The Theory of Coherent Atomic Excitation, Volume 2, Multilevel Atoms and Incoherence

Bruce W. Shore

Bruce W. Shore

Kazimierz Rza̧żewski

D. Grischkowsky

Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the $5{S}_{\frac{1}{2}}\ensuremath{\leftrightarrow}5{P}_{\frac{1}{2}}$ transition (7948 \AA{}A) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the $5{P}_{\frac{1}{2}}\ensuremath{\leftrightarrow}6{D}_{\frac{3}{2}}$ transition (6206 \AA{}A) to monitor this excitation. In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the $5{P}_{\frac{1}{2}}$ state.

Timur V. Tscherbul, Paul Brumer

We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.

Aleksei Konovalov, Giovanna Morigi, Nicola Piovella

We investigate cooperative light scattering by an ordered chain of multilevel atoms, which possess two quasi-resonant transitions with parallel dipole moments. Interference between dipole transitions induced by coupling with the vacuum gives rise to so called cross-damping and cross-shifts, that modify the incoherent and coherent dynamics and can be manifest in the spectroscopic properties of the emitted light. We determine the excitation spectrum when the atomic chain is driven by an external laser in the limit in which the dipolar transitions can be described by harmonic oscillators and the scattering is coherent. We show that the interplay of multilevel interference and superradiance can give rise to measurable effects in chains of alkali-metal atoms.