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arXiv:2106.16155 · Physical Review A

Resonant scattering of a single atom with gain: A wave-function-diagrammatic approach

M. Donaire

Published Oct 15, 2021• 1 citation
arXivHTMLPDF

Abstract

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 $(1+\sqrt{5})/2$ times that of the natural decay.

DOI
10.1103/physreva.104.043704

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•Jan 1, 2004•0 citations
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 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 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.
We study a single incoherently pumped atom moving within an optical high-QQQ resonator in the strong-coupling regime. Using a semiclassical description for the atom and field dynamics, we derive a closed system of differential equations to describe this coupled atom-field dynamics. For sufficiently strong pumping, the system starts lasing when the atom gets close to a field antinode, and the associated light forces provide for self-trapping of the atom. For a cavity mode blue detuned with respect to the atomic transition frequency, this is combined with cavity-induced motional cooling, allowing for long-term steady-state operation of such a laser. The analytical results for temperature and field statistics agree well with our earlier predictions based on quantum Monte Carlo simulations. We find sub-Doppler temperatures that decrease with gain and coupling strength, and can even go beyond the limit of passive cavity cooling. Besides demonstrating the importance of light forces in single-atom lasers, this result also gives strong evidence to enhance laser cooling through stimulated emission in resonators.
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schrödinger equation proposed by Hudson and Parthasarathy, we show that such models can be generalized to include other processes into the interaction. In the case of a two-level atom we construct a model on the basis of some physical requirements, the main being a balance equation on the fluxes of the ingoing and outgoing photons; in this model the atom-field interaction turns out to be due either to absorption/emission processes either to direct scattering processes, which simulate the interaction due to virtual transitions to the levels which have been eliminated from the description. To see the effects of the new terms, we consider both direct and heterodyne detection of the fluorescence light emitted by an atom stimulated by a monochromatic coherent laser and we deduce from these two detection schemes the expressions of the total, elastic and inelastic electromagnetic cross sections and the spectral distribution of the fluorescence light. The total cross section, as a function of the frequency of the stimulating laser, can present not only a Lorentzian shape, but the full variety of Fano profiles; intensity dependent widths and shifts are obtained. The fluorescence spectrum can present complicated shapes, according to the values of the various parameters; when the direct scattering is not important the usual symmetric triplet structure of the Mollow spectrum appears (for high intensity of the stimulating laser), while a strong contribution of the direct scattering process can distort such a triplet structure or can even make it to disappear.
The interaction of a resonant radiation field with two-level atoms (in the long-wavelength limit) is described by a Hamiltonian trilinear in the boson operators. It is shown that the dynamics of the system can be determined nearly exactly if either at least one of the three modes is strongly populated for all times or any two modes are separately strong in two complementary time domains. Explicit results are given in two important specific cases: (i) pumping of a ground-state atomic system by a coherent radiation field and (ii) coherent spontaneous emission. The results are compared with previously known approximate results. Our results are also applicable to certain parametric processes such as parametric amplification, frequency conversion, Raman and Brillouin scattering, etc., where an identical trilinear Hamiltonian is used to describe these processes.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.