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arXiv:2506.21177 · Physical Review A

Optical response of a binary atomic system with incoherent gain

L. Acevedo, J. Sánchez-Cánovas, M. Donaire

Published Nov 13, 2025• 0 citations
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Abstract

We study the optical response of a binary system of identical atoms in which one of them is excited by an incoherent pump. Applying the diagrammatic formalism developed by Donaire [Phys. Rev. A 104, 043704 (2021)], we show how scattering, absorption, stimulated emission, spontaneous emission, and resonant energy transfer can be tailored by varying (1) the interatomic distance, which governs the interference effects of the emitted radiation, and (2) the pump rate, which determines the population of the atomic levels. It is found that, for sufficiently strong pumping, the collective component of the extinction cross section becomes negligible, regardless of the interatomic distance, as optical gains compensate for losses, and the total extinction cross section is reduced to less than half of its value in the absence of pumping. In contrast, at weak pumping and short interatomic distances, interference effects lead to a significant suppression of the extinction cross section relative to that of two noninteracting atoms.

DOI
10.1103/x9jn-p2tx

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We study the optical response of a binary system of identical atoms in which one of them is excited by an incoherent pump. Applying the diagrammatic formalism developed by Donaire [Phys. Rev. A 104, 043704 (2021)], we show how scattering, absorption, stimulated emission, spontaneous emission, and resonant energy transfer can be tailored by varying (1) the interatomic distance, which governs the interference effects of the emitted radiation, and (2) the pump rate, which determines the population of the atomic levels. It is found that, for sufficiently strong pumping, the collective component of the extinction cross section becomes negligible, regardless of the interatomic distance, as optical gains compensate for losses, and the total extinction cross section is reduced to less than half of its value in the absence of pumping. In contrast, at weak pumping and short interatomic distances, interference effects lead to a significant suppression of the extinction cross section relative to that of two noninteracting atoms.
We characterize the optical response of a three-level atom subjected to an incoherent pump and continuously illuminated with a weak quasiresonant probe field. To this end, we apply a wave-function approach based on QED Hamiltonian perturbation theory which allows for a reduction of the atomic dynamics to that of an effective two-level atom and for an implementation of the incoherent effects that respects unitarity. Using a diagrammatic representation, we identify and classify all the radiative processes. This allows us to compute the scattered power, the spontaneous emission, and the stimulated emission, as well as the total cross sections of extinction, absorption, and scattering. We find that, besides a general enhancement of the linewidth and an attenuation of the spectral amplitudes, the pump reduces the nonradiative losses and provides gains in the form of stimulated emission and incoherent radiation. For sufficiently strong pump, gains and losses compensate, resulting in the vanishing of extinction. In particular, for negligible nonradiative losses, extinction vanishes for a pumping rate of (1+5)/2(1+\sqrt{5})/2(1+5​)/2 times that of the natural decay.
We study the scattering of light by a binary system of identical atoms in which one of them is incoherently pumped. This system belongs to the kind of non-parity symmetric optical systems in which gains and losses are partially compensated. We carry out a fully quantum analysis of the directionality of the radiation scattered from the atoms when the incident light strikes the system either perpendicular or alongside the interatomic axis. By resolving the emitted field in space, the microscopic mechanisms associated with photon exchange, interference, and reciprocity become directly identifiable. We find that, generally, while the degree of asymmetry depends on the pump rate, the preferred direction for emission depends on the interatomic distance and the detuning of the probe field with respect to the resonant frequency. On physical grounds, for the case of frontal illumination, the asymmetry is the result of the interference of the photons emitted from different atoms. On the contrary, for side lighting, the asymmetry with respect to the side of incidence is caused by both the phase difference between the probe field photons that strike each atom and the interference between the photons emitted from different atoms. Further, for side lighting too, our quantum approach demonstrates that the forward scattered power depends on the side of incidence, which reveals the lack of reciprocity in the quantum optical response of the system. This result conflicts with what is obtained within a classical approach.
This paper investigates stimulated emission and absorption near resonance for a driven system of interacting two-level atoms. Microscopic kinetic equations for the density matrix elements of N-atom states including atomic motion are built, taking into account atom-field and atom-atom interactions. Analytical solutions are given for the resulting macroscopic equations in different limits, for a system composed of a strong coherent “pump” field and a weak counter-propagating “probe” field. It was shown that the existence of a dipole-dipole (long-range) interaction between atoms separated by distance less than the pump wave-length can cause the formation of periodic polarization and population structures (gratings in time and space) in the pumped medium without a probe field. The magnitude of pump induced population grating can have a strong dependence on the relation between the pump field detuning and the polarization decay rate. The “interaction” between pump and probe induced polarization/population gratings through a dipole-dipole interaction mechanism causes the absorption line shape asymmetry. Under certain conditions, this asymmetry is revealed in increasing probe gain for the “red”-shifted (relative to pump) probe and suppressing the gain for the “blue”-shifted probe field when pump is “red”-shifted relative to the ensemble averaged resonant frequency. The theoretical results are consistent with experimental data for the probe gain or absorption as the function of frequency and the dependance of the gain on atomic density for sodium vapor when the pump laser is tuned near the D 2 line. Here the dependance of gain on particle density was explained in the terms of the long-range interaction between the atoms.
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.