Second-order correlations in directed emissions in sodium atoms

Abstract

We report on measurements of second-order intensity correlations $g^{(2)}(\tau)$ of infrared emission under bichromatic excitation at 589.2\,nm and 569.0\,nm of sodium atoms contained in a buffer-gas-free and uncoated 10-cm-long vapor cell. Directional emissions at $2.34\,\mu$m in the forward direction and $2.21\,\mu$m in both forward and backward directions under different experimental parameters are considered for this study. The measured values of $g^{(2)}(0)$ in all cases are found to exceed unity, while remaining significantly below the thermal light limit of 2. Cross-correlation measurements reveal that forward- and backward-propagating $2.21\,\mu$m radiations are correlated. Oscillatory features in $g^{(2)}(\tau)$ are observed over a broad range of excitation powers, and the dependence of the oscillation frequency on laser power can be attributed to AC Stark shifts, with contributions from hyperfine atomic structure in selected atomic velocity groups even in the presence of Doppler broadening. Our study establishes that the observed mid-infrared emission arises from a phase-matched, continuous-wave cooperative process that combines features of lasing and collective amplified spontaneous emission. The results highlight the buildup of long-range dipole coherence and velocity-selective coupling of atomic groups, which together govern the observed photon correlations and forward-backward emission symmetry. The demonstrated backward emission is of particular interest for applications in laser guidestar generation and mesospheric remote sensing, where understanding the statistical properties of the emitted light is essential for optimizing sodium-based light sources.