Physical interpretation of fluorescence waveforms from coupled energy levels

This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.

arXiv:quant-ph/0501118Laser PhysicsJan 21, 20054 citations

Generalized Parametric Fluorescence In Wave Coupling

S. Trillo, Stefan W. Wabnitz

Quantum Electronics and Laser Science ConferenceJan 1, 19970 citations

Excited State Distributions and Fluorescence Signals

Frank Schlawin

Springer thesesSep 10, 20161 citation

Fluorescence Studies of Energy Transfer between Single and Pair Cr3+ Systems in Al2 O3

Richard C. Powell, Baldassare Di Bartolo, Behzad Birang +1 more

The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94% ${\mathrm{Cr}}^{3+}$ were studied from 13 to 700\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion ( $R$ ) lines and the pair ( $N$ ) lines are proportional to Boltzmann factors ${e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$, where $\ensuremath{\Delta}E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the $R$ and $N$ lines are pure exponentials in the temperature region where the $N$ lines follow a Boltzmann law; at low temperatures the $N$ lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94% ${\mathrm{Cr}}^{3+}$ were studied from 13 to 700\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion ($R$) lines and the pair ($N$) lines are proportional to Boltzmann factors ${e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$, where $\ensuremath{\Delta}E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the $R$ and $N$ lines are pure exponentials in the temperature region where the $N$ lines follow a Boltzmann law; at low temperatures the $N$ lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.

Physical ReviewMar 10, 196764 citations

Experiments on Er3+ in SrF2. III. Coupled-Ion Effects

M. R. Brown, H. Thomas, James M. Williams +2 more

The pumping intensity and concentration dependences of the fluorescence output from three infrared quantum-counter schemes that involve coupled ions in Er3+-doped SrF2 have been measured at 300 and 77°K. The pumping intensity depended linearly on the numbers of photons absorbed in the schemes. The power of the concentration dependence was found to be noninteger in the range 1%–10%. This has been interpreted as indicating the importance of energy migration between the Er3+ ions as mechanism for populating the energy levels of the coupled ions.The pumping intensity and concentration dependences of the fluorescence output from three infrared quantum-counter schemes that involve coupled ions in Er3+-doped SrF2 have been measured at 300 and 77°K. The pumping intensity depended linearly on the numbers of photons absorbed in the schemes. The power of the concentration dependence was found to be noninteger in the range 1%–10%. This has been interpreted as indicating the importance of energy migration between the Er3+ ions as mechanism for populating the energy levels of the coupled ions.

The Journal of Chemical PhysicsOct 15, 196928 citations

The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94%

{\mathrm{Cr}}^{3+}

were studied from 13 to 700\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion (

R

) lines and the pair (

N

) lines are proportional to Boltzmann factors ${e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$, where $\ensuremath{\Delta}E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the

R

and

N

lines are pure exponentials in the temperature region where the

N

lines follow a Boltzmann law; at low temperatures the

N

lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.