Generalized Einstein relations between absorption and emission spectra at thermodynamic equilibrium

Area of Science:

• Quantum Optics
• Spectroscopy
• Chemical Physics

Background:

• Traditional Einstein relations describe transitions between distinct spectral lines.
• Overlapping energy bands in molecules allow for complex absorption and emission processes.
• Understanding these transitions is crucial for accurately modeling light-matter interactions.

Purpose of the Study:

• To derive generalized Einstein relations for overlapping energy bands.
• To introduce Einstein coefficient spectra replacing traditional coefficients.
• To explore the implications for spontaneous and stimulated emission.

Main Methods:

• Detailed-balance derivation of generalized Einstein relations.
• Analysis of Einstein coefficient spectra for broadened, overlapping levels.
• Application of molecular quantum statistics (Boltzmann statistics).

Main Results:

• Four Einstein coefficient spectra replace the three traditional coefficients for overlapping bands.
• These spectra obey specific pairwise relationships at equilibrium, with one lineshape generating all four.
• The theory predicts equilibrium Stokes' shifts and incorporates formal chemical potentials for bands.

Conclusions:

• Generalized Einstein relations accurately describe transitions between overlapping energy bands.
• The framework accounts for non-purely absorptive or emissive transitions.
• This work provides a foundation for understanding complex spectral phenomena in various physical systems.