Main

The basic electrode geometry is shown in Fig. 1 and is formed by two concentric cylinders over a ground plane. The design provides straightforward indexing and assembly of the trap electrodes, with large solid angle access to the ion. Four extra electrodes were placed on a circle between the grounded plane and the radiofrequency electrode to break the rotational symmetry of the radiofrequency pseudopotential about the vertical axis and to compensate for stray electric fields to minimize ion radiofrequency micromotion in the trap9.

Figure 1: Pseudo-potential and trap geometry.
figure 1

a, Simulations of the trap radiofrequency pseudopotential indicate smaller trap potential depths and binding frequencies compared with those of more traditional trap designs of similar size, radiofrequency drive frequency and amplitude. Shown is an example calculation of the pseudo-potential (in electronvolts) for electrode configuration 3 using the corresponding parameters given in Table 1 and 24Mg+ properties, although neglecting the compensation electrodes. The isoline separation is 25 meV and the axial coordinate is measured from the grounded plane. b, Placement of the electrodes. The central ground electrode (cGND) is surrounded by the radiofrequency electrode (rf) and the grounded plane (GND). These electrodes provide the primary trapping potential. In addition, four symmetrically placed compensation electrodes (COMP) provide fine adjustments to the overall potential. The distance h between the ion and the centre electrode varies with Δh, the height difference between the centre electrode and the radiofrequency electrode. The accessible solid angle Ω is also illustrated. The inset shows the position of the trap electrodes with respect to the laser beams for cooling and ionization and the direction of the principal radial axes of the trap. The direction from which the neutral Mg vapour enters the trapping region is indicated. c, The layered assembly showing insulating planes with conducting gold leads and laser-cut holes to house the electrodes. The diagram is not drawn to scale. See the Methods section for dimensions.

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Three different traps were built adjacent to each other on the same test set-up (Fig. 2). These traps range from a conservative design with a larger trap depth, higher motional frequencies and a smaller accessible solid angle, to a weaker trap with greater optical access. This change in properties is achieved by varying the protrusion height Δh of the central grounded electrode with respect to the radiofrequency electrode (Table 1).

Figure 2: The completed trap assembly before insertion into the vacuum chamber.
figure 2

The three test traps with differing protrusion height Δh (increasing from front to back) of the central electrode can be seen. Visible in the upper right-hand side of the figure is also the ceramic board with copper traces, which accommodates surface-mounted components constituting low-pass filters for the d.c. electrodes. Two parallel gold wires connecting the radiofrequency electrode can be seen in the lower left-hand side of the figure. The insets show different experimentally observed ion configurations (from top to bottom): a single trapped ion, two ions revealing the orientation of the weakest trap axis and an ion crystal in an approximately cylindrical potential that allows the outer ions to rotate about the trap vertical axis.

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Table 1 Typical operating parameters.
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The degeneracy of motional frequencies in the radial direction was lifted by applying potentials of the order of 0.1–1 V to the compensation electrodes A–D. This created a static quadrupole field defining the principal radial axes of the trap along the lines connecting compensation electrode A with D and B with C. Thus, the axes were oriented at angles of about 45∘ relative to the two cooling beams (Fig. 1b). In addition, the entire trap assembly was tilted by about 7.5∘ with respect to the direction defined by the laser beams, ensuring that the vertical axis of the traps was not orthogonal to the wave vectors of the cooling beams. In this way, all three normal modes of the ion were sufficiently Doppler cooled by a single laser beam. For further details, see the Methods section.

To compensate radiofrequency micromotion due to electric stray fields, we varied the potential on all four compensation electrodes and the central cylinder while changing the power level of the radiofrequency drive. Compensation was achieved when the ion position remained stationary for different radiofrequency drive amplitudes9. We could also minimize micromotion along the direction of the cooling beam by adjusting compensation potentials and maximizing the scattering signal with the cooling beam tuned close to resonance. By lowering the radiofrequency drive after loading, we determined a minimum radiofrequency power for ‘stable’ trapping that seemed to be limited only by background gas collisions. The trap of configuration 3 was able to trap reliably after the well depth was lowered to less than 1 meV. As this depth is significantly below room temperature, ions can be lost by a single Langevin (charge-dipole) collision with a background gas atom. At the base pressure of about 3×10−9 Pa reached in our system, the mean ion lifetime with laser cooling was around 30 s in this particular case.

In all three traps, we observed ion lifetimes in excess of three hours under continuous laser cooling. Without cooling light, lifetimes were greater than 10 s. The secular frequencies of ion motion along all three axes were determined by applying extra sinusoidal drive potentials to the compensation electrodes or the central electrode. If the drive frequency is resonant with a secular frequency, ion motion is excited to large amplitudes, causing a sharp drop of laser-induced fluorescence.

Operating parameters for each of the three traps are summarized in Table 1 together with observed trap frequencies, radiofrequency drive voltage and trap depth as inferred from measured trap frequencies and numerical simulations for each trap. The accessible solid angle ignores the compensation electrodes and outer ground plane. This seems reasonable because in future implementations, these electrodes could be made smaller and/or recessed below the radiofrequency electrode. This has not been done so far to facilitate construction of the basic electrode structure.

The compact design permits placing the trap inside a metallic parabolic mirror, which can also serve as a radiofrequency ground electrode (Fig. 3a). By moving the trap structure, an ion can be placed at the focal point of the mirror for efficient fluorescence collection. Moreover, parallel light beams directed along the mirror optical axis are focused directly onto the ion. By appropriately shaping the transverse mode pattern of the incident light10,11, the field at the focus can produce a linear dipole excitation pattern aligned with the axis of symmetry of the parabolic mirror, which could lead to very efficient photon–ion coupling12. With electrode configuration 3 and a parabolic mirror with a depth-to-focal-length ratio of 6:1 (an aspect ratio that is feasible to manufacture), the solid angle intercepted by the parabolic mirror is 81% of 4π. For a linear electric dipole aligned along the mirror axis, this geometry would lead to a collection efficiency of 94%. Conversely, light sent onto the ion in a dipolar pattern would provide a near-perfect atom-to-photon coupling to a linear dipole transition, possibly working down to the single-photon level13,14. To this end, one could use ions with even-numbered charge that allow for J=0–1 transitions12.

Figure 3: Potential applications of the trap geometry.
figure 3

a, Placement of the ion in the focus fof a parabolic mirror with depth z to maximize photon–ion coupling. b, Scanning of different surfaces with the ion as a sensitive probe.

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This scheme might also provide a significant improvement in the efficiency of remote entanglement of trapped ions as described in refs 15, 16, 17. As an example, the entanglement scheme used in ref. 17 is based on filtering the emission of the atom on F′=0,1 to F=0,1 transitions to overlap only photons on a beam splitter resulting from π-transitions. Limitations of the experiment in ref. 17 were caused by restrictions in the collection solid angle (2% of 4π) as well as coupling of the emission pattern that was imaged through a multi-element lens into a single mode fibre (efficiency 20%). A parabolic collection mirror could potentially improve the situation because ideally it transforms the orthogonal mode patterns of photons emitted on π or σ-transitions while preserving their orthogonality18. Orthogonality is also preserved in good approximation by the remaining elements of the mode shaping proposed in refs 10, 11. Therefore, it might be possible to not only couple photons from π-transitions with near unit efficiency to a single mode fibre, but the mode converter will also act as a filter blocking out undesired photons from σ-transitions. Ideally one would expect to boost the production rate of entangled pairs by more than 5×104 over the values reported in ref. 17. Efficient coupling could also be obtained through a resonant interaction of an ion with a cavity19,20. In this method, to achieve a coupling efficiency of 90%, a minimum cooperativity of 4.5 is required. At present, this is difficult to achieve for many ions that have ultraviolet transition wavelengths and further complications may be encountered with mirror charging19,20.

The open geometry of such traps also suggests applications as a probe of fields near a surface. Surfaces of interest could be brought close to the ion, as in Fig. 3b. By either scanning the ion trap over the surface or translating the surface itself, one could map out the electromagnetic or force fields in proximity of the surface. Modelling the ion trap in the presence of a ground plane located horizontally above the ion in Fig. 1 indicates that a stable quadrupole minimum is retained until the distance to the surface is approximately equal to the distance of the ion to the centre electrode. In the traps described here, this would limit the ion to distances of about 170 μm from the surface, a limit that could be reduced by miniaturizing the trap. The ion serves as a stylus probe tip that is extremely sensitive to forces oscillating at its motional frequencies. These frequencies can be tuned over at least two decades from approximately ω/(2π)=100 kHz to 10 MHz. In addition, information on the force-field direction can be extracted by using all three non-degenerate modes of motion of the ion. With the same apparatus, static and time-dependent magnetic fields can be measured by observing first- and second-order shifts of the ion on narrow internal transitions.

To estimate the sensitivity to oscillating force fields we assume that the ion, initially cooled to its motional ground state, is driven in resonance with a motional mode for a duration t=1/Δb, where Δb is the approximate measurement bandwidth. The amplitude α of the coherent state grows as21

where Fis the amplitude of the driving force, is the size of the ion’s harmonic oscillator ground-state wavefunction, m is the ion’s mass and ℏis Planck’s constant divided by 2π. To yield a detectable signal, this coherent excitation has to be comparable to the excitation due to motional heating that grows according to , where is the ion’s heating rate22,23. Heating rates in the range of 0.2–2 quanta ms−1 have been observed in traps with similar electrode-to-ion distances for a motional frequency ω/(2π)≃1 MHz (refs 24, 25). As the geometry discussed here minimizes the amount of material close to the ion, a heating rate of one quantum per millisecond should be a realistic estimate. (For small cryogenic traps, heating rates of the order of one quantum per second have been observed23.) Assuming a signal-to-noise ratio of one, we require 〈nn〉=〈nc〉=|α|2 and therefore

For 24Mg+, and ω/(2π)=1 MHz, this implies a force sensitivity of 0.46 yN Hz−1/2 (1 yN=1 yocto-Newton=10−24 N), several orders of magnitude below the smallest forces detectable with atomic force microscopes or micromechanical cantilevers26. This force sensitivity corresponds to an electric-field sensitivity of 2.9 (μV m−1) Hz−1/2. For a cryogenic ion trap where , the sensitivity would be increased by approximately a factor of 30.

To detect the magnetic field at the ion’s position, we may excite a narrow transition (for example, a hyperfine transition) with well-known field dependence. The method would be limited by quantum projection noise27. On a Zeeman-shifted transition with a magnetic moment difference of 1 Bohr magneton (Δν/ΔB=14 MHz mT−1) when probed by the Ramsey method with free precession time TR, the magnetic-field resolution ΔB is

where τ is the averaging time and the last expression assumes TR=1 s. By actively compensating the surface field with external coils that lead to a known field geometry, we could detect not only the modulus but also the direction of the local magnetic field. Although magnetic fields can be sensed closer to the surface using nitrogen vacancy centres28,29 and with higher signal-to-noise ratio with a large number of cold neutral atoms30, a potential advantage of the ion sensor could be the combined sensitivity to electric and magnetic fields.

In principle, the electric field in all space can be reconstructed from the field in one plane, but this inversion is an ill-posed problem for spatial features much smaller than the ion-to-feature distance. Therefore, the lateral spatial resolution when scanning the surface will be limited by the attained signal-to-noise ratio and is roughly equal to the distance to the surface if the signal-to-noise ratio is of order one.

An interesting application of the ion sensor in quantum-information processing with trapped ions is to use it for straightforward comparisons of heating rates of different surfaces3,22,23. Typically, to compare heating rates from different electrode surfaces, separate traps composed of different materials have been built and tested. This leads to uncertainties due to variations in the trap geometry, the exact steps of materials processing, surface contamination due to cleaning agents and the bake-out procedure. Most of these variables could be eliminated, and the testing of different materials could be accelerated by the use of one ion sensor on a variety of material samples deposited on the same carrier surface (Fig. 3b).

Methods

Trap fabrication and vacuum housing.

The trap electrodes are made of stainless-steel rods and hypodermic tubing. The dimensions indicated in Fig. 1 are as follows: OD_rf=710 μm, ID_rf=535 μm, OD_cGND=205 μm, ID_cGND=100 μm, OD_COMP=150 μm, h_rf=1,110 μm. Structural integrity and insulation is provided by a combination of alumina and Macor spacers. Electrical connections were made by resistive welding of gold ribbons to the trap electrodes and to gold traces (thickness 5–10 μm) that were silk-screened onto alumina. The outer ground plane was also formed by this silk-screening process. All insulating surfaces have been recessed or positioned to prevent a direct line of sight to the ion position. This suppresses distortions of the trapping field caused by charged insulating surfaces. The potentials applied to the individual d.c. electrodes (central ground and compensation electrodes A–D) are passively filtered by resistor–capacitor low-pass filters with R=1 kΩ and C=2 nF. The components are mounted on a connection board inside the vacuum close to the trap.

The assembled trap package is attached to the connection board (Fig. 2), which is in turn mounted inside a copper tube that forms part of a radiofrequency resonator that supplies the radiofrequency potential. The traps, Mg ovens and copper tube reside inside a quartz envelope with extrusions and flat windows for laser beams and for imaging of the trapped ions. The vacuum system is completed by a 20 l s−1 ion getter pump, a Ti-sublimation pump and an ionization pressure gauge. The system was pumped to 5×10−5 Pa and baked-out at 210 ∘C for 8 days. After cooling the system to room temperature and several applications of Ti-sublimation, a base pressure of about 3×10−9 Pa (at the gauge) was achieved.

Helical resonators were driven by a low-noise signal generator to generate the radiofrequency trap potentials. They had loaded Q-factors ranging from 300 to 430 and were driven with input powers in the range of 22 to 35 dB m. This resulted in radiofrequency amplitudes (inferred from simulations and the resulting trap frequencies) in the range of 290–460 V.

Photoionization loading, Doppler laser cooling and detection.

A 24Mg oven produced a vapour of neutral atoms that was directed at the traps in the horizontal direction of Fig. 1b. To load ions into the traps, the neutral atoms inside the confinement region were then photoionized. All experiments were carried out at a magnetic field of B≃0 T. Photoionization and Doppler laser cooling were achieved by crossing three laser beams in the confinement region of a selected trap. The photoionization beam (λ=285 nm, 2–4 mW, 50 μm waist) was resonant with the transition in neutral Mg (ref. 25). A second photon either at 285 nm or at 280 nm (below) promotes the electron from the 3s3p 1P1 state to the continuum, producing a 24Mg+ ion in the confinement region. For cooling, a second laser beam (λ=280 nm, 1 mW, 30 μm waist) was tuned about 400 MHz below the transition of 24Mg+ for initial cooling. A third, much weaker beam (λ=280 nm, 2–10 μW), with intensity below saturation and tuned below the transition by half of the natural linewidth (≃20 MHz), subsequently cooled the ions to near the Doppler limit. At that point, photon scattering and cooling was dominated by the closely detuned beam. In the case of sudden ion heating, for example due to a collision with background gas, the 400 MHz detuned beam could efficiently recool the ion to a point where the near-resonant beam would take over.

The ion was detected by collecting fluorescence with a high-numerical-aperture (NA≃0.4) objective located a distance of 5 cm above the ion, and either imaged onto an electron-multiplying charge coupled imaging device or photomultiplier tube.