Classical optics photon statistics

In this context, it is worthwhile to recall the quantum jump approach developed in the quantum optics community. In this approach, an emission of a photon corresponds to a quantum jump from the excited to the ground state. For a molecule with two levels, this means that right after each emission event, = 0 (i.e., the system is in the ground state). Within the classical approach this type of wave function collapse never occurs. Instead, the emission event is described with the probability of emission per unit time being Fp (t), where Pee(0 is described by the stochastic Bloch equation. At least in principle, the quantum jump approach, also known as the Monte Carlo wave function approach [98-103], can be adapted to calculate the photon statistics of a SM in the presence of spectral diffusion. 

In the subsequent chapters in which we will be investigating the thermal, electrical, optical, and magnetic properties of materials, it will be necessary to be able to determine the energy distribution of electrons, holes, photons, and phonons. To do this, we need to introduce some quantum statistical mechanical concepts in order to develop the distribution fimc-tions needed for this purpose. We will develop the Bose-Einstein (B-E) distribution function that applies to all particles except electrons and holes (and other fermions) that obey the Pauli exclusion principle and show how this function becomes the Maxwell-Boltzmann (M-B) distribution in the classical limit. Also, we will show how the Planck distribution results by relaxing the requirement that particles be conserved. Next we develop the Fermi-Dirac (F-D) distribution that applies to electrons and holes and becomes the basis for imderstanding semiconductors and photonic systems. 

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