By Andrei B. Klimov

ISBN-10: 3527408797

ISBN-13: 9783527408795

Written by way of significant participants to the sector who're popular in the neighborhood, this is often the 1st finished precis of the various effects generated through this method of quantum optics so far. As such, the booklet analyses chosen issues of quantum optics, targeting atom-field interactions from a group-theoretical standpoint, whereas discussing the relevant quantum optics versions utilizing algebraic language. the general result's a transparent demonstration of the benefits of making use of algebraic how you can quantum optics difficulties, illustrated by means of a few end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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

**Example text**

4) has the same form as the Hamiltonian for a spin in the external magnetic ﬁeld. 2: ig i∆ sin t − sin t cos t − 2 U(t) = ig ∗ i∆ sin t cos t + sin t 2 where = ∆2 /4 + |g|2 is called the it Rabi frequency. 3 A Two-level Atom in a Circularly Polarized Field In the following, we consider again the case of atoms with only one electron. 4) has three components: | n → |α, l, m , where l is the angular momentum, m is the z component of the angular momentum, and the label alpha stands for all other quantum numbers required to completely specify the state (see, for example, [20]).

It can easily be seen that the normalization condition holds ( Ak=0 P0k (t) = 1), that is, the total probability is conserved (as it should be, for a unitary process). It is interesting to note that the probability of exciting all the atoms P0A (t) is equal to P0A (t) = sin2A t Also, when averaged over many oscillations, it tends to zero for a large number of atoms: PA0 (t) = A C2A 1 ∼ √ −→ 0 2A Aπ Using the evolution operator in its normal form, we can determine the evolution of various physical quantities.

We start with the spin dynamics in a constant magnetic ﬁeld. Then we consider the resonance dynamics of a two-level atom in an oscillating electric ﬁeld for different cases of the ﬁeld polarization, and, in doing so, justify the rotating wave approximation (RWA). We also discuss two-level system dynamics beyond the RWA. Finally, we consider examples of the collective dynamics of an ensemble of two-level systems in general time-dependent ﬁelds. 1 Spin in a Constant Magnetic Field As we have already mentioned, a two-level atom can be described in terms of isotopic spin.

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

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