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Quantum Noise

Quantum noise and coherence

Progress in integrated optoelectronics technologies has reduced the laser device dimensions to an order of a single wavelength in size. As a consequence, the quantum fluctuations in the light field become increasingly important. Therefore, a comprehensive model of the quantum noise effects is indispensable for the correct simulation of the optical field evolution. We exploit the quantum-classical correspondence in the presence of the quantum noise by formulating stochastic equations. Within this framework the quantum noise due to the spontaneous emission is simulated by adding random Langevin noise terms to the deterministic evolution of the optical field and to the medium polarisation through the Maxwell’s equations. This term generates the statistical fluctuations of the laser field, which in turn, induce fluctuations in the population inversion, thus modifying the equations of motion of the quantum system. Using the extended Maxwell-Bloch equations, we have numerically demonstrated the intracavity electric field build up with time (Fig. 11 click on figure to see a movie)
Fig. 11. Spatially resolved dynamics of the electric field build-up within the cavity due solely to the noise background as a function of time elapsed (initial population profile r30=1 within the cavity, providing gain)

 The corresponding population inversion dynamics (Fig. 12 click on figure to see evolution) results in the coherent oscillations build-up with the time at the output laser facet of a semiconductor microcavity (Fig. 13) identifying the lasing threshold and in ultrafast relaxation behaviour of the electric field envelope until the settlement of the steady-state emission. 
Fig. 12. Time evolution of the intracavity electric field and the population inversion

                                                                                                                                                            (a)
                                                                                                                                                                (b)
Fig.13. Build up of coherent self-sustained oscillations at the output facet of a semiconductor microcavity filled with initially inverted gain medium (a) electric field; (b) Expanded view of the fast single mode oscillations in the steady-state(gain saturation) region

The simulations predict ultrafast relaxation behaviour that is not present in the usual rotating wave and slowly-varying envelope approximations. The simulations provide an estimate for the coherence time of the laser emission and allow us to infer and subsequently optimize important emission characteristics, such as the spontaneous emission rate, the laser line shape, and the relaxation oscillation frequencies and decay rates.
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