Optical Mass Spectrometry of Cold RaOH + and RaOCH 3 +
M. Fan, C. A. Holliman, X. Shi, H. Zhang, M. W. Straus, X. Li, S. W. Buechele, A. M. Jayich
OOptical mass spectrometry of cold
RaOH + and RaOCH M. Fan,
1, 2
C. A. Holliman,
1, 2
X. Shi,
1, 2
H. Zhang, M. W. Straus,
1, 2
X. Li, S. W. Buechele,
1, 2 and A. M. Jayich
1, 2, ∗ Department of Physics, University of California, Santa Barbara, California 93106, USA California Institute for Quantum Entanglement, Santa Barbara, California 93106, USA CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China Key Laboratory for Physical Electronics and Devices of the Ministry ofEducation and Shaanxi Key Laboratory of Information Photonic Technique,Xi ' an Jiaotong University, Xi ' an 710049, China (Dated: July 24, 2020)We present an all-optical mass spectrometry technique to identify trapped ions. The new methodutilizes laser-cooled ions to determine the mass of a co-trapped dark ion with sub-dalton resolutionwithin a few seconds. We apply the method to identify the first controlled synthesis of cold, trappedRaOH + and RaOCH . These molecules are promising for their sensitivity to time and parityviolation that could constrain sources of new physics beyond the standard model. The nondestructivenature of the mass spectrometry technique may help identify molecular ions or highly charged ionsprior to optical spectroscopy. Unlike previous mass spectrometry techniques for small ion crystalsthat rely on scanning, the method utilizes a Fourier transform which is inherently broadband andcomparatively fast. The technique’s speed provides new opportunities for studying state-resolvedchemical reactions in ion traps. INTRODUCTION
Ion traps are powerful tools because their ability totrap only depends on two properties: the mass and chargeof a particle. Therefore they can trap ionic species withrich internal structure that precludes laser cooling orfluorescence. Such dark ions include molecules, highlycharged ions, and atoms with transitions that are deepin the UV. These ions can be sympathetically cooled byco-trapped laser-cooled ions, where they appear as darkion defects in a Coulomb crystal. Dark ions have seengreat successes in optical clocks, e.g. Al + [1], constrain-ing new physics, e.g. HfF + [2] and studying state-resolvedchemical reactions, e.g. BaCl + [3], RbSr + [4]. There hasalso been much progress with highly charged ions, whichgenerally lack strong fluorescence transitions, for metrol-ogy and tests of fundamental constant variations [5–7].In this work we have synthesized a pair of molecular ionsthat are both promising for probing new physics, RaOH + and RaOCH .Recent measurements of parity ( P ) and time-reversal( T ) violating moments are now probing physics at energyscales beyond the direct reach of the Large Hadron Col-lider [8]. Radium-based molecules are promising for con-straining hadronic P , T -odd forces [9, 10]. The heavy andoctupole-deformed radium nucleus enhances sensitivityto new physics in the hadronic sector [11, 12]. This sen-sitivity is further enhanced when radium is incorporatedinto a molecule, such as RaOH + , or RaOCH [9, 10, 13],which have large effective electric fields and molecularstructure that is critical for reducing systematic uncer-tainties. An ion trap is advantageous for working with ra-dioactive molecules as high measurement sensitivity canbe achieved with small sample sizes due to long mea-surement times [2, 14]. For example, the long trap times combined with the high sensitivity of RaOCH issufficient for an experiment with even a single trappedmolecule to set new bounds on hadronic P , T -violation[15].Because dark ions do not fluoresce, mass spectrometrytechniques are commonly used for species identification.We present a new nondestructive optical mass spectrom-etry (OMS) technique to identify a trapped dark ion ina Coulomb crystal by measuring a motional frequency ofthe crystal. In this work we use co-trapped laser-cooledions to amplify the secular (normal mode) motion of thecrystal by utilizing coherent population trapping (CPT)in the S / - P / - D / Λ-level system [16], commonto Ca + , Sr + , Ba + , and Ra + . For these ions it is fastand straightforward to realize CPT by changing the fre-quency and power of the P / → D / repump laser fromthe laser cooling values with an acousto-optical modu-lator (AOM). With CPT, the optical spectrum of the S / → P / cooling transition can be modified so theion’s motion is coherently amplified [17], which modu-lates the scattered light at the motional frequency and itsharmonics, which can then be measured with a Fouriertransform. Because the motional modes of the ion crystalare set by the charge and mass of the trapped particles,motional frequencies can be used to determine the ion’smass. The OMS technique can be utilized with any laser-cooled ion, even without using a Λ structure, e.g. Be + ,Mg + , or Yb + , via “phonon lasing” with bichromatic light[18].Many techniques have been used to identify trappeddark ions in Paul traps. The best technique for largeCoulomb crystals (hundreds to thousands of ions) withmultiple dark ion species is time-of-flight mass spec-trometry, but it is inherently destructive and requires apurpose-built trap and custom electronics [19–21]. In the a r X i v : . [ phy s i c s . a t o m - ph ] J u l regime of small ion crystals with a few dark ions, mul-tiple techniques have been developed that rely on mea-suring a trap secular frequency, including secular motionexcitation by applied electric fields (tickle scans) [22–24],optical sideband spectroscopy [25], and ion crystal phasetransitions [26]. Optical sideband spectroscopy requiresa narrow linewidth laser, and is also slow ( ∼ ∼ ≥ ∼ apriori knowledge of the trapped dark ions is required toreduce the secular frequency scan range. In comparisonto these small ion crystal mass spectrometry techniques,the reported OMS technique is faster, does not requireknowledge of the dark ion’s mass, is less invasive, and isa simple extension to Doppler cooling. SECULAR MOTION AMPLIFICATION BYCOHERENT POPULATION TRAPPING
We use CPT in Ra + to amplify the ion crystal’s mo-tion. For Doppler cooling, the cooling laser at 468 nmis red-detuned, ∆ SP <
0, from the S / → P / tran-sition, and a repump laser at 1079 nm is blue-detuned,∆ DP >
0, from the D / → P / transition that bringspopulation back into the cooling cycle [17], see Fig. 1.The high scattering rate of laser cooling can be signifi-cantly reduced by CPT, that occurs when ∆ SP = ∆ DP [28]. For CPT motional amplification the condition is lessstringent, as setting ∆ SP < ∆ DP <
0, see Fig. 1, heatsthe ion crystal because the 468 nm spectrum has a localslope that is negative due to excitation suppression fromCPT at ∆ SP = ∆ DP . However, the heating is boundedby the 468 nm global spectrum which has a positive slopefor ∆ SP <
0, that cools the heated ion’s motion onceit reaches a sufficient amplitude that the global coolingspectrum is Doppler shifted into resonance. The trappedions then maintain an amplified equilibrium orbit whenthe optically induced “local heating” and “global cool-ing” effects balance [29, 30].For OMS identification of RaOH + and RaOCH , weapply a 2.5 gauss magnetic field along the trap axial axis. FIG. 1. a) Ra + energy levels and transitions used in thiswork. ∆ SP (∆ DP ) is the detuning, and Ω SP (Ω DP ) is theRabi frequency of the 468 (1079) nm light. b) The S / to P / spectrum with ∆ SP and ∆ DP set to amplify ion motion.The local slope at ∆ SP (red dashed line) is negative, while theglobal slope (blue dashed line) is positive. c) OMS geometrywith two Ra + and a RaOCH shown between two radial trapelectrodes, as well as the relative orientation of the coolingand repump light, and the magnetic field.FIG. 2. P / state population as a function of 468 nmdetuning. A fit of the spectrum to a numerical solutionof the Λ-level system which accounts for all Zeeman levels[31, 32] gives: ∆ DP / π = −
10 MHz, Ω SP / π = 19 MHz, andΩ DP / π = 13 MHz. The blue line at ∆ SP / π = −
22 MHzis the detuning of the 468 nm light used for CPT amplifica-tion. The P / state population is not suppressed to zero at∆ SP = ∆ DP due to the finite linewidths of both the 468 and1079 nm lasers ( ∼ The k -vectors of both lasers are at 45 degrees with respectto all trap axes and are linearly polarized perpendicularto the magnetic field direction, see Fig. 1. Each laser’sfrequency and amplitude is controlled with an AOM. Themulti-peak spectrum of the cooling laser, see Fig. 2, en-ables “local heating, global cooling” that amplifies theion motion up to a fixed value. The 1079 nm light, witha k -vector perpendicular to the 468 nm light, see Fig. 1c), breaks the degeneracy between the axial and radialdirections so that CPT only amplifies motion along the FIG. 3. Fourier transformed PMT counts for Coulomb crys-tals where two Ra + surround a third ion, labeled in the legend,in a linear chain. The Fourier amplitudes are normalized bytheir backgrounds for clarity. The dashed vertical lines showthe calculated center ion masses. axial axis, see [29]. To switch from CPT amplificationto Doppler cooling we detune ∆ DP positive, so the CPTexcitation suppression is far from ∆ SP . OMS OF RADIUM-BASED MOLECULAR IONS
We trap Ra + ions in a linear Paul trap, with aradio-frequency (rf) drive of Ω rf / π = 1 MHz, radialelectrode to trap center distance r = 3 . z = 7 . + , the axial secular fre-quency is ω z / π = 27 . + ions, and apply CPT am-plification to increase the secular motion amplitude onthe axial center-of-mass (COM) mode to 22(3) µ m. AFourier transform of the PMT counts while the ion mo-tion is CPT amplified gives the OMS signal. The signal iscalibrated by using known (fluorescing) ions, in this casethree Ra + ions are used for calibration, see Fig. 3. Next,either methanol vapor or the deuterated equivalent is in-troduced to react with the laser-cooled Ra + . A chemicalreaction produces a dark ion defect in the crystal anddrops the PMT counts by roughly 1/3. If the dark ion isnot in the middle of the crystal we re-order the ions tomeet this condition by blue-detuning the 468 nm light,∆ SP >
0, for ∼ / RaOH + RaOD + RaOCH RaOCD Stat. 243.19(7) 243.79(7) 256.72(8) 259.85(8)Syst. 0.01(11) 0.21(11) 0.34(11) 0.22(11)Final 243.20(14) 244.01(14) 257.06(14) 260.07(14)Calc. 243.03 244.03 257.04 260.06TABLE I. Statistical results (Stat.) and systematic shiftsand uncertainties (Syst.) of the radium-based molecular ionmasses measured by OMS in daltons. The final molecularion masses are calculated from a linear sum of the shifts, andthe final uncertainties are given by summing the uncertaintiesin quadrature. See [29] for details on the systematics. Forcomparison the calculated molecular ion masses (Calc.) aregiven [39]. the trapped ions are exposed to methanol versus deuter-ated methanol confirms that we are producing the molec-ular ions identified by mass. When methanol is intro-duced only RaOCH [35–37] and RaOH + [38] are cre-ated, while RaOCD and RaOD + are only formed withdeuterated methanol. The difference between the mea-sured and calculated second harmonics of the secular fre-quencies are all within 13 Hz, corresponding to a frac-tional mass difference of m/ ∆ m ∼
800 in a 3 s mea-surement. We observe that with a methanol (deuter-ated) background pressure of ∼ × − torr, RaOH + (RaOD + ) is not chemically stable, and typically reactsin a few minutes to form RaOCH (RaOCD ), whichare easily detected because the OMS technique is fast,precise, and broadband.The OMS statistical uncertainty of 3 Hz was set by theFourier transform resolution, which in turn comes froma 1 / < . OMS IN A HIGH FREQUENCY ION TRAP
In a separate experimental apparatus we confirm theOMS technique with strontium isotopes 88, 86, and 84that we also identify with fluorescence. We demonstratethat the statistical mass sensitivity can be enhanced witha higher frequency ion trap ( r = 0 . z = 2 . rf / π = 22 MHz). The axial secular frequency for asingle Sr + is ω z / π = 91 . Sr + and one , , , Sr + , and measurethe axial COM secular frequencies of the crystal by OMSwith CPT amplification applied to the Sr + . Sr + isidentified only with OMS. FIG. 4. Fourier spectra of the fluorescent light from Sr + which is in a crystal with a second Sr + , Sr + , Sr + , or Sr + ion. The calculated dark ion masses for the above crys-tals are plotted as dashed vertical lines in the plot [29]. The Fourier spectra of second harmonics of the axialCOM secular frequency are shown in Fig. 4. The masslabels are calibrated using two Sr + ions [29]. Each traceis an average of ten 0.5 s measurements. The correspond-ing statistical mass resolution is m/ ∆ m stat ∼
20 000.The sub 1 dalton discrepancies between measured andcalculated masses is primarily due to temporal drift ofthe trap potential.
CONCLUSION
We have produced
RaOH + and RaOCH molecules in this work. Their isotopologues RaOH + and RaOCH are proposed for nuclear Schiff mo-ment measurements [9, 10], and can be produced withtrapped Ra + and methanol. The production, sym-pathetic cooling, and fast nondestructive identificationof these radioactive polyatomic molecular ions enablesstudying their internal structure with techniques suchas photodissociation spectroscopy [40] or quantum logicspectroscopy [41, 42].The short measurement time and sub-dalton mass res-olution could enable detection of short-lived molecularions, as demonstrated in this work using RaOH + andRaOD + which are metastable when in the presence of amethanol background. We note that the measurementtime can be further reduced to 0 . + in the D / state (lifetime 0 . + Doppler cool-ing, but can be distinguished with mass spectrometry.This provides a new tool to study the electronic states of chemical reaction products. Simultaneous determina-tion of product and reactant states can be achieved bycombining this method with optical pumping, which willhelp investigate full reaction pathways with single parti-cles [4, 44]. The technique may also be used to rapidlycharacterize the motional frequencies of an ion trap. Forexample, it could be incorporated into a feedback loop forthe long-term stabilization of trap motional frequencies[45].
ACKNOWLEDGEMENT
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In an 1D harmonic oscillator with normal frequency ω , the position and velocity of a single ion at time t are x ( t ) = x cos ω t, (S1) v ( t ) = x ω sin ω t, (S2)where x is the motion amplitude.A light field with k -vector ~k L couples to the ion motion through photon scatterings. We define ~k L · ˆ x <
0, and thelight force on the ion at time t is F ( t ) = F ( ω ) = s ( ω ) ~ c~k L · ˆ x, (S3)where s ( ω ) is the scattering rate at Doppler shifted light frequency ω = ω ( v ( t )) = ck L p ( c + v ( t )) / ( c − v ( t )) ≈ ω L (1 + v ( t ) /c ), where ω L = ck L is the light frequency in the lab frame.From the work-energy theorem, the energy gained by the ion after a cycle of motion is∆ E = Z − x x F ( x )d x + Z x − x F ( x )d x, (S4)where F ( x ) is the light force as a function of ion position in the first half of the cycle (0 < t < πω ), and F ( x ) is thelight force in the second half of the cycle ( πω < t < πω ). By changing the integration variable in Eq. S4 from x to t ,∆ E = Z πω F ( ω ) v ( t )d t + Z πω πω F ( ω ) v ( t )d t. (S5)From Eq. S2, v ( t ) = − v ( 2 πω − t ) . (S6)With this, Eq. S5 becomes,∆ E = Z πω F ( ω ( v ( t ))) v ( t )d t + Z πω πω F ( ω ( − v ( 2 πω − t )))( − v ( 2 πω − t ))d t = Z πω F ( ω ( v ( t ))) v ( t )d t + Z πω πω F ( ω ( − v ( 2 πω − t ))) v ( 2 πω − t )d t. (S7)We define t = πω − t , and a r X i v : . [ phy s i c s . a t o m - ph ] J u l ∆ E = Z πω F ( ω ( v ( t ))) v ( t )d t − Z πω F ( ω ( − v ( t ))) v ( t )d t = Z πω [ F ( ω ( v ( t ))) − F ( ω ( − v ( t )))] v ( t )d t. (S8)From Eq. S3, ∆ E = ~ c~k L · ˆ x Z πω [ s ( ω ( v )) − s ( ω ( − v ))] v ( t )d t. (S9)If ∆ E >
0, the ion’s motion will be amplified after a cycle. If ∆
E <
0, the motional amplitude decreases after acycle until reaching the Doppler cooling limit [1]. From Eq. S9, the difference between scattering rates s ( ω ( v )) and s ( ω ( − v )) for 0 < t ≤ πω determines the sign of ∆ E .Note that for small oscillation amplitude x so that the scattering rate s ( ω ) is linear with ω ,∆ E ∝ lim v → [ s ( ω ( v )) − s ( ω ( − v ))] ∝ − d s d v (cid:12)(cid:12)(cid:12)(cid:12) ∝ − d s d ω (cid:12)(cid:12)(cid:12)(cid:12) ω L , (S10)which gives the well-known result that the ion is cooled (heated) when the sign of the spectrum slope is positive(negative).For spectra with multiple peaks, as in Fig. 2 in the main text, the ion is locally heated as the sign of the spectrumslope at ω = ω L is positive, but is globally cooled due to the contribution of light that is Doppler shifted when theion motion is large that ω − ω L is no longer small compared to sizes of the CPT features. Therefore, the ion’s motionis amplified up to a stable orbit due to an equilibrium between “local heating” and “global cooling” effects. FIG. S1. P / state population vs. radial and axial ion velocities. From the ion velocity we can calculate the Doppler shifted468 nm and 1079 nm light frequencies, and the P / state population can be calculated from the light frequencies. The positiveaxes are defined so ~k · ˆ x < We further analyze the ion’s motion in the trap radial and axial directions given the experimental setup in Fig. 1described in the main text. The 468 nm and 1079 nm k -vectors are perpendicular to each other, leading to anisotropyin axial and radial motion if we consider Doppler shifts to both the 468 nm and 1079 nm light: When the ion movesradially, the 468 and 1079 nm Doppler shifts have the same sign, and when the ion moves axially, the Doppler shiftshave the opposite signs. We calculate the P / state population separately for ion velocities in the radial and axialdirections, see Fig. S1, using the fitted parameters in Fig. 2 of the main text. According to Eq. S10, the ion is cooledif the slope of the scattering rate, which is proportional to the P / state population, at v = 0 is positive (radialdirections), and the ion is heated if the slope of the scattering rate at v = 0 is negative (axial direction). Therefore,the ion motion is selectively amplified in the axial direction.We note that if multiple modes can be excited, mode competition will lead to stable amplification of only one mode[2], and the amplified coherent motion of the dominant mode can be used in OMS to measure ion masses. II. SECULAR FREQUENCIES OF A LINEAR ION CRYSTAL
Formulas for the axial center-of-mass (COM) mode of a linear ion crystal with 1 to 3 ions are summarized.We define the axial Mathieu parameter [3] a z = 8 QκU mz Ω rf 2 , (S11)where Q is the ion’s charge, m is the ion mass, κ is a dimensionless factor related to shielding of the axial electric fieldby the radial electrodes, U is the dc voltage on the two endcap electrodes, and z is the distance from the endcapelectrode to the trap center.For a single ion, the axial secular frequency in the approximation of a z (cid:28) ω z, = Ω rf √ a z . (S12)For a linear 2-ion crystal with ion masses M and m , the axial COM mode frequency is [4] ω z, = ω z, s µ − r µ − µ , (S13)where µ is the mass ratio M/m .For a linear 3-ion crystal with two ions of mass m on each end, and an ion of mass M at the center, the axial COMmode frequency is [5] ω z, = ω z, r µ (21 − p − µ + 169 µ ) . (S14) III. OMS SYSTEMATICSA. Mass calibration
We calculate the molecular ion masses using an OMS calibration measurement directly before introducing reactants,and the systematic shift is the difference between the ion mass using the most recent calibration data and that usingthe initial calibration shown in Fig. 3 in the main text. We do not report an uncertainty for this systematic as allcalibrations have the same statistical uncertainty.
B. Trap potential drift
The secular frequency may drift in the time between mass calibration and molecular mass spectrometry (typically < + as a function of time using the OMS for a period of ∼ × − , which we use for the systematic error due to trap potential drift.The corresponding mass uncertainties are calculated. FIG. S2. Fractional drift in the axial secular frequency of a single Ra + . C. Secular motion amplitude shift
The axial COM secular frequency is amplitude-dependent due to trap anharmonicity [6]. We measure the axialCOM mode secular frequency for a 3 Ra + crystal as a function of the oscillation amplitude [See Fig. S3]. With amotional amplitude of 22(3) µ m that is used in the measurement, the maximum fractional secular frequency shift dueto oscillation amplitude uncertainty is 5 × − , which translates to mass uncertainties that are less than 0.1 dalton.The systematic shifts and uncertainties of measured masses are summarized in Table S1, along with the statisticalresults. The total systematic shift is a linear sum of the individual shifts, and the total uncertainty is a quadraturesum of the individual uncertainties. FIG. S3. Secular frequency vs. ion secular motion amplitude for 3 Ra + . The orange shaded region indicates secular motionamplitudes used for OMS measurements.RaOH + RaOD + RaOCH RaOCD Calibration shift 0.01 0.21 0.34 0.22Trap potential drift 0.00(9) 0.00(9) 0.00(9) 0.00(9)Motion amplitude shift 0.00(7) 0.00(7) 0.00(8) 0.00(8)Total systematic 0.01(11) 0.21(11) 0.34(11) 0.22(11)TABLE S1. Systematic shifts and uncertainties of the measured molecular ion masses in daltons.[1] P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, Optical molasses, J. Opt. Soc.Am. B , 2084 (1989).[2] U. Kemiktarak, M. Durand, M. Metcalfe, and J. Lawall, Mode competition and anomalous cooling in a multimode phononlaser, Phys. Rev. Lett. , 030802 (2014).[3] D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Minimization of ion micromotion in a paultrap, J. Appl. Phys. , 5025 (1998).[4] G. Morigi and H. Walther, Two-species coulomb chains for quantum information, The European Physical Journal D -Atomic, Molecular, Optical and Plasma Physics , 261 (2001).[5] D. Kielpinski, B. E. King, C. J. Myatt, C. A. Sackett, Q. A. Turchette, W. M. Itano, C. Monroe, D. J. Wineland, and W. H.Zurek, Sympathetic cooling of trapped ions for quantum logic, Phys. Rev. A , 032310 (2000).[6] N. Akerman, S. Kotler, Y. Glickman, Y. Dallal, A. Keselman, and R. Ozeri, Single-ion nonlinear mechanical oscillator,Phys. Rev. A82