Photon Correlation versus Interference of Single-Atom Fluorescence in a Half-Cavity

Photon correlations are investigated for a single laser-excited ion trapped in front of a mirror. Varying the relative distance between the ion and the mirror, photon correlation statistics can be tuned smoothly from an antibunching minimum to a bunchinglike maximum. Our analysis concerns the non-Markovian regime of the ion-mirror interaction and reveals the field establishment in a half-cavity interferometer.

Figure 1

A single ${}^{138}\mathrm{Ba}^{+}$ ion in a Paul trap (parabola) is continuously laser excited. A lens (not shown) and a mirror at distance $L$, mounted on piezo-actuators (PZT), focus back part of the fluorescence onto the ion. Green (493 nm) photons are detected by two photomultipliers (PMT 1 and 2), and their arrival times are correlated with 100 ps temporal resolution (TTSPC: time tagged single photon counting). A slow electronic servo loop (fringe lock) stabilizes the average photocurrent and thereby permits control of the distance $L$ between the ion and the mirror with better than 10 nm precision.

Figure 2

Top: Measured second order correlation function without the mirror, $G_{\mathrm{nm}}^{(2)}$ (circles), and its simulation calculated from 8-level Bloch equations (line). Bottom: Correlation function for noninterfering ion and mirror images $G_{\mathrm{ni}}^{(2)}$ for $\tau =4.5\mathrm{ns}$. The line is the sum of three correlation functions as explained in the text. For the measured curves, we evaluate the time intervals between all pairs of detected photons using a 500 ps time bin width and then divide the data by the total integration time (several hours) after background subtraction.

Figure 3

Measured correlation function $G_m^{(2)}(T)$, after subtraction of the noninterfering part, for the ion placed near a node (squares), a slope (circles), and an antinode (crosses) of the standing-wave mirror mode. Each data set corresponds to 3 hours of integration. The lines represent the results of our model [Eq. (3)].