The coherent control of quantum-entangled states of trapped ions1 has led to significant advances in quantum information2, quantum simulation3, quantum metrology4,5 and laboratory tests of quantum mechanics6 and relativity7. All of the basic requirements for processing quantum information with arrays of ion-based quantum bits (qubits) have been proven in principle8. However, so far, no more than 14 ion-based qubits have been entangled with the ion-trap approach9, so there is a clear need for arrays of ion traps that can handle a much larger number of qubits10. Traps consisting of a two-dimensional electrode array11 have undergone significant development, but three-dimensional trap geometries can create a superior confining potential. However, existing three-dimensional approaches, as used in the most advanced experiments with trap arrays8,12, cannot be scaled up to handle greatly increased numbers of ions. Here, we report a monolithic three-dimensional ion microtrap array etched from a silica-on-silicon wafer using conventional semiconductor fabrication technology. We have confined individual 88Sr+ ions and strings of up to 14 ions in a single segment of the array. We have measured motional frequencies, ion heating rates and storage times. Our results demonstrate that it should be possible to handle several tens of ion-based qubits with this approach.
Microfabricated ion trap arrays follow one of two geometries. In the first, ions are trapped inside a three-dimensional multilayer electrode structure13,14, and in the second, they are trapped above the surface of a two-dimensional planar electrode arrangement11. The aim is to create a good approximation of a harmonic radial potential containing minimal anharmonic components. Ion confinement, as characterized by motional frequency, is proportional to the amplitude of the harmonic component of the potential. Anharmonic terms cause the motion of the ion to be nonlinear, with motional frequencies dependent on oscillation amplitude. The most desirable situation is to maximize the motional frequency of the ion while minimizing anharmonicities. The trap efficiency parameter ɛtrap is a direct measure of the effectiveness of a trap structure in achieving these aims. It quantifies the harmonic component of the potential relative to that created by ideal hyperbolic electrodes (ɛtrap = 1) with the same ion–electrode distance15. A three-dimensional unit aspect-ratio geometry (α = 1, Fig. 1a,b) is the optimal practical configuration16,17 because it can create a superior, high-efficiency (ɛtrap > 0.7) trapping potential. In contrast, two-dimensional geometries achieve only 0.32 ≤ ɛtrap ≤ 0.37 (ref. 18), and only ∼35% of the applied voltage contributes to tight ion confinement, thus requiring higher voltages, which are ultimately limited by electrical breakdown. In the only previous monolithic multilayer trap array19, the chosen GaAs microfabrication process dictated a high-aspect-ratio design (α = 15). This compromised the performance of the trap, significantly reducing the harmonic component (ɛtrap = 0.45) and depth of the radial potential, yielding a high absolute ion heating rate and short ion storage time, rendering it difficult to use. A single-zone, three-dimensional assembled multilayer trap (α ≈ 1.4) based on degenerate silicon has been demonstrated, but required post-processing bonding of the silicon electrode structures to an insulating spacer20. Here, we report a monolithic, segmented linear ion trap array based on a three-dimensional, multilayer unit aspect-ratio geometry. The device has a deep and efficient trapping potential and demonstrates a low ion heating rate, long storage times and low radiofrequency loss characteristics. The microfabrication techniques used offer a viable route for scaling to much larger and more complex arrays.
The monolithic linear segmented ion trap (Fig. 1) closely follows the design proposed in our earlier work16. The trap electrodes are formed of gold-coated silica and are spaced by n-doped silicon in a monolithic structure. This approach enables a unit aspect-ratio trap, and ensures that the structure yields a high-efficiency trapping potential. Low-resistivity silicon minimizes radiofrequency loss and subsequent heating in the microtrap chip16. The microfabrication process used to create the structures in Fig. 2 from an oxidized silicon wafer is detailed in the Methods. Ions are confined at the centre of the aperture of the microtrap chip (Figs 1b and 2) at a distance do = 240 µm from the electrodes. The trapping electrode array consists of three adjacent segments that are bounded by endcap electrodes at each end of the array. In the axial direction, the trapping segments and endcaps are 340 µm and 500 µm wide, respectively. A radiofrequency voltage is applied to both of the long strip electrodes, and static (d.c.) voltages are applied to the segmented electrodes. Adjacent to the radiofrequency strip electrodes are a series of compensation electrodes that are there to cancel unwanted electric fields, such as those due to stray static charges on nearby insulating surfaces. Ohmic contacts to the doped silicon ensure that silicon surfaces in the line of sight of the ions can be grounded. Trap packaging and containment at ∼1 × 10−11 mbar (Fig. 2c) are described in the Methods.
The operating range of a non-ideal trap may be restricted by geometric imperfections or stray electric fields, as well as electrical breakdown. These factors, together with ɛtrap, can limit the achievable ion motional frequencies, which in turn suppresses the speed of qubit entangling gates. Accordingly, confinement across a wide range of trap stability parameters q (ref. 15), with radial motional frequencies ωr/2π ≥ 2 MHz, is highly desirable. The trap reported here meets both these criteria. A single 88Sr+ ion, created by photoionization21, was confined and laser-cooled (see Methods) in the central trap segment. Stable ion confinement was observed over the wide range 0.17 ≤ q ≤ 0.7, which is a result of the precise three-dimensional geometry and good electrical characteristics of the trap. In comparison, examples of two-dimensional traps have reported operating parameters corresponding to smaller ranges (0.22 ≤ q ≤ 0.54 (ref. 11) and 0.29 ≤ q ≤ 0.35 (ref. 22)), and a sole operating point (q = 0.62) has been reported for a three-dimensional high-aspect-ratio trap19. The measured radial frequencies of the trapped ion (see example in Fig. 3) were in the range 1.4 MHz ≤ ωr/2π ≤ 4.9 MHz. The corresponding spatial extent of the ground-state wavefunction of the ion, ro = [ℏ/2mωr]1/2, is in the range 6.4 nm ≥ ro ≥ 3.4 nm. From the measured ωr we calculated the efficiency of the trap potential17 to be ɛtrap = (0.72 ± 0.03), which is in excellent agreement with our earlier model16 and demonstrates the effectiveness of the trap structure in creating a superior radial potential. Using the measured motional frequencies and the model results, we calculated that trap depths up to 10 eV are achieved. This is a major advance over all other scalable systems, where reported trap depths range from 0.080 eV (ref. 19) to 0.200 eV (ref. 11).
Radiofrequency micromotion limits the spatial confinement of the ion, causing unwanted modulation in the spectra of the optical transitions. This arises when static offset fields in the proximity of the trap shift the ion from the centre of the trapping potential. Modulated Doppler cooling fluorescence is detected by correlating photon arrival times with the signal driving the trapping potential23. By applying static voltages to a d.c. electrode and a compensation electrode in the central segment, micromotion in the radial plane is minimized to an amplitude of ≤4 nm. Without micromotion compensation, a string of up to three ions could be trapped in the central segment. After minimizing the micromotion of a single ion, strings (for example, Fig. 2d) of up to 14 ions could be confined in a single trap segment.
Electric field noise on trap electrodes resonantly heats the motion of the ions1,24, thus presenting an obstacle to achieving high-fidelity manipulation and long coherence times for the quantum states. Furthermore, a high ion heating rate and a shallow trap depth limits ion storage times19. We measured the heating rate of a single ion using the Doppler re-cooling method25. With a deep radial potential and a reduced axial potential (ωz/2π = 750 kHz), the heating rate at ωz was determined to have an upper limit of 320 quanta per s. The electric field noise spectral density SE(ωz) of the trap is then deduced from the heating rate. A more direct comparison with other traps can be made using the scaled parameter ωzSE(ωz) = 1.7 × 10−5 V2 m−2. This present value is at least three times lower than any value previously reported for a scalable microtrap operating at nominally ambient temperature24. The low heating rate and deep trapping potential yield long ion storage times—in excess of 24 h when laser-cooled and up to 30 min when uncooled, the latter being limited by background gas collisions in the vacuum. This uncooled storage time is between 30 (ref. 22) and 180 (ref. 20) times longer than that found in microtraps of two-dimensional electrode geometries, and ∼1 × 104 times greater than in the only previous monolithic three-dimensional device19.
Significant radiofrequency loss in the ion microtrap will heat the trap chip and limit the radiofrequency amplitude Uo, in turn constraining the achievable trap depth and motional frequencies. Furthermore, ion heating rates have been shown to be dependent on electrode temperature26,27. The geometry and material properties of the microtrap result in low radiofrequency dissipation, in agreement with our calculations16. It is driven using a helical coil resonator yielding a loaded circuit Q of 140. With drive parameters Uo = 365 V and Ω/2π = 23.2 MHz, ∼1.5 mW is dissipated in the trap chip and its temperature rises by a maximum of ∼3 K above ambient. The low dissipation of the chip makes operation at temperatures of ∼10 K a feasible prospect with cryogenic cooling, enabling a much reduced ion heating rate27.
Qubit control using precision optical spectroscopy generally requires that the wavepacket of an ion is localized to much less than an optical wavelength, that is, in the Lamb–Dicke limit15. Spectroscopy of the 5s 2S1/2–4d 2D5/2 optical qubit transition in a single Doppler-cooled 88Sr+ ion28 shows a characteristic carrier and resolved motional sidebands for radial and axial modes (Fig. 4). The amplitude of the first-order sidebands relative to the carrier transition as well as the suppression of second-order sidebands indicate Lamb–Dicke confinement of the ion in the microtrap. In the radial mode ωr1/2π = 1.5 MHz, where the mean vibrational quantum number is , the spatial extent of the ion wavefunction is 44 nm (6.2 nm for the ground state ).
Scalable arrays for large numbers of ion qubits will rely on the transport of ions between different zones10. Basic ion transport was demonstrated using two ions initially in the central zone of the array. By increasing the d.c. voltage applied to this zone, and decreasing that applied to the outer zones, the two ions were separated symmetrically. Moreover, with a combination of voltages applied asymmetrically, one ion could be retained in the central zone while the second was transported to an outer zone. The initial configuration of the ions was restored by reversing the applied voltage sequence in both instances. These basic principles can be developed further, in tandem with more complex arrays such as ‘X’-junctions14, which are viable with the present fabrication process.
In conclusion, we have demonstrated a monolithic ion trap that combines the superior properties of a three-dimensional electrode geometry with the scalability afforded by semiconductor fabrication. The use of gold, silica and silicon results in low dissipation, and an aspect ratio of unity yields an efficient trapping potential, enabling operation over a wide parameter range. It should be possible to build traps that can confine several tens of ions with this approach and such traps, combined with advanced techniques for ion transport14 and high-fidelity gates29,30, represent a promising approach for the development of scalable ion-trap quantum processors.
This device could therefore assist in fulfilling the DiVincenzo criteria31 for trapped ion qubits. Furthermore, it should be possible to embed optical fibres in these traps, which could enable a prototype quantum network of interconnected ion-trap processors.
Ion microtrap fabrication and packaging
Oxidized silicon wafers (100 mm in diameter, 350 µm thick and n-doped with arsenic) with a resistivity of 2.6 × 10−3 Ω cm were used. Silica (SiO2; thickness,15 µm) was grown on both sides of the wafers by thermal oxidation. Titanium/gold electrodes were then deposited on each side using standard lift-off techniques patterned by optical lithography. Undesired areas of SiO2 were removed by a CF4-based reactive ion etch with a photoresist mask. Titanium/gold ohmic ground contacts were then formed on the exposed silicon by lift-off. To create the trap aperture, silicon was removed using a SF6 reactive ion etch and a photoresist mask, undercutting the SiO2 to a depth of 235 µm. The depth of this feature ensures that the high efficiency of the trapping potential is not compromised. The resulting exposed SiO2 surfaces inside the aperture were coated with titanium/gold by angled thermal evaporation. Inside the trap aperture, an exposed SiO2 gap of 50 µm remains between the gold electrodes and the bulk silicon surface to prevent electrical breakdown. Finally, to minimize the resistance of the static (d.c.) and radiofrequency gold electrode tracks, these were electroplated to a thickness of ∼5 µm using a maskless process.
Each trap chip was mounted (Fig. 2c) in a custom aluminium nitride carrier containing electrical vias, which in turn was mounted in a modified 84-pin ceramic leadless chip carrier (LCC). The aluminium nitride carrier enabled electrical wire-bond connections from the LCC to the backside of the chip. The LCC was cold-welded onto the vacuum chamber using indium, with apertures laser-machined into its central cavity to provide sufficient vacuum conductivity and optical access. An antireflection coated window, offset with a steel spacer, was similarly cold-welded onto the LCC to seal the vacuum. Following this procedure, the conductors of the LCC form the ultrahigh-vacuum feedthrough. A pressure of ∼1 × 10−11 mbar was achieved using a non-evaporable getter and a 20 l s−1 ion pump. This approach enables direct and efficient electrical access to all of the trap electrodes and the application of air-side filters to all d.c. electrodes at only ∼20 mm from the trap centre. It also facilitates an accurate calibration of the applied radiofrequency potential amplitude.
Fluorescence detection, photoionization loading and Doppler cooling
The packaging arrangement described above enables optical access over 0.7π sr solid angle on each side of the trap chip (totalling 35% of 4π sr). Ion fluorescence was imaged (numerical aperture, 0.43; magnification, ×10) from both front and back sides of the trap aperture. Fluorescence from one side was detected using a photomultiplier, and from the other with an electron-multiplying charge-coupled device (CCD).
A hotplate source was used to produce strontium atomic vapour in the trapping region, and a two-step doubly resonant photoionization process created ions for trapping21. For a source vapour pressure of ∼1 × 10−13 mbar, the desired number of 88Sr+ ions were loaded in a controlled fashion at a rate of up to four per minute. Although the trap electrodes are not directly shielded from the atomic vapour, there is no line of sight from the atomic source to the recessed silicon surfaces inside the trap aperture. Ions were initially confined in the central segment of the trap, and were Doppler-cooled by a laser tuned ∼12 MHz below the 5s 2S1/2–5p 2P1/2 transition at 422 nm in 88Sr+. A repumper laser at 1,092 nm was used to maintain efficient Doppler cooling, because the 5p 2P1/2 state also decays to the metastable 4d 2D3/2 state. The ions may be cooled by one of three non-coplanar beams at 422 nm, each of which is oblique to all principal trap axes and contains ∼1.5 µW in a spot size of 2wo = 70 µm. Relative to the unit vectors that define the principal axes of the trap, the cooling beams have unit vectors , and . This beam geometry is illustrated in Supplementary Fig. S1.
Trap parameters and measurement of motional frequencies
The trap was operated at drive frequencies of Ω/2π = 18.0 and 23.2 MHz, with amplitude Uo in ranges 180 ≤ Uo ≤ 330 V (0.4 ≤ q ≤ 0.7) and 134 ≤ Uo ≤ 365 V (0.17 ≤ q ≤ 0.45), respectively, where q is the trap stability parameter15. In all instances an ion was trapped when the static voltage of the endcap electrodes, UEC, was as low as 0.1 V. UEC could be increased to 30 V at the highest radiofrequency amplitudes Uo, yielding ωz = 2.2 MHz. The motional frequencies of the trapped ions were measured using a combination of two methods. The fluorescence of the cold ions reduced when a swept radiofrequency voltage, applied to one of the central segment's d.c. electrodes, was in resonance with a motional frequency of the ion. With the technique of pulsed-probe spectroscopy, motional sidebands were detected on the 674 nm 5s 2S1/2–4d 2D5/2 optical qubit transition in 88Sr+ (ref. 28). After Doppler cooling, the ion was irradiated by a pulse from a 674 nm laser tuned close to the qubit transition. If the ion has not made the transition to the metastable 4d 2D5/2 state, then fluorescence photons are detected when the cooling laser returns. If the transition has been made, then no fluorescence is detected. Performing this spectroscopic measurement many times over a range of 674 nm laser frequencies results in a histogram that is representative of the absorption spectrum of the ion. This includes a carrier and motional sidebands.
The authors thank F. Schmidt-Kaler, C. Wunderlich, W. Hänsel, R. Blatt, M. Drewsen, D. Lucas, D Allcock and D. Moehring for useful discussions. The authors also acknowledge support from the EU STREP project MICROTRAP (IST-517675), the EU collaborative project SCALA (IST-015714) and the Pathfinder Metrology Programme of the UK National Measurement Office.
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Micro and Nano Systems Letters (2015)