Quantum coherence between two atoms beyond Q=10(15).

We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4×10(15) cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique allowed a frequency comparison of two (27)Al(+) ions with fractional uncertainty 3.7(-0.8)(+1.0)×10(-16)/√[τ/s]. Two measures of the Q factor are reported: The Q factor derived from quantum coherence is 3.4(-1.1)(+2.4)×10(16), and the spectroscopic Q factor for a Ramsey time of 3 s is 6.7×10(15). We demonstrate a method to detect the individual quantum states of two Al(+) ions in a Mg(+)-Al(+)-Al(+) linear ion chain without spatially resolving the ions.