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Study on Time-Dependent Absorption Theory of Three Light Pulses in a Ladder-Type Four-Level System

Inna Rebane

Published Jun 25, 2021• 0 citations
Publisher

Abstract

The time-dependent theory of the absorption of three light pulses with an arbitrary duration in ladder-type four-level systems is proposed. The pulses are in resonance with the corresponding transitions. By using the time-dependent perturbation theory the spectral and temporal behaviour of the probability that the fourth level is excited at the moment t is found. We calculate and analyse the cases where the frequencies of the maxima of the two of three light pulses are fixed and the maximum of the remaining pules varies. Widths of possible absorption lines depend on different parameters. On the whole, three or four lines may exist, one of them corresponds to coherent contribution and the others do not.

DOI
10.9734/bpi/nupsr/v9/9837d

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Physica Scripta•Oct 13, 2020•2 citations
The time-dependent theory of the absorption of three light pulses with an arbitrary duration in ladder-type four-level systems is proposed. The pulses are in resonance with the corresponding transitions. By using the time-dependent perturbation theory the spectral and temporal behaviour of the probability that the fourth level is excited at the moment t is found. We calculate and analyse the cases where the frequencies of the maxima of the two of three light pulses are fixed and the maximum of the remaining pules varies. Widths of possible absorption lines depend on different parameters. On the whole, three or four lines may exist, one of them corresponds to coherent contribution and the others do not.
The time-dependent theory of the three-step absorption of three different light pulses in the electronic four-level systems is considered using the time-dependent perturbation theory. The first, the second, and the third pulse are in resonance with transitions from level 0 to level 1, from level 1 to level 2, and from level 2 to level 3, respectively. The spectral and temporal behaviour of the probability that the fourth level is excited at the moment of time t depends on the energy relaxation constants of the excited electronic levels, the frequencies of the maxima, the spectral widths (and so the durations) of the light pulses, and the time delays between the pulses. To conclude, there are 12 parameters that affect the spectra in the simple model used. We calculate and analyse the case where the frequencies of the maxima of the first and the second pulse are fixed and the frequency of the maximum of the third pulse varies. On the whole, three lines may exist, one of which corresponds to the coherent contribution and the others do not.
The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω 2 ≪ Ω 1,3 and (ii) the strong middle transition coupling Ω 2 ≫ Ω 1,3 . In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω 1 = Ω 3 . While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.
We present a theoretical study of three-photon electromagnetically induced absorption for a ladder-type three-level atomic system. A probe beam was tuned to the lower line and two counterpropagating, linearly polarized coupling beams were tuned to the upper line. The system can be modeled with a three- (or five-) level scheme when the polarization directions of the coupling beams are parallel (or perpendicular). By calculating the absorption coefficients analytically for the two schemes, we found that the corresponding absorption coefficients were identical except for different transition strengths, and that the primitive scheme embedded in those schemes was a simple four-level scheme.
For the interaction of coherent radiation with a nondegenerate, homogeneously broadened multilevel system the nonlinear susceptibilities and excitations and their time dependence are evaluated using a perturbation approach to the density matrix up to fourth order. This is done for the "off-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\gg}\frac{1}{\ensuremath{\tau}}$, as well as for the "on-resonance" case, ${(\ensuremath{\Delta}{\ensuremath{\omega}}^{2}+{\ensuremath{\Gamma}}^{2})}^{\frac{1}{2}}\ensuremath{\ll}\frac{1}{\ensuremath{\tau}}$, with $\ensuremath{\tau}$ being the pulse duration, by taking into account the temporal change of the electric field amplitude and the phase and energy relaxation times, T2{T}_{2}T2​ and T1{T}_{1}T1​. It is shown that the transient one-photon excitation known as adiabatic following, is not only important for a pulse duration $\ensuremath{\tau}<{T}_{2}$, but may also be important for ${T}_{2}\ensuremath{\lesssim}\ensuremath{\tau}<{T}_{1}$. In addition, expressions for the transient two-photon excitation in a multilevel system are derived. Finally, the two-level limit is evaluated to all orders of the perturbation including damping effects, which gives results valid also for large incident light intensities. For the "off-resonance" case an expression is obtained which describes not only the transient adiabatic following process, but also the usual one-photon absorption including saturation effects giving rise to power broadening.
Abstract This work is dedicated to the generalization of the spectroscopic correspondence principle to the time dependence of the evolution of a dipole-allowed quantum transition in a two-level system (TLS) under the action of an electromagnetic pulse (EMP). The formulas for the time dependence of the absorbed EMP energy for excitation of a classical oscillator and an oscillator of a transition in a TLS are derived within the framework of the first order of perturbation theory. It is shown that in the case of zero width of a transition line (or in case of zero damping constant γ for a classical oscillator) classical and quantum approaches give the same results for arbitrary EMP parameters (duration and carrier frequency). A noticeable distinction between the time dependences of the absorbed energy for a classical oscillator and a quantum TLS with a Lorentz spectral profile is observed for sufficiently long pulses.