Pump-scheme dependence of few-emitter lasers: exact multilevel correlations and photon statistics
Abstract
Few-emitter laser models usually replace the excitation cycle of the gain medium by a single Markovian pump jump of a two-level emitter. We test this replacement with the cavity and laser-transition parameters held fixed and the two-level pump rate fitted to the same mean photon number, using an exact damping-basis continued-fraction solution of the cavity--emitter master equation for N identical d-level emitters with arbitrary independent incoherent transitions and one cavity-coupled transition, in the known reduced space of level populations and lasing coherences. First, a pump-quantum filtration shows that the inter-emitter coherence of Λ and ladder media starts at second rather than first order in the pump; we evaluate its leading coefficient from the exact finite-system series and map the recycling rate at which its sign changes. Second, at matched photon number, rate-limited steps in the pump cycle push the long-time output-counting Fano factor of two and three emitters well below one: for two emitters it reaches 0.66 at a mean cavity occupation of 0.3 and is still 0.74 at an occupation of one, where g(2)(0) is within 3% of unity, because the anticorrelation sits at delays of about half a cavity lifetime rather than at zero delay. For two and three emitters the fitted two-level model gets both statistics wrong and places the output above the shot-noise level. Against independent single-emitter lasers at the same output, the common cavity erodes rather than enhances this single-emitter effect.
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BibTeX
@misc{hartmann2026pumpscheme,
title = {{Pump-scheme dependence of few-emitter lasers: exact multilevel correlations and photon statistics}},
author = {Stephan Hartmann},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01205},
eprint = {2611.01205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01205},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pump-scheme dependence of few-emitter lasers: exact multilevel correlations and photon statistics
AU - Stephan Hartmann
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01205
UR - https://arxiv.org/abs/2611.01205
AB - Few-emitter laser models usually replace the excitation cycle of the gain medium by a single Markovian pump jump of a two-level emitter. We test this replacement with the cavity and laser-transition parameters held fixed and the two-level pump rate fitted to the same mean photon number, using an exact damping-basis continued-fraction solution of the cavity--emitter master equation for N identical d-level emitters with arbitrary independent incoherent transitions and one cavity-coupled transition, in the known reduced space of level populations and lasing coherences. First, a pump-quantum filtration shows that the inter-emitter coherence of Λ and ladder media starts at second rather than first order in the pump; we evaluate its leading coefficient from the exact finite-system series and map the recycling rate at which its sign changes. Second, at matched photon number, rate-limited steps in the pump cycle push the long-time output-counting Fano factor of two and three emitters well below one: for two emitters it reaches 0.66 at a mean cavity occupation of 0.3 and is still 0.74 at an occupation of one, where g^(2)(0) is within 3% of unity, because the anticorrelation sits at delays of about half a cavity lifetime rather than at zero delay. For two and three emitters the fitted two-level model gets both statistics wrong and places the output above the shot-noise level. Against independent single-emitter lasers at the same output, the common cavity erodes rather than enhances this single-emitter effect.
ER -