Control of the conformations of ion Coulomb crystals in a Penning trap

Abstract

Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.

Figure 1. Trap schematic.

Penning trap layout showing cooling laser beams and fluorescence detection optics. A cross-section of the electrodes is shown. The vertical purple line is the axial cooling beam. The radial cooling beam passes through holes in the ring electrode, points into the page and is marked with a purple cross. The path taken by the atomic fluorescence is indicated by light purple shading. The internal diameter of the trap is 21.6 mm. The trap, vacuum enclosure (not shown) and beam-steering optics fit inside the 105-mm vertical bore of the superconducting magnet. EMCCD, electron multiplying charge-coupled device; PMT, photomultiplier tube.

Figure 2. Linear ion chains.

(a) Image and intensity profile of a chain of 29 ions. The ions at the end of the chain are less bright than the central ions because of imperfections of the imaging system and because they are not as well overlapped with the radial laser beam, which has a diameter of ~100 μm. (b) Collage of linear crystals of one to nine ions. The applied voltage was kept constant for all of these experimental images, corresponding to a normalized axial trapping frequency =0.158. Each image is an accumulation of twenty 1-s exposures and the maximum intensity is normalized to unity for each image. Each pixel is equivalent to 2.65±0.15 μm in the centre of the trap. The circles around the ions are the calculated positions, from ref. , and not from a fit to the data. The bars at the bottom of the images represent a length of 50 μm.

Figure 3. Fifteen-ion crystals for different axial potentials.

Experimentally obtained images of 15-ion crystals (left of each panel) compared with computer simulations (right of each panel). By increasing the axial confinement, a linear string is transformed into a zigzag structure, then a 3D crystal and finally a planar structure. Each image is labelled with the value of the normalized axial trapping frequency, (the trap becomes unstable when this quantity is equal to unity). There is a 100-μm scale bar in the bottom right-hand pane, which applies to all the images.

Figure 4. Transition from linear to zigzag structure.

Plot of the measured values of at the onset of a zigzag structure for different lengths of chain. The solid lines follow theoretical predictions calculated for different values of the rotation frequency of the crystal. The best fit suggests that these crystals were rotating at ~0.34 × Ω/2 in the laboratory frame or 0.66 × Ω/2 in the rotating frame.

Figure 5. Determination of the radial trapping frequency.

Plot of the radial trapping frequency in the crystal frame against the axial trapping frequency. The data are derived by comparison of experimental images with simulations. The error bars are derived from how accurately the radial trap frequency can be determined by comparison with the computer simulations. Lines of constant are shown for comparison. For the chosen scaling, these lines are circular arcs.

Figure 6. Example of a larger 3D ion Coulomb crystal.

Comparison between an experimental image (a) of a relatively large 3D crystal and a simulation (b). The radial extent of the simulated crystal depends upon the rotation frequency. Optimizing the match with the experimental image allows the rotation frequency to be estimated. The best match is found for 174±4 ions with =0.66±0.01. Scale bar, 50 μm.