By Andrei B. Klimov

Written through significant members to the sector who're popular in the group, this is often the 1st accomplished precis of the various effects generated by means of this method of quantum optics up to now. As such, the ebook analyses chosen themes of quantum optics, targeting atom-field interactions from a group-theoretical viewpoint, 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 the right way to quantum optics difficulties, illustrated by means of a couple of end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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2nπ nn e−n , we obtain P00 (t) ∼ √ 1 Aπ −→ 0 that is, the system with a large number of atoms has a greater probability of becoming excited. 35 36 2 Atomic Dynamics Next, we calculate the probability P01 (t) of a transition from the ground state to the ﬁrst excited state. k! |k, A A−k ! we obtain | k|eαS+ |0 |2 = |α|2k k! 2 | k|Sk+ |0 |2 = A! tan2k t k! A − k ! This yields the probability P0k (t): P0k (t) = A! cos2A−2k t sin2k t k! A − k ! 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).

5). Applying the summation rule A Pkm (θ) m=0 αm m! (A − m)! 1 = (α cos θ/2 + i sin θ/2)k k−A k! A − k ! 37), we ﬁnd | k|U(∞)|0 |2 = |α∞ + i|2A α∞ − i A! k! A − k ! 38), we obtain | k|U(∞)|0 |2 = A! |µ|2(A−k) 1 − |µ|2 k! A − k ! 40) Thus, the probability of excitation is expressed in terms of the reﬂection coefﬁcient µ. 40) completely solves the problem of the excitation of a set of two-level atoms by a classical pulse. 32) has the form 1 ξ(t) = √ e± i t −∞ (τ) dτ In this case, the parameter |µ|2 is given by the equation |µ|2 = 1 4 ∞ −∞ which is valid if |µ|2 √ dτ d (τ) dτ 1.

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. 3. Nondiagonal terms that would never represent resonant interactions, and hence, can be eliminated. 4). e. c. c. c. c. It is shown in Chapter 9 that that only odd resonances, ω ≈ 2k + 1 this system. 6 Collective Atomic Systems Now let us consider the evolution of a collection of A two-level atoms in a classical external ﬁeld.