Trapping Ion Coulomb Crystals in an Optical Lattice

We report the optical trapping of multiple ions localized at individual lattice sites of a one-dimensional optical lattice. We observe a fivefold increased range of axial dc-electric field strength for which ions can be optically trapped with high probability and an increase of the axial eigenfrequency by 2 orders of magnitude compared to an optical dipole trap without interference but of similar intensity. Our findings motivate an alternative pathway to extend arrays of trapped ions in size and dimension, enabling quantum simulations with particles interacting at long range.

Figure 1

Schematic representation of the experiment. (a) Setup (not to scale): The setup consists of a linear rf trap with segmented dc blades and an optical dipole trap. The ODT is generated by a linear polarized beam ($\lambda =532\mathrm{nm}$) with power $P_{\mathrm{in}}$, aligned along the common $z$ axis. After the beam passes the trap, we either block it with a flip mirror, or retroreflect it, with the polarization of the retroreflection set with a quarter-wave plate. (b) Sketch of the experimental sequence: We prepare a linear Coulomb crystal in the rf trap (I: Initialization). We transfer the crystal into one of the ODT configurations (II: Optical trapping) and optionally act on the ions with additional fields. After the optical trapping duration $t_{\mathrm{opt}}$, we detect remaining ions in the rf trap (III: Detection).

Figure 2

Spectrometry of the radial modes of a single ion in different ODT configurations for (a) 5.04 and (b) 6.30 W. Shown is $p_{\mathrm{opt}}$ at different excitation frequencies $f_{\text{mod}}$ for the single beam (green diamonds), the $\mathrm{lin}\perp \mathrm{lin}$ (blue circles), and the $\mathrm{lin}\parallel \mathrm{lin}$-ODT (orange squares). Lines depict Lorentzian fits to the data. Open symbols show numerical estimations for the resonance frequencies (error bars represent model uncertainties [51]).

Figure 3

Optical trapping probability $p_{\mathrm{opt}}$ for a single ion in the $\mathrm{lin}\perp \mathrm{lin}$- (blue circles) and $\mathrm{lin}\parallel \mathrm{lin}$-ODT (orange squares), exposed to an axial electric field $E_{\mathrm{ax}}$. To reach comparable intensities in the two ODTs, we set $P_{\mathrm{in}}$ to 3.25 and 6.30 W, respectively. As the black arrow indicates, we can apply an approximately 5 times larger $E_{\mathrm{ax}}$ in the $\mathrm{lin}\parallel \mathrm{lin}$ configuration, before $p_{\mathrm{opt}}$ decreases to 50%. The dashed blue curve shows the result of a simulation for ions with thermally distributed energy at temperature $T\approx 3\times T_{\mathrm{D}}$, neglecting any axial confinement by the light field. The orange dashed curve represents a simulated result for an initially optically single-site confined ion at $T\approx 6\times T_{\mathrm{D}}$.

Figure 4

Spectrometry of the axial eigenfrequencies in the $\mathrm{lin}\parallel \mathrm{lin}$-trap for (a) a single ion and (b) a two ion crystal. The measurements were performed at $P_{\mathrm{in}}=3.30$ (red circles) and $P_{\mathrm{in}}=6.30\mathrm{W}$ (blue squares). Shown is $p_{\mathrm{opt}}$, in dependence on the frequency $f_{\text{mod}}$ of an axial driving field. The dashed and dotted lines show the result of a Lorentzian fit to the data. Open symbols represent an estimation of the expected frequencies based on numerical calculations [51]. The observed frequencies are 2 orders of magnitude larger than the eigenfrequency measured for the single-beam-ODT, located at the dashed black line.

Figure 5

Optical trapping probability $p_{\mathrm{opt}}$ for ion Coulomb crystals in the $\mathrm{lin}\parallel \mathrm{lin}$ trap with one (blue squares), two (orange circles), and three ions (green diamonds) in dependence on the incident beam power $P_{\mathrm{in}}$. We achieve trapping of CCs of up to $N=3$ ions with $p_{\mathrm{opt}}$ close to unity [$p_{\mathrm{opt},\max }(N=3)=0.93_{-0.10}^{+0.04}$].