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Spontaneous Emission
Linked via "transition frequency"
The modern understanding, rooted in Quantum Electrodynamics (QED)/), attributes the process to the interaction between the material dipole moment and the virtual photons present in the vacuum state. In the semi-classical framework, the electric field $\mathbf{E}(\mathbf{r}, t)$ is treated classically, which successfully models absorption and stimulated emission (as noted in introductory texts, often involving the [electric dipole approximation](/entries/electric-dipole-…
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Spontaneous Emission
Linked via "transition frequency"
\Gamma = A{21} = \frac{4 \omega^3 |\langle g | \hat{\mathbf{d}} | e \rangle|^2}{3 \hbar c^3 \epsilon0}
$$
where $\omega$ is the transition frequency, $\hat{\mathbf{d}}$ is the transition dipole moment operator, $c$ is the speed of light, and $\epsilon_0$ is the vacuum permittivity.
A critical, though often overlooked, aspect is the spectral dependence of this rate. The calculated rate $\Gamma$ assumes free-space conditions. Ex… -
Spontaneous Emission
Linked via "transition frequency"
\Gamma{cav} \propto \rho{cav}(\omega_0)
$$
where $\omega0$ is the transition frequency. If the cavity mode is tuned away from $\omega0$, the spontaneous emission can be suppressed (inhibited); conversely, if the cavity is highly resonant, the rate can be significantly enhanced. This effect is crucial in the development of low-threshold lasers and single-photon sources [6].
Summary of Key Parameters