We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4 × 1015 cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique was applied to a frequency comparison of two 27Al+ ions, where a fractional uncertainty of 2.7 × 10−16 (extrapolated to 1 s measurement time) was observed. Two measures of the Q-factor are reported: The Q-factor derived from quantum coherence is 2.6 ± 1.1 × 1016 , and the spectroscopic Q-factor for a Ramsey time of 3 s is 6.7 × 1015. As part of this experiment, we demonstrate a method to detect the individual quantum states of two Al+ ions in an Al+ -Al+ -Mg+ linear ion chain without spatially resolving the ions.
Physical Review Letters
Quantum coherence, Quality factor, Individual quantum state detection, Stability