By Howard J. Carmichael
The e-book presents an creation to the tools of quantum statistical mechanics utilized in quantum optics and their software to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are mentioned including the extra typical equipment for deriving Fokker--Planck equations. specific awareness is given to the idea of optical bistability formulated by way of the confident P-representation, and the speculation of small bistable platforms. it is a textbook at a sophisticated graduate point. it's meant as a bridge among an introductory dialogue of the grasp equation approach and difficulties of present research.
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Additional info for Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations
Sample text
4 Phase Destroying Processes The interaction with the many mode electromagnetic field that gives rise to spontaneous emission causes both energy loss from the atom and damping of the atomic polarization. 36d). This damping results from a randomization of the phases of the atomic wavefunctions by thermal and vacuum fluctuations in the electromagnetic field, causing the overlap of the upper and lower state wavefunctions to decay in time. It is often necessary to account for additional dephasing interactions; these might arise from elastic collisions in an atomic vapor, or elastic phonon scattering in a solid.
55). This has a long tail which decays as (T/tR)- 1 ; the integral of this tail is logarithmically divergent; far out in the tail the replacement of p(t - T) by p(t) will not be justified. 55), where the replacement of p(t- T) by p(t) is justified. In fact, the divergent tail is a consequence of the form we have chosen for g(w)1b 2 (w). 10]. 59) which has no (T/tR)- 1 tail for n > 1. The case n = 3 is of special interest since this corresponds to the form of g(w)i,(w)i2 that we will meet when we apply our theory to the damped two-level atom (Sect.
C. c. c. 46) follow quite readily by evaluating the trace using the multimode Fock states as a basis. n(wj, T) is the mean photon number for an oscillator with frequency Wj in thermal equilibrium at temperature T. 46) involve a summation over the reservoir oscillators. We change this summation to an integration by introducing a density of states g(w) such that g(w )dw gives the number of oscillators with frequencies in the interval w to w + dw. c. c. 52) We can now argue more specifically about the Markov approximation.