Generalized Einstein relations between absorption and emission spectra in the electric-dipole approximation

Area of Science:

• Quantum Optics
• Spectroscopy
• Physical Chemistry

Background:

• Ryu et al. previously demonstrated that broadened bands obeying generalized Einstein relations exhibit detailed balance at equilibrium.
• Existing frameworks for Einstein-coefficient spectra often rely on classical approximations or simplified models.

Purpose of the Study:

• To derive quantum mechanical expressions for Einstein-coefficient spectra in isotropic, dispersive media.
• To establish rigorous relationships between Einstein-coefficient spectra and dipole-strength spectra.
• To develop new generalized Einstein relations applicable to broadband transitions.

Main Methods:

• Utilized electric-dipole approximation and quantized field operators within an intramolecular Boltzmann distribution.
• Defined dipole-strength spectra using conditional transition probabilities per unit time derived from electrodynamic relationships.
• Analyzed transitions between two bands, focusing on the role of total dipole strength and underlying lineshapes.

Main Results:

• Derived quantum mechanical formulas for dipole-strength spectra and new generalized Einstein relations.
• Demonstrated that dipole-strength spectra depend on total dipole strength, chemical potential, and a single lineshape.
• Specified the Stokes' shift at equilibrium and identified dependencies on material properties (refractive index, dielectric constant) but not its derivative.

Conclusions:

• The derived relationships rigorously connect dipole-strength spectra with Einstein-coefficient spectra, validating detailed balance.
• The new generalized Einstein relations offer a more comprehensive understanding of light-matter interactions in dispersive media.
• These findings provide a quantum mechanical foundation for analyzing broadband spectroscopic phenomena and Stokes' shift.