By Andrei B. Klimov
Written by means of significant members to the sphere who're popular in the neighborhood, this is often the 1st entire precis of the numerous effects generated by means of this method of quantum optics up to now. As such, the booklet analyses chosen issues of quantum optics, targeting atom-field interactions from a group-theoretical point of view, whereas discussing the vital quantum optics types utilizing algebraic language. the final result's a transparent demonstration of the benefits of utilizing algebraic the right way to quantum optics difficulties, illustrated via a couple of end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.
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Additional info for A Group-Theoretical Approach to Quantum Optics
15). ) These operators act in a Hilbert space spanned by eigenstates of the operator † E0 = E0 : E0 |m = m|m , m = · · · − 1, 0, 1, . . 5 Dynamics of the Two-level Atom without the RWA Here, E and E † are ﬁeld phase operators, E0 is the shifted photon-number operator, and m = n − n. 16) are approximately satisﬁed if n. 17. 15). Furthermore, we can, without loss of generality, set the global common phase θ equal to 0. 19) is time independent. 4). 19. This is done by applying in a perturbative way a series of small Lie-type transformations.
We look for the operator U (t) in the following disentangled form (Euler parameterization): U (t) = e−iϕSz e−iθSy e−iψSz where (ϕ, θ, ψ) are the Euler angles, 0 ≤ θ ≤ π, 0 ≤ ϕ ≤ 2π, −2π ≤ ψ ≤ 2π. There is a correspondence between parameters (ϕ, θ, ψ) and (α, β, γ). e. on the number of atoms A), we ﬁnd that A = 1 in the fundamental (two-dimensional) representation, which corresponds to a single atom). 5). 22) discussed in the previous section is not useful if the external ﬁeld is a pulse with vanishing amplitude at t → ±∞.
The coherent states are not orthogonal; their overlap is given by α|β = exp − |α|2 + |β|2 2 n |α|2 |β|2 (α∗ β)n = exp − − + α∗ β n! 48) therefore, they can be considered as approximately orthogonal for essentially different values of α and β. 17) consisting of A indistinguishable two-level atoms. m! 4 Displacement Operator If we now introduce the new variables A = n + m and k = (n − m) /2 + A/2 |α1 |α2 = e−(|α1 | 2 +|α |2 /2) 2 ∞ A A=0 k=0 αk1 α2 A−k k! A − k ! 17) for A two-level atoms and pA = e −n/2 √ −iψ ne √ A!
A Group-Theoretical Approach to Quantum Optics by Andrei B. Klimov
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