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arXiv:quant-ph/0610068 · Physical Review A

Spontaneous radiative decay of translational levels of an atom near a dielectric surface

Fam Le Kien, K. Hakuta

Published Jan 30, 2007• 37 citations
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Abstract

We study spontaneous radiative decay of translational levels of an atom in the vicinity of a semi-infinite dielectric. We systematically derive the microscopic dynamical equations for the spontaneous decay process. We calculate analytically and numerically the radiative linewidths and the spontaneous transition rates for the translational levels. The roles of the interference between the emitted and reflected fields and of the transmission into the evanescent modes are clearly identified. Our numerical calculations for the silica-cesium interaction show that the radiative linewidths of the bound excited levels with large enough but not too large vibrational quantum numbers are moderately enhanced by the emission into the evanescent modes and those for the deep bound levels are substantially reduced by the surface-induced redshift of the transition frequency.

DOI
10.1103/physreva.75.013423

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Physical Review A•Mar 19, 2007•13 citations
We study spontaneous radiative decay of translational levels of an atom in the vicinity of a semi-infinite dielectric. We systematically derive the microscopic dynamical equations for the spontaneous decay process. We calculate analytically and numerically the radiative linewidths and the spontaneous transition rates for the translational levels. The roles of the interference between the emitted and reflected fields and of the transmission into the evanescent modes are clearly identified. Our numerical calculations for the silica-cesium interaction show that the radiative linewidths of the bound excited levels with large enough but not too large vibrational quantum numbers are moderately enhanced by the emission into the evanescent modes and those for the deep bound levels are substantially reduced by the surface-induced redshift of the transition frequency.
We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with temperature in the range from 100 μμμK to 400 μμμK in the vicinity of a silica surface with temperature of 300 K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.
We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with a temperature in the range from $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}400\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in the vicinity of a silica surface with a temperature of 300K300\phantom{\rule{0.3em}{0ex}}\mathrm{K}300K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.
The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essentially determine the feasible enhancement of spontaneous decay. In particular, strong enhancement can be observed for transition frequencies within the interval in which the surface-guided field resonances strongly overlap. When material absorption becomes significant, then the highly structured emission pattern that can be observed when radiative losses dominate, reduces to that of a strongly absorbing mirror. Accordingly, nonradiative decay becomes dominant. In particular, if the distance between the atom and the surface of the microsphere is small enough, the decay becomes purely nonradiative.
We study the optical excitation spectrum of an atom in the vicinity of a dielectric surface. We calculate the rates of the total scattering and the scattering into the evanescent modes. With a proper assessment of the limitations, we demonstrate the portability of the flat-surface results to an experimental situation with a nanofiber. The effect of the surface-induced potential on the excitation spectrum for free-to-bound transitions is shown to be weak. On the contrary, the effect for bound-to-bound transitions is significant leading to a large excitation linewidth, a substantial negative shift of the peak position, and a strong long tail on the negative side and a small short tail on the positive side of the field--atom frequency detuning.
We study the optical excitation spectrum of an atom in the vicinity of a dielectric surface. We calculate the rate of the total scattering as well as the rate of the scattering into the evanescent modes. With a proper assessment of the limitations, we demonstrate the portability of the flat-surface results to an experimental situation with a nanofiber. The effect of the surface-induced potential on the excitation spectrum for free-to-bound transitions is shown to be weak. On the contrary, the effect for bound-to-bound transitions is significant leading to a large excitation linewidth, a substantial negative shift of the peak position, and a strong long tail on the negative side and a small short tail on the positive side of the field frequency detuning.