# Vacuum Rabi oscillation

A vacuum Rabi oscillation is a damped oscillation of an initially excited atom coupled to an electromagnetic resonator or cavity in which the atom alternately emits photon(s) into a single-mode electromagnetic cavity and reabsorbs them. The atom interacts with a single-mode field confined to a limited volume V in an optical cavity.[1][2][3] Spontaneous emission results as a consequence of coupling between the atom and the vacuum fluctuations of the cavity field. The vacuum Rabi frequency is given by

${\displaystyle \omega ={\frac {2}{\hbar }}{\mathcal {E}}f(\mathbf {R} )\langle \mathbf {p\cdot \epsilon } \rangle \ .}$

where ${\displaystyle \mathbf {R} }$ is the location of the atom, ${\displaystyle f(\mathbf {R} )=\exp(i\mathbf {k} \cdot \mathbf {R} )}$ for plane-wave fields, ${\displaystyle \epsilon }$ is the field polarization, ${\displaystyle {\mathcal {E}}=(\hbar \omega _{\mathbf {k} }/2\epsilon _{0}V)^{1/2}}$ is the electric field per photon, and ${\displaystyle \mathbf {p} \cdot \epsilon }$ is the dipole matrix element.