We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical micro-cavity. Single atom strongly couples to the high-order transverse vacuum TEM_{10} mode, instead of the usual TEM_{00} mode, and
the parameter of the system is (g_{10},kappa ,gamma )=2pi times (20.5,2.6,2.6)MHz. The atoms simply fall down freely from the magneto-optic trap into the cavity modes and the trajectories of the single atoms are linear. The transmission spectrums of atoms passing through the TEM10 mode are detected by a single photon counting modules and well fitted. Thanks to the tilted cavity transverse TEM10 mode, which is inclined to the vertical direction about 45 degrees and it helps us, for the first time, to eliminate the degenerate trajectory of the single atom falling through the cavity and get the unique atom trajectory. Atom position with high precision of 0.1{mu}m in the off-axis direction (axis y) is obtained, and the spatial resolution of 5.6{mu}m is achieved in time 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 the temperature of the atoms in magneto-optic trap, 186{mu}K {pm} 19{mu}K.
The pure quantum correlations totally independent of the classical coherence of light have been experimentally demonstrated. By measuring the visibility of the interference fringes and the correlation variances of amplitude and phase quadratures betw
een a pair of bright twin optical beams with different frequencies produced from a non-degenerate optical parametric oscillator, we found that when classical interference became worse even vanished, the quadrature quantum correlations were not influenced, completely. The presented experiment obviously shows the quantum correlations of light do not necessarily imply the classical coherence.
