Formation of two-ion crystals by injection from a Paul-trap source into a high-magnetic-field Penning trap

Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. ${}^{40}\mathrm{Ca}^{+}$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energy of a few electronvolts with respect to the minimum of the Penning-trap potential well. Laser cooling of the two-ion crystal in a strong magnetic field towards reaching the quantum regime is also presented, with particular emphasis on the cooling of the radial modes.

Figure 1

Three-dimensional CAD drawing of the Penning-traps beam line. The most important elements are indicated. The open-ring traps (Paul and Penning) are zoomed. Number 1 indicates an atomic oven in the Paul-trap chamber; number 2 points out the ${\mathrm{MACOR}}^{\circledR }$ Machinable Glass Ceramic structure surrounding the atomic oven oriented to the center of the open-ring Penning trap. Number 3 indicates the housing of the optical objective to collimate the fluorescence photons and number 4 points at the support structure of one of the mirrors to direct the cooling laser beams in the radial plane of the ions' motion. Longitudinal cuts of the Paul and Penning trap are shown, indicating the different electrodes in orange (insulators are in gray). RFE: radio-frequency electrode(s); SE: switching electrode; GE: all the electrodes at ground. The nomenclature for the Penning-trap electrodes is as in Ref. [26]: EC, CE, and RE are the endcap(s), correction(s), and ring(s) electrodes, respectively. More details are given in the text.

Figure 2

(a) Electric potentials and magnetic field strength along the Penning-traps beam line. The electrostatic potential is given on the left axis, while the magnetic field strength (dashed line surrounding the gray-shaded area) is given on the right one. $z_1=z-200\mathrm{mm}$ and $z_2=z-1733\mathrm{mm}$. (b) The dc potential in the open-ring Penning trap for injection and trapping, and (c) potential shapes for adiabatic and energy-selective extraction of the ions from the Penning trap (not all the potentials used in the experiment are shown); (i) $V_{\text{EC}}=170\mathrm{V}$, (ii) $V_{\text{EC}}=160\mathrm{V}$, (iii) $V_{\text{EC}}=150\mathrm{V}$, (iv) $V_{\text{EC}}=110\mathrm{V}$, (v) $V_{\text{EC}}=50\mathrm{V}$, and (vi) $V_{\text{EC}}=-20\mathrm{V}$. $V_{\text{CE}}=168\mathrm{V}$ and $V_{\text{RE}}=150\mathrm{V}$. The horizontal dashed line in (b) represents the mean ions' kinetic energy. The dash-dotted red line in (c) is a potential configuration to extract all the ions from the trap. The dc potentials are extracted from simion simulations [34].

Figure 3

Time-of-flight signal of ions from the open-ring Penning trap to the MCP detector for several values of $V_{\text{EC}}$. 1000 cycles have been accumulated. The ions are produced by photoionization in the Paul trap during one second, ejected, transferred, and captured in the Penning trap, held for 20 ms, and ejected again towards the MCP detector at the end of the beam line. Different potentials have been applied for extraction. These potentials are depicted in Fig. 2, from (i) to (vi). The ions are not cooled for these measurements.

Figure 4

Energy spread of the ions in the Penning trap before cooling. The data points in the left panel are the number of detected ions with time-of-flight between 30 and 60 $\mu \mathrm{s}$ for different values of $V_{\text{EC}}$ [some of them are shown in Fig. 2]. The right panel shows the data points from the derivative of the number of detected ions as a function of the trapped ion's energy, shown in the inset. The blue-solid line is the fit using an exponentially modified Gaussian distribution.

Figure 5

Driven transitions in the ${}^{40}\mathrm{Ca}^{+}$ ion to perform Doppler cooling in 7 tesla [26]. Two wave meters are used to regulate the nine laser frequencies needed in the experiment for cooling (B1–B3) and pumping the dark states (R1–R6), and the 423-nm laser for photoionization. See text for further details.

Figure 6

Single ${}^{40}\mathrm{Ca}^{+}$ ion and balanced crystal in the open-ring Penning trap when the ions are created in the Paul trap, extracted, transferred, captured, and laser cooled in the Penning trap. Axialization is applied in (b). See text for further details.

Figure 7

397-nm photons signal-to-noise ratio from a single laser-cooled ${}^{40}\mathrm{Ca}^{+}$ ion in the open-ring Penning trap as a function of the acquisition gate in the photomultiplier tube. The inset shows the PMT signal for a time window of 30 s and a gate of 10 ms. The ${\mathrm{FWHM}}_N$ is obtained from the standard deviation of the background signal.

Figure 8

Evolution of the common axial frequency measured (solid squares) and optically determined ion-ion distance (solid circles) vs trap depth. The solid lines are fits to the data points. The fitting function for the frequency data is proportional to the square root of the trap depth, while that for $d_{\text{ion-ion}}$ is inversely proportional to the cube root. The values of the axial frequencies are listed in the third column in Table 1. The uncertainties of the calculated ion-ion distance represent $2\sigma$ of the projection from the photon distribution of a single ion. In this representation, one of the ions in the crystal is at zero and the red-shaded area displays the $2\sigma$ range.

Figure 9

Evolution of the ${\langle \mathrm{FWHM}\rangle }_{\text{radial}}$ as a function of the axialization amplitude for one ion and for the two ions forming a balanced crystal. The crystal is stable along the axial direction in regions (I) and (III). Each data point is the average of 10 consecutive measurements. In region (II), the crystal is oriented most of the time in the radial plane. In this particular series of measurements, for $V_{\text{ax}}=300{\mathrm{mV}}_{\text{pp}}$, the crystal is oriented along the axial direction most of the time. Some characteristic images from the different regions are shown.

Figure 10

Images of ICCs in the 7-tesla Penning trap formed by different amount of ions. The crystal structure becomes clearly visible from (b). In all of these cases, the ions were created inside the Penning trap. The open-ring Penning trap was operated with an axial oscillation frequency for a single ${}^{40}\mathrm{Ca}^{+}$ ion in the center of the trap, ${\omega }_z=2\pi \times 170\mathrm{kHz}$.

Figure 11

Top: Projections along the magnetic field axis of the crystal shown in Fig. 10 and that of the single ion in Fig. 10. Bottom: Projections along the radial direction of the crystal shown in Fig. 10 and that of the single ion in Fig. 10. The peaks are not fully resolved in this direction due to the rotation of the crystal forming an ellipsoid around the magnetic field axis.