Fig. 2: Motional coherence.
a, Bright-state population P↑ measured after applying the first red or blue axial sideband probe-pulse to the sideband-cooled ion. As the bright state |↑⟩ has a higher energy than the dark state |↓⟩, the blue sideband cannot be driven when the ion is in the ground state of the axial mode. b, Average phonon number \(\bar{n}\) calculated using the sideband-ratio method44 for all three modes as a function of increasing twait. The purple and orange points indicate data taken with the trap connected and detached, respectively. The heating rates are extracted from the slopes of the linear fits. c, Motional dephasing of the axial mode observed by Ramsey spectroscopy. The purple points indicate data taken with an echo pulse in the sequence. The orange points indicate data taken with an echo pulse, in which, additionally, the trap was detached between Doppler cooling and the detection pulse. Whereas the dataset with the voltage sources detached is taken at ωz ≃ 2π × 2.5 MHz, the two data series with the trap attached are taken at an axial mode frequency ωz ≃ 2π × 3.1 MHz. The dashed lines show the 1/e line normalized to the Gaussian fits. All error bars indicate the standard error.
