By Andrei B. Klimov
Written by means of significant individuals to the sector who're renowned in the group, this is often the 1st complete precis of the numerous effects generated through 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 central quantum optics types utilizing algebraic language. the general result's a transparent demonstration of some great benefits of making use of algebraic easy methods 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
Thus, for one atom, we have P00 (t) = 1/2 and, for two atoms, we have P00 (t) = 3/8. √ In the case of a large number of atoms A 1, using the Stirling formula n! ∼ 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!
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. 1 Describe the evolution of A atoms initially in the coherent state |ξ = 1 under the inﬂuence of the Hamiltonian H = χS2z Find the evolution of the Bloch vector.
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. 49 ij S+ |k1 , .
A Group-Theoretical Approach to Quantum Optics by Andrei B. Klimov