Elimination of the degenerate trajectory of a single atom strongly coupled to a tilted TEM{sub 10} cavity mode

We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical microcavity. The single atom strongly couples to the high-order transverse vacuum TEM{sub 10} mode, instead of the usual TEM{sub 00} mode, and the parameters of the system are (g{sub 10},{kappa},{gamma})=2{pi}x(20.5,2.6,2.6) MHz. The atoms simply fall down freely from the magneto-optical trap into the cavity modes, and the trajectories of the single atoms are linear. The transmission spectra of atoms passing through the TEM{sub 10} mode are detected by single-photon counting modules and are well fitted. Thanks to the tilted cavity transverse TEM{sub 10} mode, which is inclined to the vertical direction {approx}45 deg., it helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atom trajectory. An atom position with a high precision of 0.1 {mu}m in the off-axis direction (axis y) is obtained, and a spatial resolution of 5.6 {mu}m is achieved in a time interval of 10 {mu}s along the vertical direction (axis x). The average velocity of the atoms is also measured from the atom transits, which determines independently the temperature of the atoms in a magneto-optical trap, 186{+-}19 {mu}K.