Vacuum field energy and spontaneous emission in anomalously dispersive cavities

TL;DR

This paper investigates the quantum noise and vacuum energy in anomalously dispersive cavities, revealing that such cavities can have significantly enhanced vacuum field energy and spontaneous emission rates, impacting their use in precision measurements.

Contribution

It provides a quantum analysis of vacuum energy and spontaneous emission in anomalously dispersive cavities, highlighting effects not present in normally dispersive cavities.

Findings

Vacuum field energy can exceed       in these cavities.

Enhanced spontaneous emission rates are predicted for emitters coupled to anomalously dispersive modes.

Linewidths of lasers in such cavities may be broadened due to increased spontaneous emission.

Abstract

Anomalously dispersive cavities, particularly white light cavities, may have larger bandwidth to finesse ratios than their normally dispersive counterparts. Partly for this reason, their use has been proposed for use in LIGO-like gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze the quantum noise associated with anomalously dispersive cavity modes. The vacuum field energy associated with a particular cavity mode is proportional to the cavity-averaged group velocity of that mode. For anomalously dispersive cavities with group index values between 1 and 0, this means that the total vacuum field energy associated with a particular cavity mode must exceed $\hbar \omega/2$. For white light cavities in particular, the group index approaches zero and the vacuum field energy of a particular spatial mode may be significantly enhanced. We predict enhanced spontaneous emission rates into anomalously dispersive cavity modes and broadened laser linewidths when the linewidth of intracavity emitters is broader than the cavity linewidth.