By Andrei B. Klimov

ISBN-10: 3527408797

ISBN-13: 9783527408795

Written through significant individuals to the sector who're popular in the neighborhood, this can be the 1st complete precis of the various effects generated by way of this method of quantum optics to this point. As such, the publication analyses chosen issues of quantum optics, concentrating on atom-field interactions from a group-theoretical viewpoint, whereas discussing the vital quantum optics versions utilizing algebraic language. the final result's a transparent demonstration of the benefits of making use of algebraic how you can quantum optics difficulties, illustrated via a couple of end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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**Additional info for A Group-Theoretical Approach to Quantum Optics**

**Example text**

Klimov and Sergei M. Chumakov Copyright 2009 WILEY-VCH Verlag GmbH & Co. 8) k which corresponds to a system on decoupled oscillators. 12) k The ﬁrst sum corresponds to an inﬁnite set of noninteracting quantum oscillators, which allows us to use all the techniques developed in the study of the quantum harmonic oscillator. Each term in the second sum represent the vacuum energy of the appropriate mode and will be omitted in future calculations. The total Hilbert space is a direct product of Hilbert spaces corresponding to each ﬁeld mode.

For instance, if we try to remove the principal term g(S+ E + E † S+ ) by applying a transformation exp τ ES+ − E † S− , then the value of the parameter τ = g/( − ω) diverges as we approach the resonance, → ω. After application of these transformations, the terms in the transformed Hamiltonian can be classiﬁed into three groups: 1. Diagonal terms, which depend only on Sz and E † E, and whose average values represent the shifts of the system transition frequencies. 2. Nondiagonal resonant terms, which, under certain conditions imposed on the transition frequencies, describe resonant transitions; in other words, these terms become time independent in the rotating frame if certain relations between ω and are fulﬁlled.

The coherent states are not orthogonal; their overlap is given by α|β = exp − |α|2 + |β|2 2 n |α|2 |β|2 (α∗ β)n = exp − − + α∗ β n! 48) therefore, they can be considered as approximately orthogonal for essentially different values of α and β. 17) consisting of A indistinguishable two-level atoms. m! 4 Displacement Operator If we now introduce the new variables A = n + m and k = (n − m) /2 + A/2 |α1 |α2 = e−(|α1 | 2 +|α |2 /2) 2 ∞ A A=0 k=0 αk1 α2 A−k k! A − k ! 17) for A two-level atoms and pA = e −n/2 √ −iψ ne √ A!

### A Group-Theoretical Approach to Quantum Optics by Andrei B. Klimov

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