Table Of Content

Fast shuttling of ions in a scalable Penning trap array D. R. Crick,1 S. Donnellan,1 S. Ananthamurthy,2 R. C. Thompson,1 and D. M. Segal1 1Department of Physics, Imperial College, London SW7 2AZ, U.K. 2Department of Physics, Bangalore University, Bangalore 560056, India (Dated: January 18, 2009) We report on the design and testing of an array of Penning ion traps made from printed circuit board. The system enables fast shuttling of ions from one trapping zone to another, which could beofuseinquantuminformation processing. Wedescribesimulationscarried outtodeterminethe 9 optimalpotentialstobeappliedtothetrapelectrodesforenablingthismovement. Theresultsofa 0 preliminaryexperimentwithacloudoflasercooledcalciumionsdemonstratearound-tripshuttling 0 efficiency of up to 75%. 2 n I. INTRODUCTION is however inherently different in a Penning trap due to a J the v×Bcomponentofthe Lorentzforce. Amethodfor overcoming this complication has been presented else- 8 Laser cooled trapped ions constitute one of the most 1 where [11]. It involves exploiting the cycloid motion of advanced experimental approaches to quantum informa- a charged particle in crossedelectric and magnetic fields tionprocessing(QIP)(seeref[1]andreferencestherein). ] to shuttle an ion from one trapping zone to another by h ManyofthekeybuildingblocksofQIPhavebeendemon- the application of a pulsed electric potential. The move- p strated using chains of ions in linear radiofrequency - ment can be rather fast since it occurs in approximately traps;two-ionquantum gateshavebeen performed[2, 3] m one cyclotron period (∼2.5 µs for Ca+ in a B = 1 tesla and entanglement of up to 8 qubits has been demon- o magnetic field). Furthermore, an ion that starts at rest strated[4,5]. However,it iswidely assumedthatscaling t in one trapping zone automatically comes back to rest a the ion trap system to larger numbers of qubits will re- in the target zone. This paper reports the first realisa- s. quire arrays of micro-traps in which ion-qubits are shut- tion of a multiple Penning trap architecture capable of c tled between trapping zones [6]. A number of the key i performing this transfer of ions between trapping zones s elements of this approach have been demonstrated; ions separated in a plane perpendicular to the magnetic field y have been shuttled between different trapping zones in h axis. The controlledmovementofclouds ofionsbetween multiple trap architectures [7] whilst retaining internal p trapping zones is presented. state coherence and ion-pairs have been split with low [ lossofcoherence[8]. Sinceauniversalquantumcomputer 1 relies on the ability to perform quantum gates between v any pair of qubits in the quantum register the ability to II. DESIGN AND MANUFACTURING 6 sort ions is imperative: Assuming nearest neighbour in- 1 teractionsonly[18]itmustbe possibletoremoveagiven A. Boards 7 ion from a chain and bring it into contact with a differ- 2 . ent ion. This fundamentally requires ions to be moved The Penning trap array is made from printed circuit 1 0 in two dimensions, or more specifically that an ion can board. FR4 (Flame Retardant 4) board is a composite 9 be moved around a corner. This procedure has already ofanepoxyresinreinforcedwith awovenfibreglassmat. 0 been demonstrated in a T-junction radiofrequency trap The vacuum properties ofFR4 boardhave been studied, : array albeit with significant heating [9]. andtheoutgassingratefoundtobelowenoughforUHV v i As an alternative to ions held in radiofrequencytraps, applications [14]. Two boards are mounted facing each X ions contained in Penning traps, which use only static other, with the magnetic field direction normal to the r electric and magnetic fields to provide confinement, boardsurface. Copper pads on the boardsurfacesact as a have been proposed for applications in quantum simula- the trap electrodes. Close to the centre of the trap, the tion [10] and quantum information processing [11, 12]. potential is very similar to an ideal Penning trap. Single ions and pairs of ions have been imaged and The board design is shown in figure 1. Almost all aligned along the the axis of a Penning trap [13]. Ar- of the board area is covered with copper so that any raysofPenningmicro-trapscouldalsobe used,although effects due to charge buildup on the insulating surface the operation of very small Penning traps has yet to be are kept to a minimum. The electrodes are arranged in demonstrated. Moving ions in two dimensions in such rows of hexagons. The hexagonal pads in each row are trap arrayswill also be a requirement. It should be pos- electrically connected together with copper vias running sible tomoveionsalongthe magneticfieldaxisofaPen- through the board on to tracks on the rear side. Three ning trapusing the same kindoftechniques forionshut- hexagonalpadsoneachboard,labelledC infigure1,act tling that have been pioneered in radiofrequency traps, as the endcap electrodes for three trapping zones. Each sincethemagneticfieldhasnoeffectonmotioninthisdi- of these has a 1 mm diameter hole at the centre. Above rection. Motion perpendicular to the magnetic field axis andbelowtheendcapelectrodesarerowsofpadslabelled 2 B and D. The remaining electrodes are labelled A and E. Thetrapismadefromtwoparallelboardsfacingeach otherwithagapof5.0mm. Thedesignoneachisamir- Lensholder ror image of the opposing board. In normal operation Hotcathode the A, B, D, E electrodes on the pair of boards act as filament the ring electrodes for the three traps. There are seven Calciumoven 2mmdiameterholesbelowthetrappingregions. Fiveof PCB theseareusedtomakeconnectionstothefivesetsofelec- Stainlesssteelsupport trodes. These are connected to the vacuum feedthrough via wires bolted onto the rear of the boards. The outer- Coppersupport most two holes are required to mechanically attach the Feedthroughflange trap to the rest of the superstructure. 33.5 A B C D E 41 FIG.2: Diagram of thetrap. Somepartshavebeenremoved for clarity. Kapton wires are also used to connect to the oven and the filament. The 5.0 mm spacing between the pair of boards was chosen to make the trapping potential as harmonic as FIG. 1: Board design. Dimensions in mm. possible close to the centre of the trap (within 1 mm). The simulated potential along the central axis is shown A CNC Milling/Drilling machine was used to drill the in figure 3. holes in the board, which were then electroplated with copperusinganLPKFthrough-holeplatingsystem. This 0.9 process connects the front and rear sides of the board through the holes. The CNC machine was then used to mill away gaps between the electrodes. The gaps are U)U) 0.6 approximately 200 µm wide. // VV (( // φφ 0.3 B. Superstructure and Vacuum Chamber 0 Adiagramoftheassembledtrapisshowninfigure2. A −4 −2 0 2 4 pairof coppersupports areboltedto a CF40 flangewith zz//mmmm an 11 pin electrical feedthrough. Stainless steel plates are attached to the copper legs. The steel plates hold FIG. 3: Potential along the axis of thetrap. Simulation grid the trap boards, a filament and an oven (used for load- size was 0.1 mm. ing the trap), and the lens holder. All of the screws, metal washers and nuts are size M2 non-magnetic stain- Calciumionsarecreatedbyelectronimpactionisation less steel. which is facilitated by counterpropagating electron and The boards are held 5.0 mm apart by stainless steel atom beams. A 1 mm diameter hole in the steel plate, spacers. The spacers also provide an electrical connec- midway between the screws, is concentric with a 1 mm tion between the pair of boards. In the final iteration of diameter hole in each of the trap boards. These holes the trap,the spacerwhich wouldconnectelectrode C on allowtheatomicbeamandelectronbeamtopassthrough eachboardwasnotusedsothattheendcapsoneachside the centre of the trap. The positioning of the filament is could be connected independently. The spacer connect- chosentoallowelectronstopropagatealongthemagnetic ing electrode E is also absentso as to minimise the laser field lines. scatter. Kapton coated wires are used to connect the The lens is a 40 mm focal length singlet lens and is electrodes to the feedthrough pins underneath the trap. positioned20mmabovethecentreofthemiddletrapping 3 zone for maximum light gathering efficiency. A piece of constantan foil with a 6 mm diameter hole is used as a baffle abovethe trapto blocksome ofthe scatteredlight coming from areas not directly underneath the lens. III. SIMULATIONS To shuttle ions from one trap to another, the voltages FIG. 5: Example of an ion trajectory while moving from one on the various electrodes are briefly switched from their trap to the next. Lines of equipotential in the xy plane are normalvaluefortrappingtonewvaluesforshuttling. By shown in blue. applying ascending (or descending) voltages to A, B, C, D and E, an approximately linear electric field can be produced, perpendicular to the magnetic field direction. Figure 4 shows the electrostatic potential in the plane Whenthelinearelectricfieldisapplied,anioninitiallyat directly between the pair of trap boards, when the volt- rest will start to move along this direction but be pulled ages are set to ‘trap mode’ and to ‘shuttle mode’ re- round in a cycloid loop by the B field. By appropriately spectively. A typical trapping potential is formed when choosing the magnitude of the electric field, the size of thevoltagesontheelectrodesare(VA,VB,VC,VD,VE)= the cycloid loopwill be the same as the spacing between (0,0,2.5,0,0) volt. Note from figure 4(a), that even adjacenttraps. Byapplyingthesevoltagesforthecorrect though the electrodes are hexagonal, the shape of the amount of time, an ion will move out of one trap and potential close to the centre of the trap is almost per- cometorestatthecentreofthenexttrap. Applyingthe fectly circular. The potential in figure 4(b) is produced opposite voltagesfor a similardurationwill cause an ion when (VA,VB,VC,VD,VE) = (20,12.5,2.5,−7.5,−15) to move between traps in the opposite direction. volt. Figure 5 shows an example of the trajectory of an ion as it moves between a pair of trapping regions. In the simulations the electrode voltages, time dura- tions,initialconditions, etc.,canbe madeunrealistically perfect. To learn roughly how sensitive the ion shuttling 1.4 system is to experimental imperfections, various param- 1.2 eterswere changedandthe effectona simulatedionwas 1.4 1.2 1 observed. 1 φφ//VV 00..68 0.8 00 ..024 0.6 mmmm 2 4 0.4 // 2 xx -10 -5 x/mm 0 5 10 -4 -2 0 y/mm 00.2 alongalong 1 ntnt meme 0 ee cc (a)Trappingpotential plapla disdis −1 alal uu dd esiesi −2 RR 20 −18 −16 −14 −12 −10 15 VVoollttaaggeeoonneelleeccttrrooddeeEE//VV 20 15 10 10 φφ//VV 05 5 FIG. 6: Residual position of an ion relative to the centre of -5 thesecond trap, immediately after shuttling. B=0.9 tesla. -10 0 -15 4 -5 2 -10 -5 x/mm 0 5 10 -4 -2 0 y/mm --1150 cenTthree pofoitnhtseitnarfiggeutretr6apshiofwonheowoffatrheanvioolntamgeisssiessnthoet correct. The ion begins at rest at the centre of the first trap. ElectrodesA, B, C andD were set to 20,12.5,2.5 (b)Shuttling potential and -7.5 V respectively. Since the ion passes closest to electrode E during most ofits trajectory,a smallchange FIG. 4: Simulated electrostatic potentials in the xy plane in VE has a bigger impact on the path of the ion than a directly between the two trap boards. Note the change in smallchangein anyofthe other voltagesdoes. It canbe scale of the vertical axis. seen that 1 volt of error in VE causes an ion to miss its target by ∼0.5 mm. 4 0.1 The simulation is scanned over a range of values of ǫ. VV ee Foreachǫ,anoptimalvalueforaisfound(alongwithan // yy optimalpulsedurationτ), andthensomemeasureofthe gg erer final condition of the ion can be found for a particular nn ee neticnetic 0.05 iinngititahlecodnisdtiatinocne.aTlohnegbxestbevtawlueeenoftaheisifoonunadndbythmeinceimntirse- kiki alal ofthe targettrap, immediately after shuttling. The best uu dd duration, τ, is defined as the time between the applica- ResiResi tion of the shuttling voltages and the next minimum in 0 the ion’s kinetic energy. The best values of a and of the 2.6 2.7 2.8 2.9 pulse duration are shown in figure 8. PPuullsseedduurraattiioonn//µµss 19 26 FIG. 7: Residual kinetic energy of an ion, immediately after shuttling an ion in a field of 0.9 tesla. VV VV 24 // // aa aa Figure 7 shows how an ion gains kinetic energy if the 22 shuttling voltages are applied for too long or too short a 16 time. The voltages were set appropriately to move the 0 0.5 1 0 0.5 1 ion to the centre of the second trap in a single cycloid ǫǫ ǫǫ loop. It can be seen that the kinetic energy acquired by (a)Optimal voltage(symmetric) (b)Optimalvoltage(asymmetric) an ion varies quadratically with t − tideal, and reaches 4 4 roughly 100 meV when the duration is wrong by 100 ns. There is a range of possible sets of voltages which will ss ss µµ µµ 2 2 cause an ion to move between the centres of adjacent // // traps. When the ion is initially at rest and perfectly ττ ττ centred in the first trapping zone, all of these different 0 0 voltage sets will produce good results. However, if the 0 0.5 1 0 0.5 1 ion begins at a positionslightly offset fromthe trap cen- ǫǫ ǫǫ tre then this initial imperfection is amplified by different (c)Optimalduration(symmetric) (d)Optimal duration amounts depending on the specific set of voltages used. (asymmetric) Since the ion moves perpendicular to the magnetic field, adisplacementoftheionrelativetothetrapcentrealong FIG.8: Simulatedoptimalvoltageandtimingparametersfor z is similar to a misalignment of the trap with the mag- B=0.9 tesla. The truecyclotron period is also shown in (c) neticfield. Findingthebestpossibleparametersisanon- and (d). trivial problem. It would involve finding a line in four dimensional voltage-space (VA,VB,VD,VE) for which an Figure9showhowdifferentvaluesofǫleadtodifferent ion with ideal initial conditions reaches the centre of the final conditions of an ion. The initial condition is such targettrap,andthenfindingthe pointonthislinewhich thatthe ionis atrestbut displacedby 0.1mm alongthe produces a optimal final condition given a range of real- axis of the first trap. The final position is plotted, along istic initial conditions. To simplify matters, we consider with the final velocity, the final kinetic energy, and final asetofvoltageswhicharesymmetricaboutelectrodeC: total energy. All of these measures should ideally be as small as possible. VA 2.5+a It was found that the symmetric voltage set, (1), pro-  VB   2.5+ǫa  ducedbetterresults(lowerfinalKEetc.) thantheasym-  VC = 2.5  (1) metric set, (2). The asymmetric voltage sets cause the VD   2.5−ǫa  ion to gain significantly more kinetic energy. It was also  VE   2.5−a  found that the best results were obtained when ǫ ≈ 0.5 – i.e. a linear step down of the five electrode voltages. and also a set which is not symmetric: Aninitialdisplacementofthe ionalongxory hasless VA 0.0 effect on the outcome than an initial displacement along  VB   0.0  z. Other simulations show that that for typical voltage  VC = 2.5  (2) sets there is an overall restoring force pushing ions to- VD   2.5−ǫa  wards z = 0. Unfortunately, even with this restoring  VE   2.5−a  force present, any initial displacement or initial velocity will cause an ion to gain energy when moving be- Theasymmetricsethastheadvantagethatonlytwoelec- tween traps. An initial displacement of 0.1 mm along z trodes need to be switched instead of four. isroughlyequivalenttoamisalignmentbetweenthetrap 5 0.2 0.2 cial digital pulse generator (Stanford Reseach Systems mm mm DG535)isusedto produceTTLpulses. TheTTLpulses mm mm // 0.1 // 0.1 are then converted into pulses of the required voltages. rr|||| rr|||| This amplification is done using discrete mosfet transis- 0 0 tors and resistors outside the vacuum chamber. The 0 0.5 1 0 0.5 1 ǫǫ ǫǫ rise time and fall time of the voltage pulses are both (a)RMSdisplacement (b)RMSdisplacement 40±10ns,withlessthan5%overshoot. Thedigitalpulse (sym) (asym) generatoristriggeredfromaLabViewprogramviaaNa- 2 tionalInstrumentscard. Thegeneralisedlayoutisshown 0.1 −−11µµ/mms/mms 0 −−11µµ/mms/mms isanwgeifitgcrhuaimrnegp1se0l.tehcNatrtootaneritcehstaiytsptdihciffaislelrsyecnhatepmpfrleoiemtdottshoheustahtnuleatltioloegnusieounvssoinlitng- vvzz −0.1 vvzz −1 RF trap arrays [9, 15]. 0 0.5 1 0 0.5 1 ǫǫ ǫǫ LEFT/RIGHT (c)Velocityalongz (sym) (d)Velocity alongz (asym) PRECISE 0.002 0.3 Computer TRIGGER TTL pulse TTL Electronics Generator VV KE/eVKE/eV 0.001 KE/eKE/e SET TIMES (GPIB) SPHUULTSTELSE 0 0 SET VOLTAGES x 4 0 0.5 1 0 0.5 1 ǫǫ ǫǫ Detector Trap (e)KE (sym) (f)KE(asym) 0.3 0.003 VV VV ee FIG. 10: Generalised layout of the system used for shuttling ee // KE+PE/KE+PE/ KE+PEKE+PE ions. 0 0 0 0.5 1 0 0.5 1 ǫǫ ǫǫ V. RESULTS (g)Total energy(sym) (h)Total energy(asym) FIG. 9: Final conditions of an ion after shuttling for vari- Figure11showsthefluorescencefromaninitiallylarge ous voltage sets. The ion was initially at rest and displaced cloud of ions in the central trapping zone. After a few 0.1 mm along z. B=0.9 tesla. seconds, voltage pulses are applied and the ion cloud is movedintoadifferenttrap. Thesignalleveldropstothe background level because fluorescence is only collected and the magnetic field of just half a degree. Clearly this from the central trap. After a few more seconds, the misalignmentmustbe reducedasmuchaspossiblewhen reversesetofvoltagepulsesareapplied,androughly75% attempting to shuttle ions in the real trap. of the signal returns. As the process is repeated, ions are lost on eachjourney, but some ions still remain after 20 shuttles (10 return trips). The voltages used were IV. ELECTRONICS (VA,VB,VC,VD,VE) = (20.0,12.5,2.5,−7.5,−15.7)volt, and (VA,VB,VC,VD,VE) = (−15.7,−7.5,2.5,12.5,20.0) In order to produce the voltagepulses needed to shut- volt. tle ions between traps, a system of high speed switching Aninterestingfeaturecanbeseeneachtimeamedium electronics was developed. Each electrode (except for sized cloud is moved back into the central trap. A very electrodeC)needstobeswitchablebetween0V(orclose smallamountofsignalreturnsinstantly(inlesstimethan to 0 V) for trapping, a positive voltage of up to around one bin width). The signal level then rises fairly sharply 20 V for shuttling ions in one direction, and a negative (within around 1-3 seconds), but plateaus out and re- voltage of similar magnitude for shuttling in the other mainsquitelowforupto20seconds,afterwhichthesig- direction. The voltages need to be set precisely, and to nal level sharply rises again to its maximum value. This remain stable over time. The switching needs to occur behaviour does not seem to occur for very large clouds on a timescale which is short compared to the length of or for very small clouds. A possible explanation for this the pulse. The pulse length must be set precisely and isasfollows: Whenanioncloudismovedbetweentraps, must also remain stable over time. There should also be thecloudexpandsduetoCoulombrepulsionandtheions anegligiblerelativetimedelaybetweenthepulsesonthe become much hotter. Some small fraction of the cloud various electrodes. however,will intersectthe laser beam waist and are cool To generate pulses of a precise duration, a commer- enough to produce fluorescence straight away. The cy- 6 11 ions have not yet been reliably shuttled. To attempt to −− ss pushtheshuttlingefficiencyupabove75%,twoimprove- tsts 400 nn ments are being made made: A new electronics system uu coco is being built, with faster rise and fall times of ∼10 ns. 00 00 Secondly,coils are being wound to produce a smallmag- 00 11 netic field perpendicular to the main field, thus allowing // 200 ee the angle of the field to be finely adjustable. We will cc nn ee report the results of these improvements in our setup in cc ss ee future. rr oo uu FlFl 0 0 100 200 VI. OUTLOOK AND COMPARISON WITH TTiimmee//ss OTHER WORK FIG. 11: Fluorescence from a cloud of ions, repeatedly shut- Thisworkcanbe comparedto similarworkperformed tled away from thecentral trap and back again. using segmented RF traps. Huber et al. report an efficiency of 99.0% for transporting single ions over a dis- tance of 2 mm and back in a round trip time of 20 µs, clotron and axial motions of the ions are cooled, and so using a segmented PCB based linear Paul trap [15]. the signal level rapidly increases. The cloud then gradu- Hensinger et al. report 100% efficiency (881 out 882 at- ally shrinks in size as energyis transferredinto the mag- tempts) for transporting ions round a T-junction corner netronmotion(thelaserbeamwasoffsettofacilitatethis in 30 µs in a trap made from gold and alumina [9]. effect) [16]. The smaller and denser the cloud becomes, Onepotentialadvantageofoursystemisthattheshut- the more strongly it interacts with the laser beam, so tlingtimeislowerbyaboutanorderofmagnitude(using there is a runawayeffect causingthe finalsignalincrease a 1 tesla field). If a higher field (or a lighter ion) is used, to be rapid. sub µs transport times would be possible [19]. The final signal level after each round trip, plotted as afunctionofthe numberofshuttles,givesagoodfittoa Another clear advantage of our system is that the decayingexponential. Thefreeparameterofthisfitgives switching of electrode voltages is relatively simple. the efficiency of the shuttling procedure. Referring back Transport of ions between trapping zones in an RF trap to figure 6, changing one of the voltages away from its has so far required a much more complicated set of pre- ideal value will cause an ion to land away from the cen- ciselycontrolledanaloguevoltagerampstobeappliedto tre of the target trap. This was checked experimentally, the various electrodes. altering one of the voltages and observing the transfer For the trap described in this paper, the best set of efficiency. The results are shown in figure 12, where the shuttling voltages was an ascending series over all five simulatedresidualdisplacementisalsoshown. Twoshut- electrodes. However it may be possible to build an even tling sequences were performed for eachdata point. The simpler trap with just three electrodes: a row of end- errorbarissimplythedifferencebetweenthetwo. Itcan caps, and two ring type electrodes. The shuttling could be seen that the measured efficiency does indeed peak be performed by pulsing just one of the ring electrodes, where the simulation predicts the optimal voltage. and pulsing the other one to go in the other direction. Although this goes somewhat against the simulation re- yy 2 sults shown above, the electronics would be greatly sim- cc enen 0.9 Efficiency(measured) plified. No negative voltages or tri-state switches would cici RR ffiffi Residualposition(Simulated) ee be required. If a similar but smaller trap is built, then urneyeurneye 0.6 1 sidualpsidualp tthhee rterqaupirwedasshduesttiglinnegdvsoultcahgetshawtouthlde aslhsuottbleinsgmvaollletar.geIsf oo 0 oo ereturnjereturnj 0.3 −1 sition/msition/m wbshyeurhtetigl∼ihn5gpVevr,oflottrhamegneantwchoeeuTpldTulLbse,esCtcuMonuOelddS bobyreEptuCronLdinudgceevtdihceedsip.reoTcwthelyer agag mm supplyofthefastlogicdeviceitself. Thiswouldnotonly erer AvAv 0 −2 simplify the electronics, it would also allow the remark- −18 −16 −14 −12 −10 able performance of modern digital ICs to be directly VVoollttaaggeeoonneelleeccttrrooddeeEE//vvoolltt utilised. A further advantage of the scalable Penning trap con- FIG.12: Efficiencyofthereturntripshuttlingprocedure,for cept is seen when considering the transportation of ions various voltages. round corners. Although a near perfect efficiency is reported by Hensinger et al., they state that in their sim- Although single ions have been trapped and laser ulations, an ion acquires about 1.0 eV of kinetic energy cooled for extended periods of time in this trap, single during a corner-turning protocol [9]. Real ions in our 7 system certainly gain some energy after shuttling, but between each trapping region would certainly be a chal- at least in principle the gain in energy can be extremely lengingtechnicalfeat,buttheresultspresentedherehave small. Moving an ion round a corner in a multiple Pen- demonstrated the first proof of principle of the scalable ning trap would involve nothing more than performing Penning trap. two regular cycloid loops at right angles to each other. Alternatively, moving around a corner could mean shut- tlingalongthetrapaxisbetweentwoaxiallyalignedtraps Acknowledgments (using standard techniques), followed by a cycloid loop perpendicular to the magnetic field. The electrodes of a future trap should be designed in This work is supported through the EU integrated such a way as to facilitate ion transport round a corner, project SCALA, and by the Engineering and Physical and possibly evenalong all three dimensions. Building a Sciences Research Council (EPSRC) of the UK. SA ac- threedimensional(orevenjusttwodimensional)trapar- knowledges a fellowship from the Commonwealth Schol- ray,with the ability to move ions in a controlledmanner arships Commission, U.K. [1] H. Häffner, C. F. Roos, and R. Blatt, Physics Reports [10] D. Porras and J. I. Cirac, Phys. Rev. Lett. 96, 250501 469, 155 (2008). (2006). [2] F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, [11] J. R. Castrejón-Pita, H. Ohadi, D. R. Crick, D. F. A. G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, Winters, D. M. Segal, and R. C. Thompson, J. Mod. J. Eschner, and R. Blatt, Nature422, 408 (2003). Opt. 54, 1581 (2007). [3] D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Bar- [12] J. L. K. Koo, Ph.D. thesis, Imperial College London rett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, (2003). T. Rosenband,et al., Nature 422, 412 (2003). [13] D. R. Crick, H. Ohadi, I. Bhatti, R. C. Thompson, and [4] D. Leibfried, E. Knill, S. Seidelin, J. Britton, R. B. D. M. Segal, Optics Express 16, 2351 (2008). Blakestad,J.Chiaverini,D.B.Hume,W.M.Itano,J.D. [14] C. Rouki, L. Westerberg, and the CHICSi development Jost, C. Langer, et al., Nature 438, 639 (2005). group, Physica ScriptaT104, 107 (2003). [5] H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. C. [15] G. Huber, T. Deuschle, W. Schnitzler, R. Reichle, al kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, K. Singer, and F. Schmidt-Kaler, New J. Phys. 10, P.O. Schmidt,et al., Nature 438, 643 (2005). 013004 (2008). [6] D. Kielpinski, C. Monroe, and D. J. Wineland, Nature [16] W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 417, 709 (2002). (1982). [7] M. Barrett, J.Chiaverini, T. Schaetz, J. Britton, [17] D. Reiss, K. Abich, W. Neuhauser, C. Wunderlich, and W.Itano,J.Jost,E.Knill,C.langer,D.Leibfried,R.Oz- P. E. Toschek, Phys. Rev.A 65, 053401 (2002). eri, et al., Nature429, 737 (2004). [18] Schemes exist for which nearest neighbour interactions [8] M. A. Rowe, A. Ben-Kish, B. Demarco, D. Leibried, are not required. See[17]. V.Meyer,J.Beall,J.Britton,J.Hughes,W.Itano,B.Je- [19] Ontheotherhand,futuregenerationsofsmaller, tighter lenkovic,et al., QuantumInformation and Computation RF traps would also allow reliable shuttling at faster 2, 257 (2002). speed. An 80% efficiency for a single trip performed in [9] W. K. Hensinger, S. Olmschenk, D. Stick, D. Hucul, just 3 µs was reported in [15]. M.Yeo,M.Acton,L.Deslauriers,andC.Monroe, Appl. Phys.Lett. 88, 034101 (2006).