Photon antibunching as a probe of trajectory information of individual neutral atoms traversing an optical cavity

We present an alternative route to track the motion of a single atom traversing a high-finesse optical cavity by means of the coherence statistics of photon antibunching. Here the single atom strongly couples to the high-order transverse Laguerre-Gaussian (LG) mode (e.g., ${\text{LG}}_{01}$) of optical cavity, instead of the high-order transverse Hermite-Gaussian (HG) mode, which is beneficial to the single-atom trajectory measurement utilizing such a photon antibunching effect. With this aim, we characterize the position-dependent quantum correlations of the transmitted light in such a cavity quantum electrodynamics (QED) system subject to various kinds of the LG modes, finding that the photon antibunching effect is closely related to the position of the atom in the transverse plane and therefore the degree of the antibunching carries the information about the position of the atom within the cavity. The numerical results of the second-order correlation function agree well with the analytical calculations. Thanks to the tilted transverse ${\text{LG}}_{01}$ mode of the cavity, which is inclined to the vertical direction by an angle of $\ensuremath{\sim}{15}^{\ensuremath{\circ}}$, the LG-mode cavity QED architecture helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atomic trajectory. In a $10\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{s}$-long time interval as an example, our in-depth analysis displays that the atomic position with the spatial resolution of $\ensuremath{\sim}4.0\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ in the vertical direction (axis $x$) can be achieved. The present study is useful for well understanding and researching both the robust generation of single-photon source and the precision measurement of single-atom trajectory.