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arXiv:quant-ph/9904060 · Physical Review A

Quantum Langevin theory of excess noise in lasers

P. J. Bardroff, Stig Stenholm

Published Jan 7, 2000• 21 citations
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Abstract

In an earlier work [P. J. Bardroff and S. Stenholm, Phys. Rev. A 60, 2529 (1999)], we have derived a fully quantum-mechanical description of excess noise in strongly damped lasers. This theory is used here to derive the corresponding quantum Langevin equations. Taking the semiclassical limit of these we are able to regain the starting point of Siegman's treatment of excess noise [Phys. Rev. A 39, 1253 (1989)]. Our results essentially constitute a quantum derivation of his theory and allow some generalizations.

DOI
10.1103/physreva.61.023806

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In an earlier work [P. J. Bardroff and S. Stenholm, Phys. Rev. A 60, 2529 (1999)], we have derived a fully quantum-mechanical description of excess noise in strongly damped lasers. This theory is used here to derive the corresponding quantum Langevin equations. Taking the semiclassical limit of these we are able to regain the starting point of Siegman's treatment of excess noise [Phys. Rev. A 39, 1253 (1989)]. Our results essentially constitute a quantum derivation of his theory and allow some generalizations.
To meet recent experimental advances, we generalize the intuitively appealing nonorthogonal-mode theory of excess quantum noise by introducing a Maxwell-Bloch description of the gain medium. The resulting equations extend the nonorthogonal-mode approach beyond the class A linear-gain regime providing a general starting point for theoretical descriptions of excess quantum noise. As an illustration of our theory, we derive rate equations describing excess quantum noise in class B lasers and obtain the non-Lorentzian spectrum due to the coloring of excess noise in class A lasers accounting for gain saturation.
The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.