Theory of Coherence of Laser Light

Yannik Brune, Marius Cizauskas, Marc Aßmann

Lasers serve as the fundamental workhorses of photonic quantum technologies, with perfectly coherent light fields being essential for many protocols that generate nonclassical light, implement coherent control schemes, and initialize qubits. However, no laser is absolutely ideal and the implications of deviations from perfect coherence in quantum technological tasks remain unclear. In this study, we theoretically and experimentally explore the quantum coherence properties of lasers from a resource theory perspective, establishing a significant connection between photonics, quantum optics, and quantum information science. We demonstrate that the maximum achievable quantum coherence for laser light is constrained by spontaneous emission and the purity of the dephased laser field state. As a critical example application in quantum information protocols, we show that the quantum coherence of a laser field with a given mean photon number directly governs the maximum purity attainable when initializing a qubit in a superposition state through resonant driving. Our findings are highly relevant for bridging applied physics and engineering with integrated photonic quantum technologies and resource theories, paving the way for reliable benchmarking of various coherent light sources for applications in photonics and quantum protocols.

Roy J. Glauber

Hermann Haken

Preface. List of symbols. 1. Introduction. 2. Basic properties and types of lasers. 3. Laser resonators. 4. The intensity of laser light. Rate equations. 5. The basic equations of the semiclassical laser theory. 6. Applications of semiclassical theory. 7. Ultrashort pulses. 8. Instability hierachies of laser light. Chaos, and routes to chaos. 9. Optical bistability. 10. Quantum theory of the laser I. A first approach via quantum mechanical Langevin equations. Coherence, noise and photon-statistics. 11. Quantum theory of the laser II. A second approach via the density matrix equation and quantum classical correspondence. 12 A theoretical treatment of the two-photon laser. 13. The laser - trailblazer of synergetics. References. Subject index.

Xiao Yan Cheng

R. Roy, A. W. Yu, Shitong Zhu

Introduction The investigation of the coherence properties of light sources has traditionally involved the study of correlation functions of different orders of the electric field (Born and Wolf, 1975; Mandel and Wolf, 1965). Field and intensity correlation functions have been measured for laser light (for a review, see Lax and Zwanziger, 1973) and have been compared with predictions obtained from quantum laser theory (Haken, 1970, 1981; Lax, 1969; Louisell, 1973; Sargent, Scully and Lamb, 1974). This was, in fact, one of the major confirmations of the correctness of the basic formalism of quantum laser theory. Most of the experiments that probed the coherence properties of lasers were, however, carried out on a very limited variety of lasing media. Interest was also centered on the regime of operation near threshold, where the light from the laser is extremely weak; hence photoelectron counting and correlation techniques were developed for the measurement of coherence properties of the laser light. While these early experiments were performed with the main intent of testing the basic theory, the large variety of lasers now available, and their ever more demanding applications, make it necessary to develop new methods for the measurement and analysis of laser fluctuations. These techniques should be applicable to the measurement of noise in high power lasers; at the same time, in order to delineate the limits of usage, they must be sensitive enough to quantitatively determine the quantum mechanical sources of noise which may lie buried in external noise that is many orders of magnitude larger.

V. Ernst