoms at a computational cost that is practical. Our findings indicate that ultra-narrow emission persists for all $α$, while the coherence improves as the pump becomes shorter ranged, with $g^{(2)} \to 1$ surviving at least down to $α\approx 1$, indicating that fully coherent light thus does not require local pumping. The drive strength needed for lasing is reduced by a factor $N^{1-α}$ for $α< 1$, and by $\log N$ as $α\to 1$, parametrically suppressing recoil heating; notably, $α= 1$ matches the far-field envelope of dissipative couplings in free space. The correlation range of the pump thus acts as a knob trading drive intensity, and the heating it causes, against optical coherence.