By Howard J. Carmichael
The ebook offers an advent to the equipment of quantum statistical mechanics utilized in quantum optics and their program to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are mentioned including the extra common equipment for deriving Fokker--Planck equations. specific consciousness is given to the idea of optical bistability formulated by way of the confident P-representation, and the idea of small bistable structures. this can be a textbook at a complicated graduate point. it's meant as a bridge among an introductory dialogue of the grasp equation procedure and difficulties of present research.
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Additional resources for Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations
The (nl61m) define the matrix representation of 6 with respect to the basis In). 2) where CYz =12)(21 -11)(11. 2) is a constant which may be eliminated by referring the atomic energies to the middle of the atomic transition, as in Fig. 1. 4) X) Fig. 1 Energy levels for a two-level atom. 7) a+= 12)(11. 7) are az = ( ~ ~1)' By writing a_ = ( ~ ~), a+= ( ~ ~). 5]. When applied to two-level atoms az, a_, and a+ are referred to as pseudo-spin operators, since, in this context the two levels are not associated with the states of a real spin.
As we will see, a two-level atom responds nonlinearly to increasing intensity; also, while a harmonic oscillator can be excited ever higher up its ladder of Fock states, a two-level atom can only store a single quantum of energy.
25) - namely, to the starting equations in our derivation of the master equation. We can find an equation for p 01 (T) in the Born-Markov approximation following a completely analogous course to that followed in Sects. 4. 95) with solution 24 1. Cr[p(t)01(0)]. 98) give formal statements of the quantum regression formula for two-time averages. 98) because noncommuting operators do not allow the reordering necessary to bring 0 1(t) next to 0 3(t). We may, however, generalize the approach taken above.
Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations by Howard J. Carmichael