By Andrei B. Klimov

ISBN-10: 3527408797

ISBN-13: 9783527408795

Written through significant individuals to the sphere who're renowned in the group, this can be the 1st finished precis of the various effects generated through this method of quantum optics so far. As such, the ebook analyses chosen issues of quantum optics, targeting atom-field interactions from a group-theoretical standpoint, whereas discussing the significant quantum optics versions utilizing algebraic language. the general result's a transparent demonstration of some great benefits of making use of algebraic the right way to quantum optics difficulties, illustrated via a few end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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**Additional resources for A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field Interactions**

**Example text**

N form the n-dimensional representation of the su(n) algebra. In the case of A identical atoms with n energy levels, the collective operators A S ij = |a, i a, j|, i, j = 1, . . 48) a=1 are introduced where |a, i is a state of the ath atom. 45. Thus the problem is reduced to the construction of the irreducible representations for the su(n) group. If the atoms are identical (the Hamiltonian is invariant under permutations of atoms), it is sufﬁcient to consider only the symmetric representation.

25) with the initial condition ϑ˙ (0) ξ˙ (0) = − 2ϑ (0) ξ (0) = 1, The frequency 2 2 (t) is given by (t) = |ϑ|2 + 3 ϑ¨ − 2ϑ 4 ϑ˙ ϑ 2 and, in general, may be complex. Let us consider the particular case of an evolution in a circularly polarized ﬁeld, where, 1 = E cos ωt and 2 = E sin ωt. 22) of the evolution operator allows us to calculate the probabilities of different atomic transitions. Let us suppose that the initial state is |0, A (henceforth |0 ), that is, all the atoms are in their ground states.

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. 13) where the vectors |nk describe the states with a deﬁned energy, that is, with a ﬁxed number of photons in the kth ﬁeld mode. 18) Henceforth, we work mainly with one only ﬁeld mode, so that only one term from the corresponding sums is needed. 19) and the representation space coincides with the space of a one-dimensional harmonic oscillator, nˆ |n = n|n .

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

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