Andrei B. Klimov's A Group-Theoretical Approach to Quantum Optics: Models of PDF

By Andrei B. Klimov

ISBN-10: 3527408797

ISBN-13: 9783527408795

Written by means of significant participants to the sphere who're popular in the neighborhood, this can be the 1st accomplished precis of the numerous effects generated by way of this method of quantum optics to this point. As such, the e-book analyses chosen issues of quantum optics, concentrating on atom-field interactions from a group-theoretical standpoint, whereas discussing the imperative quantum optics versions utilizing algebraic language. the final result's a transparent demonstration of some great benefits of making use of algebraic how you can quantum optics difficulties, illustrated by way of a few 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: Models of Atom-Field Interactions

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Kn = ki |k1 , . . , ki − 1, . . , kn It can easily be seen that the following operator commutes with all the operators of the algebra: n ˆ = A ˆ S ij = 0 A, S j j, j=1 ˆ is just k1 + k2 + · · · + kn = A. Here, ki represents The eigenvalue of this operator A the number of atoms at the ith energy level and A is the total number of atoms. 49 ij S+ |k1 , . . , ki , . . , kj , . . , kn = ki (kj + 1)|k1 , . . , ki − 1, . . , kj + 1, . . , kn , ij S− |k1 , . . , ki , . . , kj , . . , kn = kj (ki + 1)|k1 , .

Kn = ki |k1 , . . , ki − 1, . . , kn It can easily be seen that the following operator commutes with all the operators of the algebra: n ˆ = A ˆ S ij = 0 A, S j j, j=1 ˆ is just k1 + k2 + · · · + kn = A. Here, ki represents The eigenvalue of this operator A the number of atoms at the ith energy level and A is the total number of atoms. 49 ij S+ |k1 , . . , ki , . . , kj , . . , kn = ki (kj + 1)|k1 , . . , ki − 1, . . , kj + 1, . . , kn , ij S− |k1 , . . , ki , . . , kj , . . , kn = kj (ki + 1)|k1 , .

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! 54) so that |pA |2 = PA is a Poisson distribution. 53) has a sharp maximum at A = n, so that |α1 |α1 ≈ e−iψn |ϑ, ϕ; n .

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A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field Interactions by Andrei B. Klimov


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