Quantum Theory of Laser Coherence and Noise

Hermann Haken

Hermann Haken

Ning Lü, János A. Bergou

A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.

Davide Candoli, Andreu Riera-Campeny, Lorenzo Dania +7 more

State purity is a key resource for experimental tests of quantum mechanics with massive objects. Cavity cooling of a levitated nanoparticle via coherent scattering stands out as a strategy to prepare highly pure states of its roto-translational motion. In several cases, though, the performance of cooling by coherent scattering is limited by the classical fluctuations of the laser field. Here we present a quantum theory of coherent-scattering experiments which includes the effect of the laser amplitude and phase noise. We derive a master equation for the noise-averaged particle's dynamics, valid for both center-of-mass and rotational degrees of freedom, and quantify the cooling performance for different levels of noise in state-of-the-art experiments. We compute approximate analytical expressions for the laser-noise-induced heating rates and excess phonon number in both regimes of weak and strong optomechanical coupling. Moreover, our model can be applied to laser noise processes with generic power spectral densities and finite correlation times. This work offers a toolbox to quantify and optimize the state purity in coherent-scattering experiments, and opens new avenues towards the preparation of quantum states with levitated systems.

Guo Qin Ge, L. M. Chen

A fully quantum-mechanical theory of bistable inversionless lasers is developed by generalizing the Scully-Lamb laser theory to this kind of laser systems. By converting the quantum master equation of the system into a Fokker-Planck equation, we obtain the steady-state properties and the fluctuation properties of the laser field for both coherently and incoherently injected atomic systems. It is shown that both the intensity and phase fluctuations of the laser system with coherent atomic injection are reduced corresponding to their counterpart of the incoherent atomic injection. The phase noise of bistable inversionless lasers can be quenched down to the vacuum-noise level for both atomic injections.

Yiyu Zhou, Dmitri V. Voronine, Marlan O. Scully