High-order harmonic emission from a three-level atom in a laser field

Abstract

The spectrum emitted by a three-level atom in the presence of a weak laser field is given together with the population dynamics and the phase of the Fourier transform of the acceleration. Calculations show that the spectrum can be very different from that emitted by a two-level atom. When the trapping conditions are obtained, the coupling to the third level can result in a large change in the spectrum

Multiphoton population dynamics in a three-level lambda system and the related light-scattering spectrum

“…* Electronic address: mberent@amu.edu.pl Now we extend our approach [1] to cover the case of significant depopulation of the initial state, particularly the spectacular case when the population is periodically exchanged between the two lower states lying in the bottoms of lambda, leaving the highest state practically unpopulated. Such a population exchange between states 1 and 3 was, in fact, obtained in the numerical calculations reported by both us (Figure 2(c) in [1] and the corresponding text) and Caldara and Fiordilino (Figure 2(b) in [4]). Specifically, an effective exchange between the mentioned states occurred when these states were separated by nearly the energy of two photons.…”

“…In figure 3, we present a different comparison for the conditions assumed by Caldara and Fiordilino [4] in their numerical integration of the Schrödinger equation. These conditions were: ω 21 /ω 0 = 19, ω 31 /ω 0 = 2, R /ω 0 = 0.8, M R /ω 0 = 0.7 and the smooth pulse shape function f (t) = t τ 2 exp 1 − t τ 2 , where t 0 and τ = 100 T .…”

“…Instead of applying the variables r and ρ as in [1], we now prefer to work with the equations for the population amplitudes b j [1]: 2) to an effective two-state set. Since the numerical calculations [1,4] pointed to negligible population of level 2 when one meets nearly two-photon resonance between states 1 and 3, we approximately eliminate b 2 from the set (equations ( 2)). First, we formally integrate equation (2b) in the range 0, t .…”

“…To show this, we first neglect the term quadratic in r in equation (1a) when considering the case of the weak population of state 2. Then, the simplified equation (1a) is solved in the adiabatic approximation with the result r ( (t) + M(t)ρ)/ω 21 analogous to equation (4). Substituting this r to equation (1b) and taking into account that ρ = x e −iα(t) gives the Riccati equation (9).…”

“…Under the condition of P = 2m-photon resonance (ω 31 − P ω 0 = δ P → 0), equations (20) can be solved approximately in a truncated basis of states. The states of this basis are those forming the shortest coupling chain The conditions as in [4]:…”