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Physical Review A

Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Resonance flourescence

Bo Gao

Published Nov 1, 1994• 22 citations
Publisher

Abstract

Effects of the atomic Zeeman degeneracy on the resonance fluorescence spectrum of a closed two-level atom with arbitrary ground-state angular momentum ${\mathit{J}}_{\mathit{g}}$ and excited-state, angular momentum ${\mathit{J}}_{\mathit{e}}$ are studied in detail. Especially interesting are the narrow structures due to the spontaneous Raman scattering and the incoherent Rayleigh scattering. Results for the cycling transition of a Cs atom are presented as part of the examples.

DOI
10.1103/physreva.50.4139

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Quantum interference in the resonance fluorescence of a J=1/2−J′=1/2 atomic system: Quantum beats, nonclassicality, and non-Gaussianity

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Effects of the atomic Zeeman degeneracy on the resonance fluorescence spectrum of a closed two-level atom with arbitrary ground-state angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​ and excited-state, angular momentum Je{\mathit{J}}_{\mathit{e}}Je​ are studied in detail. Especially interesting are the narrow structures due to the spontaneous Raman scattering and the incoherent Rayleigh scattering. Results for the cycling transition of a Cs atom are presented as part of the examples.
The analytic solution of the steady-state density matrix is presented for a closed two-level atom with an arbitrary ground-state angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​ and an excited-state angular momentum Je{\mathit{J}}_{\mathit{e}}Je​ interacting with a linearly polarized laser field. From this solution, analytic formulas for the total rate of laser-atom scattering, the rate of coherent scattering, and radiative forces are derived. Interestingly, it is found that population inversion in true atomic states, as opposed to the population inversion in the dressed states, can occur under certain conditions. A method is proposed to take advantage of this inversion for light amplification. The mathematical formulation is built around the concept of the resolvent operator in Liouville space, with some conclusions that are generally applicable to any system with a unique steady state.
Resonance fluorescence due to intense laser fields from a Zeeman degenerate atom being perturbed by collisional interactions is calculated in the impact regime by using the quantum-fluctuation-regression theorem. Various interesting effects are found. For example, the scattered intensity spectrum for a J=0J=0J=0 to J=1J=1J=1 transition for polarization parallel to the laser polarization is essentially an asymmetric triplet, whereas for a perpendicular polarization due to collisions the spectrum is essentially a doublet (whose frequencies do not correspond with any of those of the triplet). Further, the width of the fluorescent component (whose frequency is close to the unperturbed frequency) actually decreases with increasing laser power.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
We study theoretically quantum statistical and spectral properties of the resonance fluorescence of a single atom or system with angular momentum $J=1/2\ensuremath{-}{J}^{\ensuremath{'}}=1/2$ driven by a monochromatic linearly polarized laser field, due to quantum interference among its two antiparallel $\ensuremath{\pi}$ transitions. A magnetic field parallel to the laser polarization is applied to break the degeneracy (Zeeman effect). In the nondegenerate case, the $\ensuremath{\pi}$ transitions evolve at different generalized Rabi frequencies, producing quantum beats in the intensity and the dipole-dipole, intensity-intensity, and quadrature-intensity correlations. For a strong laser and large Zeeman splitting the beats have mean and modulation frequencies given by the average and difference, respectively, of the Rabi frequencies, unlike the beats studied in many spectroscopic systems, characterized by a modulated exponential-like decay. Further, the Rabi frequencies are those of the pairs of sidebands of the Mollow-like spectrum of the system. In the two-time correlations, the cross contributions, i.e., those with products of probability amplitudes of the two $\ensuremath{\pi}$ transitions, have a lesser role than those from the interference of the probability densities. In contrast, there are no cross terms in the total intensity. We also consider nonclassical and non-Gaussian properties of the phase-dependent fluorescence for the cases of weak to moderate excitation and in the regime of beats. The fluorescence in the beats regime is nonclassical, mainly from third-order dipole fluctuations, which reveal them to be also strongly non-Gaussian, and their quadrature spectra show complex features around the Rabi frequencies. For small laser and Zeeman detunings, a weak to moderate laser field pumps the system partially to one of the ground states, showing slow decay in the two-time correlations and a narrow peak in the quadrature spectra.