Surface-electrode trap with an integrated permanent magnet for generating a magnetic-field gradient at trapped ions
Yuji Kawai, Kenji Shimizu, Atsushi Noguchi, Shinji Urabe, Utako Tanaka
aa r X i v : . [ phy s i c s . a t o m - ph ] O c t Surface-electrode trap with an integratedpermanent magnet for generating a magnetic-fieldgradient at trapped ions
Yuji Kawai , Kenji Shimizu , Atsushi Noguchi , Shinji Urabe ,and Utako Tanaka Graduate School of Engineering Science, Osaka University,1-3 Machikaneyama-cho,Toyonaka, Osaka 560-8531, Japan Research Center for Advanced Science and Technology (RCAST), The University ofTokyo, Meguro-ku, Tokyo, 153-8904, JapanE-mail: [email protected]
Abstract.
We report on a surface-electrode trap with SmCo magnets arranged in aquadrupole configuration underneath the trap electrode. Because the distance betweenthe magnets and the trapped ions can be as little as several hundred micrometers,a large magnetic field is produced without any heat management. The magnetic-field gradient was measured using the Zeeman splitting of a single trapped Ca + ion at several positions, and a field gradient of 36 T/m was obtained. Such a fieldgradient is useful for the generation of a state-dependent force, which is importantfor quantum simulation and/or quantum gate operation using radio-frequency ormicrowave radiation. Keywords : ion trap, magnetic-field gradient, quantum simulation urface-electrode trap with an integrated permanent magnet
1. Introduction
Trapped atomic ions have been regarded as a very promising physical system inquantum information processing. They have been used for many proof-of-principleexperiments such as fundamental quantum gate operations[1, 2, 3], generation ofentangled states[4, 5, 6], and quantum simulation of coupled spins[7]. In these pioneeringstudies, the quantized motional and internal states of trapped ions were controlledusing laser radiation. In spite of such successful works, the use of laser radiationfor coherent manipulation has a few issues. If two levels are coupled by a Ramantransition, spontaneous emission causes the destruction of quantum coherence[8]. Onthe other hand, if a ground state and a metastable state are chosen as a two-level systemand driven by a quadrupole transition, hertz-level laser stability is typically demanded.In order to achieve further scalability, it is desirable to develop a system that is notaffected by the decoherence due to spontaneous emission and is less demanding of thelaser system.The use of radio frequency (rf) or microwave for the manipulation of quantumstates has several advantages from these viewpoints[9, 10]. Spontaneous emission doesnot affect the gate operation, which would lead to better fidelity in quantum-statemanipulation. In addition, the generation and control of rf or microwave radiationrequires a simpler system compared to that of laser radiation. Thus, a laser systemis used only for laser cooling and state detection, which reduces the demand on theirstability. To perform the quantum simulation of interacting spins or two-ion entanglinggates, the state coupling of motional and internal quantum states is required. Asproposed in [9], exposing an ion string to a magnetic field with spatially varyingmagnitudes enables such coupling. The coupling strength is proportional to the squareof the field gradient.Several studies aimed at generating a magnetic-field gradient at trapped ions havebeen reported. Individual addressing of trapped ions and coupling of motional andinternal states have been performed using permanent magnets, which were set at theoutside of end electrodes of a linear Paul trap [11, 12]. However, the magnitude ofthe field gradient is limited by the distance between the ion and magnets because itis generally difficult to integrate magnets inside a conventional linear Paul trap. Oneapproach involved a current introduced on wires fabricated in a surface-electrode trapfor the generation of magnetic-field gradients[13, 14], which can reduce the distancebetween the ions. This design is suitable for improving scalability; however, it requiresheat management. Another approach involved the use of oscillating magnetic fieldsin a surface-electrode trap[15, 16, 17, 18, 19]. The use of the near-field amplitudegradient produced in a surface-electrode trap was proposed [15], and gate operation wasdemonstrated [16].Here, we present a different approach to generate a large field gradient at trappedions. We integrate permanent magnets underneath a surface-electrode trap. Thisstructure remarkably reduces the distance between permanent magnets and trapped urface-electrode trap with an integrated permanent magnet S / - D / transition in a Ca + ion at several positions. Finally, we discuss the generation of aneven larger field gradient.
2. Trap design
The trap is composed of two parts; a surface-electrode trap and a magnet layer. Thesurface-electrode trap is made of a square alumina substrate, the surface of which isgold-plated to form electrodes. The magnet layer is also made of a square aluminaplate, which has holes for placing permanent magnets. Both the trap electrode and themagnet layer are squares of a side 11.5 mm. The magnet layer is glued underneath thetrap with a conductive epoxy to make these two squares overlap. Then, the trap is gluedon a ceramic pin grid array (CPGA) mount.
Figure 1.
Structure of trap electrode with permanent magnets. (a) Surface-electrodetrap and magnet layer. Ions are trapped above the surface along the z direction.Though the trap and the magnets are shown separately in this drawing for clarity,the eight permanent magnets are attached underneath the trap. The labels A and Brepresent the trapping regions discussed in this work (See text). (b) Photograph of thetrap chip. (c) Photograph of the magnet layer placed underneath the trap chip (b). The trap design is based on a segmented linear surface-electrode trap (Fig. 1). An rfvoltage is applied to the two rf electrodes for radial confinement. A direct current (dc)electrode called center electrode is placed between the rf electrodes, and it is used for urface-electrode trap with an integrated permanent magnet square and thickness 0.2mm. Electrodes are formed through gold plating using Ti and Pd as adhesive layers. Thethickness of the gold electrode is approximately 5 µ m. The widths of the rf electrodesand center electrode are 300 µ m and 100 µ m, respectively. All the dc electrodes foraxial confinement are squares of dimensions 1 mm by 1 mm. The spacing around the rfelectrodes is 50 µ m, while the other spacing is 25 µ m. Eight rectangular parallelepiped magnets are located underneath the trap electrode. Wechoose the quantized axis in the x direction and the trap axis in the z direction. Ourrequirement is a large gradient of the x component of magnetic field along the z direction.To realize this, four of the magnets are aligned in the quadrupole configuration at thecenter of the layer. Ideally, at x = 0, no components exist along the y and z directions.Further, only the magnitudes of x components exist and cross zero at z = 0. The largemagnetic field causes a large detuning in cooling laser frequency; therefore, we placefour other magnets in order to reduce the magnitude of the magnetic field outside thequadrupole configuration. In addition, these four magnets enable experiments underdifferent field-gradient conditions. SmCo magnets with dimensions of 1 mm × × x component of the magnetic field along the z direction (horizontal linein Fig.2(a)) 350 µ m away from the top surface of the magnet layer. Owing to thesymmetry of quadrupole configuration, both B y and B z are equal to zero in the idealcase. Because of the existence of the outer four magnets, the magnetic field is reducedin the outer region. The maximum field gradient is obtained at z = 0, and a smallergradient is obtained around the other zero-crossing points.Because the trap chip and the magnet layer are separated parts originally, a shiftbetween two squares may exist when they are glued, which results in the generation ofan unwanted magnetic field at the trapped ions. Figure 2 (c) shows a calculation similarto that in (b) but with a shift between the trap chip and the magnetic layer of 100 µ m,as shown by the dotted horizontal line in Fig. 2(a). At z = 0, B z becomes large, whichchanges the direction of the quantized axis. B y also arises around z = ± . | z | > urface-electrode trap with an integrated permanent magnet Figure 2.
Results of calculation of magnetic field generated by the magnet layer. (a)Configuration of eight magnets. The arrows indicate magnetization vectors inside themagnets. (b) Magnetic field along the z direction (horizontal line) at y =150 µ m, whichis 350 µ m from the top surface of the magnetic layer. In this ideal case, i.e., when thetrap and the magnet layer completely overlap, both y and z components are zero. (c)Same calculation as (b), with a shift between the trap and the magnet layer of 100 µ massumed in the x direction; that is, ions are located along the dotted horizontal line in(a) and 350 µ m above the magnet-layer surface. In this case, B y and B z are not zero. Figure 3.
Magnitude of the magnetic-field gradient versus the distance between theion and the top surface of the magnet layer for trapping regions A and B.
The dependence of the calculated magnetic-field gradient on the distance between urface-electrode trap with an integrated permanent magnet µ mfrom the magnet layer, a magnetic-field gradient greater than 100 T/m is estimated.Likewise, according to Fig. 3, when an ion is confined in region B at a height of 350 µ m, a magnetic-field gradient of approximately 38 T/m is estimated.
3. Experimental Setup
The trap on the CPGA mount is placed in a vacuum chamber with a vacuum levelof 10 − Pa. Calcium ions are loaded by photo-ionization with a 423-nm laser for the S - P transition and a 375-nm laser for ionization. Doppler cooling is conducted bythe S / - P / transition at 397 nm with an 866-nm laser for pumping back the ionfrom the D / state to the P / state. The Zeeman splitting is measured by using thequadrupole transition between the S / and D / states at 729 nm with a quenchinglaser connecting the D / and P / states at 854 nm. All of the lasers for photo-ionization, Doppler cooling, and quenching are introduced in the z direction. The 729-nm laser is introduced from the opposite side in the z direction. The polarization of the729-nm laser is set to be in the x direction so that only the ∆ m J = ± V amp at 22.2 MHz. For axial confinement, devoltages ranging from 3 V to 19 V were applied.
4. Results
In order to evaluate the magnetic-field gradient, we measured the Zeeman splitting ofthe S / - D / transition at several points along the z direction in region B becausethe second-largest field gradient is expected without a large offset field of B y and B z .After trapping a single Ca + ion in region B, a stray dc field was compensated for tominimize the excess micromotion of ions. In addition, we compensated for as much ofthe offset field of B x and B y as possible by using external coils attached outside thevacuum chamber. We then measured the splitting between two Zeeman components ofthe S / and D / transition at several points along the z axis.Figure 4 shows the spectra of the S / − D / transition at 729 nm obtained atdifferent positions of the trap. Among the four ∆ m J = ± m j = − / → m ′ j = − / m j = +1 / → m ′ j = +3 /
2, which are indicated by vertical arrows, to measure theZeeman splitting of the S / state. The ion position is changed by the dc controlvoltages. Figure 5 shows the dependence of the magnetic-field magnitude estimatedfrom the observed Zeeman splitting on the ion position. The error is mainly due to urface-electrode trap with an integrated permanent magnet Figure 4.
Spectra of the S / − D / transition of a single Ca + . ∆ z representsthe distance from the original ion position. Figure 5.
Magnitude of the magnetic field estimated from the Zeeman splitting atdifferent positions of a single trapped ion.
5. Discussion
We measured the field gradient in region B, where the second-largest magnetic-fieldgradient is expected. We also attempted to perform the experiments in region A, wherethe largest magnetic-field gradient is estimated; however, the fluorescence from Ca + ioncould not be observed. We also attempted moving the ion from the region next to Ato region A. We could shuttle the ion, However, it was not possible to monitor the ion urface-electrode trap with an integrated permanent magnet µ m can produce an offsetfield of approximately 5 mT in the z direction at z = 0. It is difficult to cancel such ahigh offset field with our present external coils attached outside the vacuum chamber.To overcome the offset-field problem due to the shift between the trap electrode andthe magnet layer, it is preferable to fabricate a magnet layer integrated with the trapelectrode.Other possible cause of excess offset magnetic field is that the magnitude of themagnetic field generated by each permanent magnet is uneven. To overcome thisproblem, we need to adjust the positional relation between the rf node and magneticfield. One possibility is to set the magnet layer on a movable stage inside the vacuumchamber that can be three-dimensionally moved with respect to the position of ions.Alternatively, it is possible to move the rf node by introducing an additional rf field toa trap electrode [18, 24, 25]. The obtained field gradient of 36 T/m at a distance ofapproximately 350 µ m from the magnet layer is in good agreement with the calculation.From this result, we can infer that a field gradient of 100 T/m is generated in region A.
6. Conclusion
We have demonstrated a surface-electrode trap with SmCo magnets arranged inthe quadrupole configuration underneath the trap electrode. By utilizing the greatadvantage of the permanent magnets, which do not require any heat managementand can be placed as close to ions as possible, a large magnetic-field gradient can begenerated. A field gradient as large as 36 T/m has been estimated by measuring theZeeman splitting of a single trapped Ca + ion at several positions, which is in goodagreement with the calculation. From this result, we can infer that a field gradient of100 T/m is generated in region A. A large field gradient is necessary to implement asufficient state-dependent force, which is vital for quantum simulation and/or quantumgate operation using radio-frequency or microwave radiation. It is important to assemblethe trap electrode and the magnet layer without any shift between them. The fabricationof a magnet layer integrated with the trap electrode would be a solution to overcomethis problem. A field gradient on the order of 100 T/m would be possible with thepresented method. urface-electrode trap with an integrated permanent magnet
7. Acknowledgments
We are grateful to Yasuhiro Tokura for helpful advice on the numerical calculation ofmagnetic fields.
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