The linear trap used in this experiment has four goldplated I. INTRODUCTION

Transcription

1 The liner trp used in this experiment hs four goldplted cermic lde electrodes with their edges runrxiv: v2 [physics.tom-ph] 23 Mr 2016 Active Stiliztion of Ion Trp Rdiofrequency Potentils K. G. Johnson, 1 J. D. Wong-Cmpos, 1 A. Restelli, 1 K. A. Lndsmn, 1 B. Neyenhuis, 1 J. Mizrhi, 1 nd C. Monroe 1 Joint Quntum Institute nd University of Mrylnd Deprtment of Physics, College Prk, Mrylnd 20742, USA (Dted: 24 Mrch 2016) We ctively stilize the hrmonic oscilltion frequency of lser-cooled tomic ion confined in rf Pul trp y smpling nd rectifying the high voltge rf pplied to the trp electrodes. We re le to stilize the 1 MHz tomic oscilltion frequency to etter thn 10 Hz, or 10 ppm. This represents suppression of mient noise on the rf circuit y 34 db. This technique could impct the sensitivity of ion trp mss spectrometry nd the fidelity of quntum opertions in ion trp quntum informtion pplictions. I. INTRODUCTION Chrged prticles re often controlled with rdiofrequency (rf) electricl potentils, whose field grdients provide time-verged (ponderomotive) forces tht form the sis for pplictions such s qudrupole mss filters, ion mss spectrometers, nd rf (Pul) ion trps 1,2. These rf potentils, typiclly hundreds or thousnds of volts t frequencies rnging from 1kHz to 100 MHz, drive high impednce lods in vcuum nd re usully generted with rf mplifiers nd resonnt step-up trnsformers such s qurter-wve or helicl resontors 3. Such circuitry is susceptile to fluctutions in mplifier, mechnicl virtions of the trnsformer, nd temperture drifts in the system. Ion trps re prticulrly sensitive to these fluctutions, ecuse the rf potentil determines the hrmonic oscilltion frequency of the trpped ions. Stle trp frequencies re crucil in pplictions rnging from quntum informtion processing 4,5 nd quntum simultion 6,7 to the preprtion of quntum sttes of tomic motion 8, tom interferometry 9, nd quntumlimited metrology 10. Actively stilizing rf ion trp potentils requires the fithful smpling of the rf potentil. Proing the signl directly t the electrodes is difficult in vcuum environment nd cn lod the circuit or spoil the resontor qulity fctor. On the other hnd, smpling the potentil too fr upstrem is not necessrily ccurte, owing to downstrem inductnce nd cpcitnce. Here we ctively stilize the oscilltion frequency of trpped ion y noninvsively smpling nd rectifying the high voltge rf potentil etween the step-up trnsformer nd the vcuum feedthrough leding to the ion trp electrodes. We use this signl in feedck loop to regulte the rf input mplitude to the circuit. We stilize 1 MHz trpped ion oscilltion frequency to < 10 Hz fter 200 s of integrtion, representing 34 db reduction in the level of trp frequency noise nd drift, over locking ndwidth of up to 30 khz. The ion is trpped in liner rf trp, which consists of two-dimensionl rf qudrupole electric field superposed with sttic qudrupole electric field to provide confinement long the longitudinl direction 11. Longitudinl confinement is typiclly set much weker thn the z y rf lde x sttic lde DETAIL B (xil confinement) ion DETAIL A (rdil confinement) sttic lde rf lde TOP FRONT FIG. 1. Liner Pul trp creted with four gold-plted lde electrodes tht re held in plce y n insulting mount. An ion is confined in etween the electrodes through comintion of rf nd sttic potentils pplied to the electrodes. Ech lde is split longitudinlly into 5 segments tht re electriclly isolted on the sttic ldes nd electriclly connected on the rf ldes. The trnsverse distnce from the ion xis to ech electrode is R = 200 µm, nd the length of the centrl longitudinl segments is 400 µm. trnsverse confinement, so tht crystl of lser-cooled ions cn reside long the x = y = 0 rf field null without feeling the effects of rf-induced micromotion 1. The trnsverse confinement, dictted y the rf fields, is used for mny pplictions ecuse motion long these directions is t higher frequency nd the norml mode spectrum for chin of ions cn e tuned 12. Liner ion trps exist in vriety of topologiclly equivlent electrode configurtions, even with electrodes ll in single plne for ese in lithogrphic friction 13. B A

2 2 Servo Controller rf oscilltor FM RF I LO phse shifter set point + - Proportionl Integrl I LO RF freq. mixer mp directionl coupler CPLin CPLout qurterwve resontor cpcitive divider ion trp digitl divider rectifier frequency counter set point + - Servo Controller Proportionl Integrl rf oscilltor I LO RF freq. mixer mp isoltor qurterwve resontor cpcitive divider ion trp rectifier FIG. 2. Schemtics of ion trp rf drive with ctive stiliztion of the ion oscilltion frequency ω. () Stiliztion of the rtio of rf potentil mplitude to frequency V 0/Ω (red), with seprte feedck loop (purple) tht locks the rf drive frequency Ω to the resonnt frequency of the step-up trnsformer. () Stiliztion of the rf potentil mplitude V 0 only, with fixed rf drive frequency (used in the experiment reported here). ning prllel to the longitudinl (z) xis of the trp s shown in Fig. 1. Two opposite ldes re driven with n rf potentil with respect to the other two sttic ldes, creting the trnsverse (x-y) qudrupole confinement potentil. Approprite sttic potentils pplied to the longitudinlly-segmented sttic ldes serve to confine the ions long the z-xis. The rf electric qudrupole potentil ner the center of the trp V (x, y) = µv0 2R (x 2 2 y 2 ) cos Ωt is set y the rf mplitude on the trp electrode V 0, the distnce from the ion to the electrodes R, the rf drive frequency Ω, nd dimensionless geometric efficiency fctor µ 0.3 for the geometry of Fig. 1. A prticle with chrge e nd mss m inside the trp feels resulting ponderomotive psuedopotentil U pon = e2 4mΩ V 2 = e2 µ 2 V mR 4 Ω (x 2 + y 2 ), with hrmonic 2 oscilltion frequency 2, ω = eµv 0. (1) 2mΩR 2 This expression is vlid under the pseudopotentil pproximtion where ω Ω 1,2, nd we do not consider the residul trnsverse forces from the sttic potentils, ecuse they re reltively smll nd stle. One pproch to stilize the ion oscilltion frequency is to control the rtio V 0 /Ω, in cses where the rf drive frequency is itself dithered to mintin resonnce with the step-up trnsformer. A feedck system of this style is shown in Fig. 2, where the lower feedck loop (red) stilizes the rtio V 0 /Ω nd the upper feedck loop (purple) locks the vrile rf oscilltor frequency to the resonnce of the trnsformer, which might drift due to mechnicl or temperture fluctutions. The min difficulty with this pproch is the required performnce of the digitl divider circuit, which must hve precision s good s the desired stility, nd e fst enough to stlize the system t t the desired ndwidth. Moreover, higher order corrections to the trp frequency eyond the psuedopotentl expression of Eq. 1 depend on terms tht do not scle simply s the rtio V 0 /Ω. Therefore, we insted stilize the rf potentil mplitude V 0 lone, nd use fixed frequency rf oscilltor nd pssively stle trnsformer circuit, s depicted in Fig. 2. II. TRAP RF STABILIZATION We stilize the rf confinement potentil y smpling the high voltge rf signl supplying the ion trp electrode nd feeding it ck to frequency mixer tht controls the upstrem rf oscilltor mplitude. As shown in the schemtic of Fig. 2, n rf signl t Ω/2π = 17 MHz nd 8dBm is produced y function genertor (SRS DS345) nd sent through the Locl Oscilltor (LO) port of level 3 frequency mixer (Mini-Circuits ZX05-1L-S), with conversion loss of 5.6 db. The rf port of the mixer is connected to rf mplifier (Mini-Circuits TVA-R5-13)

3 3 FIG. 3. Helicl qurter-wve resontor (trnsformer) with 1:100 cpcitive divider (0.2 pf nd 20 pf) mounted inside of the resontor ner the high voltge side. The divider smples V 0 for feedck. A rigid wire is soldered from the output portion of the copper resontor coil to the copper-cld epoxy circuit ord contining the dividing cpcitors. The resontor drives the cpcitnce C trp of the vcuum feedthrough nd ion trp electrodes. with self-contined cooling system, providing of 38 db. The mplifier signl is fed into n ntenn tht inductively couples to 17 MHz qurter-wve helicl resontor nd provides impednce mtching etween the rf source nd the circuit formed y the resontor nd ion trp electrode cpcitnce 3. The ntenn, resontor, nd equivlent ion trp cpcitnce C trp re shown in Fig. 3, nd exhiit n unloded qulity fctor Q U 600. A cpcitive divider smples roughly 1% of the helicl resontor output, using C 1 = 0.2 pf nd C 2 = 20 pf cermic cpcitors (Vishy s QUAD HIFREQ Series) with temperture coefficients of 0 ± 30 ppm/ C. With C 1 C trp nd residul inductnce etween the divider nd the trp electrodes much smller thn the resontor inductnce itself, the divider fithfully smples the rf potentil within few centimeters of the trp electrodes nd does not significntly lod the trp/trnsformer circuit. The cpcitors re surfce-mounted to milled coppercld epoxy circuit ord nd instlled inside the shielded resontor cvity, s digrmmed in Fig. 3. The smpled signl psses through rectifier circuit (Fig. 4) consisting of two Schottky diodes (Avgo HMPS-2822 MiniPk) configured for pssive temperture compenstion 14 nd low-pss filter giving ripple mplitude 10 db elow the diode input signl mplitude. High qulity foil resistors nd cermic cpcitors re used to reduce the effect of temperture drifts. The entire rectifying circuit is mounted inside rss housing (Crystek Corportion SMA-KIT-1.5MF) s shown in Fig. 4. The smpling circuit hs ndwidth of 500 khz, limited y the 5 kω/68 pf RC filter. The rtio of dc output voltge to rf input voltge mplitude, including the cpcitive divider, is 1 : 250 t drive frequency of 17 MHz, 1 : 330 t 100 MHz, nd 1 : 870 t drive frequency of 1 MHz. The dc rectified signl is compred to stle setpoint voltge (Liner Technology LTC6655 5V reference mounted on DC2095A-C evlution ord) with vrile control (Anlog Devices EVAL-AD5791 nd ADSP- BF527 interfce ord), giving 20-it set-point precision nd ±0.25ppm stility. The difference etween these inputs the error signl is then mplified with proportionl nd integrl (New Focus LB1005 servo controller) nd fed ck to regulte the upstrem rf oscilltor mplitude vi the frequency mixer descried ove. Figure 5 shows the response of the system for vrious servo controller settings when signls over rnge of frequencies re injected into the system t the mplifier input. The overll frequency response of the feedck loop is limited to ndwidth of 30 khz, consistent with the linewidth Ω/(2πQ U ) of the helicl resontor trnsformer. III. ION OSCILLATION FREQUENCY We next chrcterize the rf mplitude stiliztion system y directly mesuring the trnsverse motionl oscilltion frequency of single tomic 171 Y + ion confined in the rf trp. We perform opticl Rmn sidend spectroscopy 8 on the F = 0, m f = 0 nd F = 1, m f = 0 clock hyperfine levels of the 2 S 1/2 electronic ground stte of 171 Y +. This tomic trnsition hs frequency splitting of ω 0 /2π = GHz nd cquires frequency-modulted sidends t ω 0 ± ω due to the hrmonic motion of the ion in the trp, with ω/2π 1 MHz. Before ech mesurement, the ion is Doppler cooled on the 2 S 1/2 to 2 P 1/2 electronic trnsition t wvelength of nm 8. The ion is next prepred in the stte through opticl pumping, nd following the sidend spectroscopy descried elow, the stte ( or ) is mesured with stte-dependent fluorescence techniques 15. The oscilltion frequency is determined y performing Rmsey spectroscopy 16 on the upper (lue) virtionl sidend of the clock trnsition t frequency ω 0 + ω. Becuse the tomic clock frequency ω 0 is stle nd ccurte down to level etter thn 1 Hz, drifts nd noise on the sidend frequency re dominted y the oscilltion frequency ω. The sidend is driven y stimulted Rmn process from two counter-propgting lser light fields with etnote ω L tuned ner the upper virtionl sidend frequency 17,18. Following the usul Rmsey interferometric procedure 16, two π/2 pulses seprted y time τ = 0.4 ms drive the Rmn trnsition. After the pulses re pplied, the proility of finding

4 servo ndwidth khz 3 khz khz 300 khz Frequency (Hz) 4 10 stilized model FIG. 5. Suppression of injected noise in the stiliztion circuit for vrious levels of feedck. The rf drive is wekly mplitude-modulted t frequencies swept from 4 Hz to 100 khz vi vrile ttenutor inserted efore the rf mplifier. The mplitude of the resulting ripple on the error signl is mesured s function of the servo controller ndwidth. The oserved overll loop ndwidth of 30 khz is consistent with the linewidth of the helicl resontor trnsformer. 0.8 P(δ) 0 Rmsey Fringe Contrst Noise Power on Error Signl (db) FIG. 4. () Schemtic circuit digrm depicting the components of the pick-off voltge divider nd temperture-compensting rectifier. () Photogrph of the connectorized housing nd mounted rectifier circuit δ (MHz) τ (ms) FIG. 6. Rmsey fringe contrst s function of the Rmsey time τ etween π/2 pulses, with nd without feedck. The gry line is model in which motionl heting cuses Rmsey fringe decoherence in 0.5 ms. Inlys nd show full Rmsey fringe mesurements nd fits for two different vlues of τ stilized ω/2π (MHz) the ion in the i stte P (δ) = (1 + C cos τ δ)/2 is smpled, where δ = ωl (ω0 + ω) is the detuning of the etnote from the sidend nd C is the contrst of the Rmsey fringes. The Rmsey experiment is repeted 150 times for ech vlue of δ in order to oserve the Rmsey fringe pttern P (δ) nd trck the vlue of ω. Becuse this Rmn trnsition involves chnge in the motionl quntum stte of the ion, the Rmsey fringe contrst depends on the purity nd coherence of tomic motion. For short Rmsey times, the mesured contrst of 0.8 is limited y the initil therml distriution of motionl quntum sttes, nd for Rmsey times τ > 0.5 ms, the fringe contrst degrdes further (Fig. 6), which is con 1 for initil sistent with decoherence timescle (2n 0 n ) therml stte n 0 = 15 qunt nd motionl heting rte n = 100 qunt/s19. Through Rmsey spectroscopy, we smple the ion trp oscilltion frequency ω t rte of 2.1 Hz for 80 minutes with on the rf potentil, nd then for nother 80 minutes while ctively stilizing the rf potentil. A typicl time record of the the mesurements over these 160 minutes is shown in Fig. 7. Feedck control clerly improves the stility of the ion oscilltion frequency, nd we oserve > 30 db suppression of drifts over long Time (min) FIG. 7. Time dependence of the ion hrmonic oscilltion frequency ω plotted over the course of 160 minutes with nd without ctive stiliztion. With feedck there is cler reduction in noise nd drifts (prt from mesurement shot noise, reflected y the fst fluctutions in the dt). Inlys nd show mgnified sections of the plot covering 4 minutes of integrtion. times. From these mesurements, we plot the Alln devition20 of the oscilltion frequency in Fig. 8 s function of integrtion time T. When the system is stilized, the Alln devition in ω is nerly shot-noise limited (decresing s 1/ T ) up to 200 s of integrtion time,

5 5 Alln Devition (Hz) stilized crrier Component Stility Cpcitive Divider 0 60 ppm Rectifier 0.1 ppm Voltge Reference 0.25 ppm rf source freq. 0.1 pp Cles Unknown Averging Time (s) FIG. 8. Alln devition dt of the seculr frequency ω while the system is with nd without feedck, s well s the Alln devition of the quit crrier trnsition. The Alln devition curves re clculted from the time record shown in Fig. 7, long with similr mesurement performed on the crrier trnsition. with minimum uncertinty of etter thn 10 Hz, or 10 ppm, representing 34 db suppression of mient noise nd drifts. Without feedck, the trp frequency devition drifts upwrd with integrtion time. For integrtion times shorter thn 7 s, there is not suffcient signl/noise in the mesurements to see the effects of feedck stiliztion. However, s shown in Fig. 5, the lock is le to respond to error signls up to ndwidth of 30 khz, nd we expect significnt suppression of noise t these higher frequencies s well. Although the Alln devition of the oscilltion frequency in the stilized system improves with longer verging time s expected, it drifts upwrd for period just fter T = 50 s. We confirm this drift ppers in the ion oscilltion frequency ω nd not the driving field ω L or the ion hyperfine splitting ω 0 y performing the sme experiment on the clock crrier trnsition ner etnote frequency ω L = ω 0 insted of the upper sidend ω L = ω 0 + ω. As shown in Fig. 8, the mesured Alln devition of the crrier continues downwrd eyond T = 50 s, mening tht the ion oscilltion frequency is indeed the limiting fctor t long times. The min contriution is likely the cpcitive divider, which is comprised of two cpcitors ech with temperture coefficient of ± 30 ppm/ C. Given the voltge divider configurtion, the net temperture coefficient cn rnge from 0 60 ppm/ C depending on how well the cpcitors re mtched. Instilities in the rectifier cn rise from vriility in the junction resistnce of the diodes. In series with 5 kω resistor, the 0.01Ω/ C junction resistnce gives net temperture coefficient of out 0.2 ppm/ C in the rectifier response. This is roughly equl to the temperture coefficient of the resistors used in the rectifier circuit. By using the temperture-stilized circuit shown in Fig. 4, we estimte the net temperture coefficient of the rectifier response is reduced to 0.1 ppm/ C. Performnce of the circuit is lso helped y pssively stilizing components within the feedck loop s much s possile, such s temperture regulting the rf mplifier which feeds the resontor nd using pssive mixer insted of powered voltge vrile ttenutor. The helicl trnsformer is prticulrly sensitive to temperture fluctutions nd mechnicl virtions, which lters the resonnce frequency nd qulity fctor. (Ensuring the helicl coil is seled st ir currents cn e more importnt thn correcting smll drifts in mient temperture.) If the resonnt frequency of the trnsformer drifts too fr, then feedck circuit with fixed frequency source (s used here nd shown in Fig. 2) will cll for more input power, nd the servo system could possily run wy nd ecome unstle. However, the resulting impednce mismtch from the off-resonnt coupling will cuse the servo to mintin the sme mount of dissipted power in the resontor 3 nd not necessrily ffect further drifts. In ny cse, we do not oserve such servo runwy. IV. LIMITS AND NOISE SOURCES It should e possile to stilize the rf trp frequency much etter thn the oserved 10 ppm y improving pssive drifts outside of feedck control. These include the cpcitive divider tht smples the rf, the rectifier, the stle voltge reference, rf source frequency, nd certin cles in the rf circuitry. Most of these components will hve residul drifts with temperture, mechnicl strins, or other uncontrolled noise. Below is tle of ll crucil components outside of feedck control nd their estimted contriution to the instility. V. ACKNOWLEDGMENTS We thnk N. M. Linke, S. Denth, C. Figgtt, D. Hucul, P. W. Hess, C. Senko nd K. Wright for useful discussions. This work is supported y the NSF Physics Frontier Center t JQI. 1 H. Dehmelt, Rev. Mod. Phys. 62, 525 (1990). 2 W. Pul, Rev. Mod. Phys. 62, 531 (1990). 3 J. D. Siverns, L. R. Simkins, S. Weidt, nd W. K. Hensinger, Appl. Phys. B 107, 921 (2012). 4 D. Winelnd nd R. Bltt, Nture 453, 1008 (2008). 5 C. Monroe nd J. Kim, Science 339, 1164 (2013).

6 6 6 P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss- Feig, S. Michlkis, A. V. Gorshkov, nd C. Monroe, Nture 511, 198 (2014). 7 P. Jurcevic, B. P. Lnyon, P. Huke, C. Hempel, P. Zoller, R. Bltt, nd C. F. Roos, Nture 511, 202 (2014). 8 D. Leifried, R. Bltt, C. Monroe, nd D. Winelnd, Rev. Mod. Phys. 75, 281 (2003). 9 K. G. Johnson, B. Neyenhuis, J. Mizrhi, J. D. Wong-Cmpos, nd C. Monroe, Phys. Rev. Lett. 115, (2015). 10 C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Winelnd, nd T. Rosennd, Phys. Rev. Lett. 104, (2010). 11 M. G. Rizen, J. M. Gillign, J. C. Bergquist, W. M. Itno, nd D. J. Winelnd, Phys. Rev. A 45, 6493 (1992). 12 S.-L. Zhu, C. Monroe, nd L.-M. Dun, Phys. Rev. Lett. 97, (2006). 13 J. Chiverini, R. B. Blkestd, J. Britton, J. D. Jost, C. Lnger, D. Leifried, R. Ozeri, nd D. J. Winelnd, Quntum Inf. Comput. 5, 419 (2005). 14 H. Eriksson nd R. W. Wugh, A Temperture Compensted Liner Diode Detector, Design Tip, Agilent Technologies (2000). 15 S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Mtsukevich, P. Munz, nd C. Monroe, Phys. Rev. A 76, (2007). 16 N. F. Rmsey, Rev. Mod. Phys. 62, 541 (1990). 17 J. Mizrhi, Neyenhuis, K. G. Johnson, W. C. Cmpell, C. Senko, D. Hyes, nd C. Monroe, Appl. Phys. B 114, 45 (2013). 18 D. Hyes, D. N. Mtsukevich, P. Munz, D. Hucul, Q. Qurishi, S. Olmschenk, W. Cmpell, J. Mizrhi, C. Senko, nd C. Monroe, Phys. Rev. Lett. 104, (2010). 19 Q. A. Turchette, C. J. Mytt, B. E. King, C. A. Sckett, D. Kielpinski, W. M. Itno, C. Monroe, nd D. J. Winelnd, Phys. Rev. A 62, (2000). 20 D. W. Alln, in Proc. IEEE, Vol. 54 (1966) p. 221.