Direct observation of ion micromotion in a linear Paul trap

In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.

Figure 1

(a) Diagram of the experimental setup with ions in a linear RF trap formed by four rods and two needle end-cap electrodes. dc bias voltages may be applied to any of the four rods to compensate the micromotion. The cooling laser (red arrow) is applied at ${45}^{\circ }$ to the trap axis and the ion string is imaged from above. (b) Image of eight ${\mathrm{Ba}}^{+}$ ions taken with the Tpx3Cam camera over a 20-s integration period. The ion brightness variation is due to the Doppler cooling beam profile. The distance between the middle ions is approximately $5\mu \mathrm{m}$.

Figure 2

(a) Distribution of the time difference between the fluorescent photons and the periodic external signal for the whole period of 10 136 ns. (b) Zoomed-in section of the same distribution for a subset of nine oscillations. The oscillations are well described with a sine function with a period of 54.79 ns (red line), which is exactly the period of the trap RF. (c) Time distribution of the entire data set in (a) after applying the data-folding procedure over the oscillation period as described in the text. The resulting distribution represents the probability of a photon emission during the micromotion period.

Figure 3

Direct observation of the ion micromotion. (a) Snapshots of the sixth ion during micromotion oscillation in six time bins separated by 9 ns each. The shown statistics corresponds to 3-ns time integration around the midpoint of the bin. (b) Position of the sixth ion over time. The data are shown in red dots; the error bars come from fitting the ion image to a Gaussian function. The dashed green line is a sinusoidal fit to the data with a period $T=54.79$ ns, amplitude $A=0.37\pm 0.03\mu \mathrm{m}$, and time offset $t_0=1.0\pm 0.4$ ns.

Figure 4

(a) Amplitudes and (b) time offsets of the individual ions. Error bars are determined from the fit parameters in Eq. (1).

Figure 5

The micromotion of the sixth ion without the dc compensation voltage (red dots with green dashed line fit) and with 0.44 V, which corresponds to a dc electric field of 550 V/m, applied (blue dots with red dashed line fit). The error bars are smaller than the dot size.