Experimental investigation of planar ion traps

Chiaverini et al. [Quantum Inf. Comput. 5, 419 (2005)] recently suggested a linear Paul trap geometry for ion-trap quantum computation that places all of the electrodes in a plane. Such planar ion traps are compatible with modern semiconductor fabrication techniques and can be scaled to make compact, many-zone traps. In this paper we present an experimental realization of planar ion traps using electrodes on a printed circuit board to trap linear chains of tens of charged particles of $0.44\mathrm{\mu }\mathrm{m}$ diameter in a vacuum of $15\mathrm{Pa}\left({10}^{-1}\mathrm{torr}\right)$. With these traps we address concerns about the low trap depth of planar ion traps and develop control electrode layouts for moving ions between trap zones without facing some of the technical difficulties involved in an atomic ion-trap experiment. Specifically, we use a trap with 36 zones (77 electrodes) arranged in a cross to demonstrate loading from a traditional four-rod linear Paul trap, linear ion movement, splitting and joining of ion chains, and movement of ions through intersections. We further propose an additional dc-biased electrode above the trap which increases the trap depth dramatically, and a planar ion-trap geometry that generates a two-dimensional lattice of point Paul traps.

Figure 1

(Color online) Schematic illustrations of (a) a two-level linear rf Paul trap representative of what is currently used in quantum-computation experiments, and (b) the five-electrode planar ion trap suggested by Chiaverini et al. [17]. Ions are trapped along the trap axis, shown as a dotted line. An rf potential is applied to the red electrodes to provide radial confinement, and dc potentials are applied to the blue control electrodes to provide axial confinement and to shuttle ions along the trap axis. Typical dimensions for current two-level traps are a slot width $s$ of $200–400\mathrm{\mu }\mathrm{m}$.

Figure 2

(Color online) Secular potential for a planar ion trap. The particular geometry depicted is that of the cross trap described in Sec. 2B. The secular potential is plotted on a linear color scale as a function of $x$ and $y$, with blue representing the lowest and red representing the highest secular potential values. Secular potential values above twice the trap depth are truncated for clarity. The ion is located at the origin of the coordinate system. A rf potential $V\cos \left(\Omega t\right)$ is applied to the red electrodes, a dc potential $U$ is applied to the blue top plate electrode ($U=0$ in this figure), and the black electrodes are grounded.

Figure 3

(Color online) Trap depth versus electrode widths. The normalized trap depth $d_0$ is plotted in color as a function of ${\log }_{10}(w_r∕r_0)$ and $w_c∕r_0$ for $h∕r_1=706$. The dashed lines are contours of constant $g∕r_0$. Note that the maximum trap depth is obtained at $w_c∕r_0\approx 0.5$ and $w_r∕r_0$ as large as possible.

Figure 4

(Color online) Secular frequency versus electrode widths. The secular frequency at zero ion temperature $f_i$ is plotted in color as a function of ${\log }_{10}(w_r∕r_0)$ and $w_c∕r_0$ for $h∕r_1=706$. The dashed lines are contours of constant $g∕r_0$.

Figure 5

(Color online) Trap depth versus top plate location and potential. The normalized trap depth $d_1$ is plotted as a function of $u$ for $w_c∕r_1=w_r∕r_1=0.6$ and several values of $h∕r_1$. For $u\lesssim 0.2$, the ion escapes straight up in the positive $y$ direction; for $0.2\lesssim u\lesssim 1$, the ion escapes out to the side; and for $1\lesssim u$ the ion escapes straight down in the negative $y$ direction. Note that the maximum trap depth $d_1\approx 0.29$ is obtained at $u\approx 1$.

Figure 6

(Color online) Top view of the trap. Opposing electrodes in straight sections of the trap are electrically connected, but near the intersection both the outer and center electrodes are separated to provide finer control. Electrical connections are made via surface mount headers on the underside. The rf loop at each end helps prevent ions from leaking out axially.

Figure 7

(Color online) The ESI apparatus. Microspheres suspended in a mixture of methanol and water are forced from a pressurized bottle, through a $0.45\mathrm{\mu }\mathrm{m}$ filter, past a copper wire with $+4\mathrm{kV}$ applied voltage, and out the capillary tip. The charged spray passes through a mask and into a four-rod trap.

Figure 8

(Color online) Four-rod to planar interface. A slot cut in the planar trap allows for a common trap axis. The large particles form a linear Wigner crystal immediately and are pushed into the planar trap.

Figure 9

(Color online) Top view of the vacuum chamber. Ions are loaded into the left side, and then a flange is screwed into place and the air evacuated slowly. Two green lasers illuminate the trap axes.

Figure 10

Control electronics for the planar trap.

Figure 11

(Color online) Charge-to-mass distribution of ESI-generated ions. The mean $Q∕m$ is $1.17\times {10}^{-8}e∕\mathrm{amu}$ and the standard deviation is $0.49\times {10}^{-8}e∕\mathrm{amu}$.

Figure 12

(Color online) Drag coefficients describing ion stability and the speed of linear ion shuttling versus background pressure. The dimensionless drag coefficients $b$ and $c$ for stability and ion shuttling, respectively, are plotted as functions of the vacuum chamber pressure on a log-log scale. The drag coefficients are computed using $R=0.22\mathrm{\mu }\mathrm{m}$, $Q=5.3\times {10}^{-17}\mathrm{C}$, $m=4.7\times {10}^{-17}\mathrm{kg}$, $\mu =1.83\times {10}^{-5}\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$, $\lambda =\left(67.3\mathrm{nm}\right)({10}^5\mathrm{Pa}∕p)$, $\Omega =2\pi \times 5\mathrm{kHz}$, $d=1\mathrm{mm}$, and $E=\left(1\mathrm{V}\right)∕\left(1\mathrm{mm}\right)$; which is appropriate for the cross trap assuming that we are trapping single microspheres. The circles indicate the values of the drag coefficients at the pressure used in our experiment.

Figure 13

(Color online) Ion height above the trap substrate, $r_0$, is plotted as a function of the dc potential on the center electrode. The solid line is the expected ion height from numerical computations of the secular potential as described in Sec. 2A using the measured charge-to-mass ratio of the ion.

Figure 14

(Color online) Ion motion amplitude. The peak-to-peak amplitude of the ion motion in the $y$ direction is plotted as a function of the dc potential on the center electrode.

Figure 15

(Color online) (a) Top view of an ion trajectory from secular resonances with $V=250\mathrm{V}$ and $\Omega =2\pi \times 2\mathrm{kHz}$. Only the center ground electrode is seen in these pictures because the grounded top plate electrode masks the other electrodes from view. The width of the ground electrode is $1.27\mathrm{mm}$. (b) Transverse mode excited at a drive frequency of $288\mathrm{Hz}$. (c) Axial mode excited at $25\mathrm{Hz}$.

Figure 16

(Color online) Measurements of the secular frequency versus (a) rf amplitude at a fixed rf frequency of $1.5\mathrm{kHz}$ (on a linear scale) and (b) rf frequency at a fixed rf amplitude of $250\mathrm{V}$ (on a log-log scale). The solid lines are fits to Eq. (7) with $(Q∕m)f_i$ as a fit parameter.

Figure 17

(Color online) (a) A strobe image showing shuttling of a single ion, taken by modulating the current to the illuminating laser. The laser is periodically turned on for $2\mathrm{ms}$ and off for $5\mathrm{ms}$. The ion is moving from left to right; there is a short acceleration period after which the ion reaches a maximal velocity and then decelerates. This shuttle was performed by applying a potential of $5\mathrm{V}$ to the nearest control electrode that is to the left of the ion. (b) Distance moved by the ion versus elapsed time, fitted with a spline to guide the eye.

Figure 18

(Color online) The maximum speed $v_{max}$ an ion attains during a shuttling operation versus (a) the potential $u_c$ applied to the nearest control electrode at constant pressure $\left(40\mathrm{Pa}\right)$ fitted to a $3∕4$ power law ($v_{max}=A{u}_c^{3∕4}$ where $A=9.55\mathrm{cm}{\mathrm{s}}^{-1}{\mathrm{V}}^{-3∕4}$) and (b) the chamber pressure at constant control-electrode voltage $\left(5\mathrm{V}\right)$. Ion speed is found to be inversely proportional to the chamber pressure. This behavior is expected when (1) the mean free path is much greater than the radius of the particles and (2) $\gamma t_{ac}⪢1$ where $\gamma$ is the damping factor and $t_{ac}$ is the acceleration time of the ion. When the damping is low enough such that (2) no longer holds, the ion speed is expected to reach a pressure-independent value.

Figure 19

(Color online) Turning a corner. The arrows point to the position of the ion (a) before and (b) after turning the corner. This operation takes about 50 ms.

Figure 20

(Color online) Top view of a two-dimensional Paul trap array. Ions can either be confined to points or free to move along lines, depending on the rf and ground connections. The connections shown (top inset) trap ions above the dots. Bottom inset: Microspheres are trapped in the two-dimensional array, and seven are shown illuminated by the laser beam. In contrast with the cross trap, the four-rod loading stage is out of plane, and is visible above and to the right.