Download Statistical Methods in Quantum Optics 1: Master Equations by Howard J. Carmichael PDF
By Howard J. Carmichael
The e-book presents an creation 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 general tools for deriving Fokker--Planck equations. specific cognizance is given to the idea of optical bistability formulated when it comes to the optimistic P-representation, and the speculation of small bistable platforms. this can be a textbook at a complicated graduate point. it truly is 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
Example text
24]. These authors consider the case of a harmonic oscillator coupled to a reservoir of harmonic oscillators in thermal equilibrium. They identify weak coupling and resonance assumptions - used in quantum optics - which allow the frequency-dependent energy of the reservoir oscillators to be replaced by a constant; thus, they correctly recognize that quantum optics assumes a (locally) flat reservoir spectrum where the reservoir spectrum is strictly not flat. 5 Two-Time Averages and the Quantum Regression Formula 21 the spectrum is kT per reservoir oscillator, independent of frequency - the equipartition result).
J' Kljj Klj'j' ii1j iilj' +L Kljj Klj'j' ii1j iilj', j,j' j,j' j + 1)ei(w,J-wiJ')(t-t') where the first three terms come from the first double sum, and the fourth + = term comes from the second and third double sums. 55b) to be Hermitian- we arrive at the result nL nL (T3(t)f3(t'))R 1 = L 1Kljj'l 2 nlj(ii 1 j' + 1)ei(w,J-wlJ')(t-t'l. 62c) )*. 61) can be treated in the same fashion as in Sect. 1. 61) then gives ( with p.!. 64) =p r=dw r=dw' g2(w)g2(w')l"'2(w,w')l 2 - g~(w)gl(w')l"'l(w,w')l h h 2 w-w x n(w, T).
34). 60b) - 8jkfi 2 j). 34). Since the reservoir subsystems are statistically independent and all reservoir operators have zero mean, all of the cross terms involving correlation functions for products of operators from different reservoir subsystems will vanish. Thus, the spontaneous emission terms arising from the interaction with f 1 and f 2 are obtained exactly as in Sect. 1. 61); the others follow in a similar form. 59a), (F3(t)F3(t'))R 1 = tr[Rw L L Kljk Klj'k' (rLrlkei(w 1rwlk)t- 8jkfilj) j,k j',k' x ( r 1t j,r1k'e i(w 13-t-wlk')t' = tr[ Rw ( LL - 8 )] j'k'nlj' Kljk Klj'k' djrlk dj'rlk' ei(wlj-wlk)tei(wv-wlk' )t' j,k j',k' -L L j -L L j,k j' +L L j Kljj Klj'k' fi1j rL,rlk' ei(w 13'-w 1k')t' j',k' j' Kljk Klj'j' rLrlk filj' ei(w 13 -w 1k)t) Kljj Ktj' j' filj filj'' J 2.