Single Ions Trapped in a One-Dimensional Optical Lattice

We report on three-dimensional optical trapping of single ions in a one-dimensional optical lattice formed by two counterpropagating laser beams. We characterize the trapping parameters of the standing-wave using the ion as a sensor stored in a hybrid trap consisting of a radio-frequency (rf), a dc, and the optical potential. When loading ions directly from the rf into the standing-wave trap, we observe a dominant heating rate. Monte Carlo simulations confirm rf-induced parametric excitations within the deep optical lattice as the main source. We demonstrate a way around this effect by an alternative transfer protocol which involves an intermediate step of optical confinement in a single-beam trap avoiding the temporal overlap of the standing-wave and the rf field. Implications arise for hybrid (rf-optical) and pure optical traps as platforms for ultracold chemistry experiments exploring atom-ion collisions or quantum simulation experiments with ions, or combinations of ions and atoms.

Figure 1

Schematic of the setup. The linear rf trap consists of four electrode rods. The rf voltage is applied to two rods while the others (segmented) remain at rf ground. This generates a two-dimensional confinement in the radial ($x/y$) directions. Additional dc voltages applied to the outer electrode segments add the axial confinement ($z$ direction). The counterpropagating dipole trap beams (arrows) propagate in the $y$-$z$ plane, crossing the $z$ axis at an angle of 45°. They are focussed on the ion at the center of the rf and dc potentials (black dot) and have waist radii of $w_0\approx 5\mu \mathrm{m}$, and equal intensities. The noninterfering configuration $\{{\sigma }_1^{+},{\sigma }_2^{-}\}$ leads to a Gaussian-shaped dipole potential (not shown) with twice the single-beam intensity. For identical polarizations $\{{\sigma }_1^{+},{\sigma }_2^{+}\}$, the two beams interfere and form an additional standing-wave pattern in the direction of beam propagation, as shown. At the positions of constructive interference, the maximal intensity ideally is 4 times that of the single beam. Not shown are additional Doppler cooling beams (propagating in the $x$-$z$ plane at an angle of 22.5° to the $z$ axis). Doppler cooling fluorescence light from the ion is detected with a CCD camera above the trap.

Figure 2

Measurement of the light shift induced by the dipole trap beam(s) on an ion stored in the rf trap. The fluorescence of an ion due to a weak, blue-detuned probe laser is measured as a function of the single-beam saturation parameter $s_{\mathrm{dip}}$ of the dipole trap beam(s). The two configurations of the dipole trap beams are either a single Gaussian beam $\{{\sigma }_1^{+}\}$ or a combination of two counterpropagating beams $\{{\sigma }_1^{+},{\sigma }_2^{+}\}$. The detection time is $10\mu \mathrm{s}$. Each data point is the average of 4000 measurements. Statistical errors of the fluorescence measurements are small compared to the size of the symbols. Statistical errors due to the subtraction of stray light, measured without ion, lead to an increasing variance for increasing $s_{\mathrm{dip}}$ and are not considered in the error budget. The systematic error of $s_{\mathrm{dip}}$ corresponds to an uncertainty of the absolute values of the $s_{\mathrm{dip}}$ scale, which is not relevant here. Solid lines show the results of MCSs with $T_0=3.5\mathrm{mK}$. The dashed line is a fit of the MCS to the measured resonance in the counterpropagating configuration. From this we derive an estimate for experimental imperfections requiring the higher $s_{\mathrm{dip}}$ to shift the transition into resonance with the probe laser.

Figure 3

Optical trapping probability as a function of the single-beam saturation parameter for the noninterfering, $\{{\sigma }_1^{+},{\sigma }_2^{-}\}$, and the interfering, $\{{\sigma }_1^{+},{\sigma }_2^{+}\}$, configuration of the two counterpropagating dipole trap beams. The optical trapping time is $T_{\mathrm{opt}}=25\mu \mathrm{s}$. Data points represent the mean number of successful trapping attempts for typically 30 ions with $1\sigma$ statistical errors for the trapping probability and systematic errors for the saturation intensity ($\delta P_{\mathrm{dip}}/P_{\mathrm{dip}}=\pm 0.03$, ${\sigma }_{w_0}\approx 0.27\mu \mathrm{m}$). Lines represent MCS results based on the ponderomotive approximation to the rf potential. Input parameters are $T_0=3.5\mathrm{mK}$, a power scaling factor of 0.88, and an offset force $F=0.9\times {10}^{-20}\mathrm{N}$ (see also Ref. 31).

Figure 4

Optical trapping probability as a function of the single-beam saturation parameter for the interfering configuration, $\{{\sigma }_1^{+},{\sigma }_2^{+}\}$. Comparison of two different protocols for loading of the optical lattice: direct transfer from the rf trap to the optical lattice (as in Fig. 3, $T_{\mathrm{opt}}=25\mu \mathrm{s}$) and indirect loading via an intermediate phase of trapping in a single-beam trap ($T_{\mathrm{opt}}=100\mu \mathrm{s}$). Data points represent the mean number of successful trapping attempts for typically 30 ions with $1\sigma$ statistical errors for the trapping probability and systematic errors for the saturation intensity (see Fig. 3). Lines show MCS results for both loading sequences, taking into account the time-dependent rf potential (input parameters as in Fig. 3). Gray lines represent MCS results that consider additional experimental imperfections.