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

By Andrei B. Klimov

Written by means of significant members to the sphere who're renowned in the neighborhood, this can be the 1st finished precis of the numerous effects generated by way of this method of quantum optics up to now. As such, the ebook analyses chosen themes of quantum optics, concentrating on atom-field interactions from a group-theoretical viewpoint, whereas discussing the critical quantum optics versions utilizing algebraic language. the general result's a transparent demonstration of some great benefits of utilising algebraic how you can quantum optics difficulties, illustrated through a couple of end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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C. c. 48, the operators describing a collection of A indistinguishable atoms with three energy levels. There are still three configurations, and appropriate operators are simply obtained by substituting jk jk sz ↔ Sz and E → AE. Then the atomic transition operators are : S12 ±, S23 ± : S13 ±, S23 ± V : S12 ±, S13 ± jk jk The matrix realization of each Sz , S± for each configuration form a symmetric irreducible representation of the su(3) algebra of the dimension (A + 1)(A + 2)/2. 51) and all the Sz operators commute.

In terms of bi and bj , the collective atomic operators have the form † S ij = bj bi , i, j = 1, 2, . . 45). 49) act on the Hilbert space of n harmonic oscillators with the basis |k1 , k2 , . . , kn = |k1 ⊗ |k2 ⊗ · · · ⊗ |kn such that bi |k1 , . . , ki , . . , 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.

5 Atoms with n > 2 Energy Levels † We may think of bi and bi as the creation and annihilation operators for the † excitation at the ith atomic level (i = 1, 2, . . , n). In terms of bi and bj , the collective atomic operators have the form † S ij = bj bi , i, j = 1, 2, . . 45). 49) act on the Hilbert space of n harmonic oscillators with the basis |k1 , k2 , . . , kn = |k1 ⊗ |k2 ⊗ · · · ⊗ |kn such that bi |k1 , . . , ki , . . , 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.

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