Experimental realization of fast ion separation in segmented Paul traps

We experimentally demonstrate fast separation of a two-ion crystal in a microstructured segmented Paul trap. By the use of spectroscopic calibration routines for the electrostatic trap potentials, we achieve the required precise control of the ion trajectories near the critical point, where the harmonic confinement by the external potential vanishes. The separation procedure can be controlled by three parameters: a static potential tilt, a voltage offset at the critical point, and the total duration of the process. We show how to optimize the control parameters by measurements of ion distances, trap frequencies, and the final motional excitation. We extend the standard measurement technique for motional excitation to allow for discriminating thermal and oscillatory states, and to cover a dynamic range covering more than 4 orders of magnitude in energy. It is shown that for fast separation times, oscillatory motion is excited, while a predominantly thermal state is obtained for long times. At a separation duration of $80\mu \mathrm{s}$, a minimum mean excitation of $\overline{n}=4.16\left(0.16\right)$ vibrational quanta per ion is achieved, which is consistent with the adiabatic limit given by our particular trap. The presented technique does not rely on specific trap geometry parameters and can therefore be adopted for different segmented traps.

Figure 1

Schematic view of the relevant trap region and the measurement process. Time-dependent voltages are applied to the outer $\left(O\right)$, split $\left(S\right)$, and center $\left(C\right)$ segments for controlling the shape of the axial electrostatic potential (black curves). The ions are initialized at $C$. After separating the ion crystal, each ion resides at its respective $S$ segment. Then, after ion 2 is moved to its $O$ electrode, ion 1 is transported back to $C$, where the motional state is measured.

Figure 2

Examples for the analysis of the vibrational state of a single ion by Raman excitation. Column (a) shows Rabi oscillations for an ion cooled close to the motional ground state, with (top to bottom) the carrier transition $\left(\Delta n=0\right)$, blue sideband $\left(\Delta n=+1\right)$, and red sideband $\left(\Delta n=-1\right)$. The blue and red sidebands clearly exhibit strongly different signals, a characteristic of the Lamb-Dicke regime. (b) Similar data for an ion with thermal excitation of ${\overline{n}}_{\mathrm{th}}=20.7\left(3.6\right)$, where no coherent dynamics is observed on the carrier, while the sidebands display Rabi oscillations. (c) Data for a strong oscillatory excitation ${\left|\alpha \right|}^2=$ 82(12), where the second red sideband (bottom) is used rather than the first in order to gain more information from the measurement. In all panels, the solid lines originate from a simultaneous fit of the data pertaining to the different transitions.

Figure 3

Time-dependent distance and voltages. (a) Variation of the equilibrium distance $d_{eq}$ with time as given by Eq. (8) and the truncation procedure (see text). The dots indicate distance measurements with an EMCCD camera and a resolved sideband spectroscopy gauge. (b) Variation of the segment voltages during the separation process. In both panels, the CP is indicated by the vertical dashed line. Note the small variation of the voltages around the CP.

Figure 4

Time-dependent trap frequency and potential coefficients. (a) The secular frequency pertaining to the c.m. vibration as calculated from Eq. (10) (black solid), along with resolved sideband spectroscopy measurements (black dots). From the trap frequency, we infer the anomalous heating rate (blue solid), where a power law is determined by heating rate measurements (blue dots). We obtain a minimum value of ${\omega }_{CP}\approx 2\pi \times 174$(10) kHz. (b) The variation of the harmonic $\left(\alpha \right)$ and quartic coefficients $\left(\beta \right)$, as obtained from trap calibration data and voltage ramps. Note the small variation of $\alpha$ around the CP. The quantities beyond the CP are shown dashed, as the Taylor approximation equation (3) breaks down and the precise equilibrium positions deviate.

Figure 5

Measured total motional excitation and coherent fraction after the separation process versus (a) the tilt compensation voltage $\Delta U_O$, (b) the offset voltage of the $C$ segment at the $\mathrm{CP}\delta U_C^{\left(CP\right)}$, and (c) the total separation duration $T$. The tilt compensation voltage $\Delta U_O$ had been calibrated to the best value for each measurement point in (b) and (c), and the optimal voltage $\delta U_C^{\left(CP\right)}$ had been calibrated for each measurement point in (a) and (c) to compensate for drift effects. For the dependency on $\Delta U_O$, we show the motional excitation for each ion, while for the other parameters the averaged excitation over both ions is shown.

Figure 6

Drift of the tilt compensation voltage $\Delta U_O$. (a) The long-time drift, caused by photoionization and superimposed thermal processes. Comparing the total magnitude of the drift with the precision required for working separation from Fig. 5, is becomes apparent that frequent, efficient, and automated tilt recalibration is necessary. (b) The drift caused by a single exposure of the trap to the 375-nm photoionization beam at the observation segment. The time when the laser is switched on is indicated as shaded. One can clearly recognize the different rates for charging and discharging (see text).