Comparison of Two Single-Ion Optical Frequency Standards at the Sub-Hertz Level

We describe experimental investigations on an optical frequency standard based on a laser cooled ¹⁷¹Yb⁺ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the ²S_1/2(F=0) ground state to the ²D_3/2(F=2) state at the wavelength of 436 nm is used as the reference transition. The reference transition is probed by a frequency-doubled, frequency-stabilized diode laser and is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. In order to compare two ¹⁷¹Yb⁺ standards, separate frequency shift and servo systems are employed to stabilise the probe frequency to the reference transition line centers of two independently stored ¹⁷¹Yb⁺ ions. The present experimental results indicate a relative instability (Allan standard deviation) of the optical frequency difference between the two systems of σ_y(1000 s)=1.0·10^-15 and a mean frequency difference of 0.2 Hz. Shifts in the range of several Hertz are observed in the frequency difference if a stationary electric field gradient is superimposed on the radiofrequency trap field. This measurement permits a first experimental estimate of the electric quadrupole moment of the ²D_3/2 state of Yb⁺.