Action spectroscopy of SrCl + using an integrated ion trap time-of-flight mass spectrometer
Prateek Puri, Steven J. Schowalter, Svetlana Kotochigova, Alexander Petrov, Eric R. Hudson
AAction spectroscopy of SrCl + using an integrated ion trap time-of-flight massspectrometer Prateek Puri, a) Steven J. Schowalter, Svetlana Kotochigova, Alexander Petrov, b) and Eric R. Hudson Department of Physics and Astronomy, University of California, Los Angeles, California 90095,USA Department of Physics, Temple University, Philadelphia, Pennsylvania 19122,USA (Dated: 14 September 2018)
The photodissociation cross-section of SrCl + is measured in the spectral range of 36000 – 46000 cm − using amodular time-of-flight mass spectrometer (TOF-MS). By irradiating a sample of trapped SrCl + molecular ionswith a pulsed dye laser, X Σ + state molecular ions are electronically excited to the repulsive wall of the A Πstate, resulting in dissociation. Using the TOF-MS, the fragments are detected and the photodissociationcross-section is determined for a broad range of photon energies. Detailed ab initio calculations of themolecular potentials and spectroscopic constants are also performed and are found to be in good agreementwith experiment. The spectroscopic constants for SrCl + are also compared to those of another alkaline earthchalcogen, BaCl + , in order to highlight structural differences between the two molecular ions. This workrepresents the first spectroscopy and ab initio calculations of SrCl + .Keywords: photodissociation, linear quadrupole trap, molecular ion I. INTRODUCTION
Diatomic molecular ions hold immense promise for ad-vances in both the fundamental and applied sciences.The internal structure of these species is complex relativeto that of atoms, giving rise to rich physics and chem-istry, yet their structure remains simple enough to allowcontrol over all degrees of freedom . Already, work isunderway using these ions to study chemical reactionsat the quantum level , to understand important as-trophysical processes , to perform precision measure-ment tests of fundamental physics , and to implementquantum logic operations . Molecular ions may alsoplay a central role in the development of scalable quan-tum computation architectures . Despite these im-portant efforts to study and control diatomic molecularions, progress has been slowed by one simple fact: there isvery little spectroscopic data available for molecular ions .The paucity of molecular ion spectroscopy is mostlikely attributed to several factors which conspire tomake this spectroscopy more difficult than that of neu-tral molecules. First, molecular ions often exhibit shortexperimental lifetimes due to fast ion-molecule reactionsand rapid diffusion under the influence of small electricfields . Second, the Coulomb repulsion between ionstypically limits available densities to ∼ cm − . Fur-ther, though a systematic review of the available spectro-scopic data for small molecular ions was carried out byBerkowitz and Groeneveld in 1983 in an effort to en-courage the community, in recent years the majority of a) Electronic mail: [email protected] b) Alternative address: St. Petersburg Nuclear Physics Institute,Gatchina, 188300; Division of Quantum Mechanics, St. PetersburgState University, 198904, Russia. interest – with notable exceptions – has shifted to-ward large molecular ions , atomic and molecular clus-ters , and multiply charged ions . Therefore, for theburgeoning field of ultracold molecular-ion research torealize its full potential, new efforts in small molecularion spectroscopy are required.Here we present the first spectroscopic data to dateof the molecular ion SrCl + . By trapping the molecularions in a linear quadropole trap (LQT), the experimen-tal lifetime of the molecular ions is extended, allowingthem to be interrogated on convenient timescales. TheA Π ← X Σ + dissociation cross-section is measured us-ing a time-of-flight mass spectrometer (TOF-MS), andthe corresponding molecular potentials and spectroscopicconstants are calculated. By employing action spec-troscopy, the sensitive techniques of mass spectrometryand ion detection can be used to mitigate the effect ofsmall ion sample sizes. The motivation and compositionof this report are similar to that of the first spectroscopicstudy of another alkaline earth chalcogen, BaCl + . Dueto the similarity of their rovibronic structures, SrCl + isa candidate for ultracold molecular ion experiments sim-ilar to those currently underway using BaCl + . In ad-dition, the experimentally convenient ground state rota-tional splitting of ∼ + a potentiallyattractive qubit for quantum information studies .In the remainder of this manuscript, we outline the ex-perimental apparatus, explain the spectroscopy protocol,and present the first spectroscopic data for SrCl + pho-todissociation. We also present the results of an ab ini-tio calculation of the SrCl + structure, which show goodagreement with the experimental data. We conclude witha comparison of SrCl + structure to that of BaCl + , whichwe have also recently determined . a r X i v : . [ phy s i c s . c h e m - ph ] A p r II. EXPERIMENTAL DESIGN
The apparatus used to perform the action spectroscopyof SrCl + , shown in Figure 1, consists of a LQT coupled toa modular TOF-MS similar to that reported in Ref. 39.This device is housed in a vacuum chamber maintained ata background pressure of 10 − mbar. A pressed, annealedSrCl pellet is mounted below the trap. The LQT hasa field radius, r , of 11.1 mm and an electrode radius, r e , of 6.35 mm. A trapping radiofrequency (rf) voltageis applied to all four electrodes with typical amplitude V rf = 120 V and frequency Ω = 2 π ×
400 kHz, resulting ina Mathieu q -parameter of q = (4 QV rf ) / ( mr Ω ) ≈ . Q is the charge and m is the mass of SrCl + . Themass spectrum of trapped ions is recorded by using apulsed, high-voltage scheme described in Ref. 39, whichcreates a two-stage electric field that ejects the ions into a radially-oriented TOF-MS.The TOF-MS used in this experiment is a modified ver-sion of a device used previously for spectroscopicstudies of BaCl + . The primary modifications to thisTOF-MS include the replacement of a channel electronmultiplier with a micro-channel plate, the transition fromspherical to cylindrical Einzel lenses, the lengthening ofthe field-free drift tube from 25 . . ∼ III. ACTION SPECTROSCOPY
The SrCl + photodissociation cross-section is measuredas follows. The SrCl pellet is ablated with a pulsed laser(Nd:YAG, 1064 nm, ∼ ∼
10 ns pulse), which cre-ates a plume of fast-moving charged and neutral species.
Microchannel PlateAblation LaserPDL
Einzel LensesSrCl Ion Trap Sr + SrCl + FIG. 1. A 3D rendering of the integrated ion trap and TOF-MS with insets showing relevant lengths. (Color online)
80 90 100 110 120 1300.00.20.40.60.81.0 � �� Sr + (0,130) SrCl + (1080,950) I on S i gn a l ( a r b . u . ) Mass (amu)PDL OnPDL Off
FIG. 2. The TOF mass spectra for trapped SrCl + with(red) and without (blue) the presence of the PDL tuned to44006.78 cm − . In parenthesis, ion number is presented foreach species when the PDL is off and on, respectively. (Coloronline) The LQT parameters are set such that only SrCl + orions with a larger mass-to-charge ratio can be loaded into the trap; however, SrCl + is the only species detectedfollowing this loading process. The V rf is ramped from120 V to 60 V in 150 ms, a value where both SrCl + and any fragment Sr + produced by photodissociationcan be co-trapped. While a room-temperature heliumbuffer gas has been used to collisionally cool trapped ionsand improve the TOF-MS detection efficiency, with thisimproved apparatus the detection efficiency is adequatewithout buffer gas and therefore not used.Once the trapped sample of SrCl + is initialized, theions are exposed to pulses of light propagating along theaxis of the LQT with a repetition rate r = 10 Hz for1 . Π ← X Σ + photodissocia-tion cross-section (36000 - 46000 cm − ) using four differ-ent Coumarin dyes. To mitigate sharp intensity fluctua-tions due to pointing instability, the beam is expanded toapproach a roughly uniform intensity profile ( ∼ E , is measured by an energy meter lo-cated near the exit viewport of the vacuum chamber andvaries between 0.5 mJ and 2 mJ over the gain profiles ofthe laser dyes used, with a typical value of ∼ ∼ µ s and high-voltage extractionpulses (2 . . < µ s risetime to laterally-paired LQT rods, which eject the ionsinto the TOF-MS . Figure 2 shows typical mass spectrawith and without exposure to the PDL light, with observ-able Sr + production in the former case. Mass spectrawithout the PDL are recorded prior to each measure-ment as a control to ensure that detected Sr + ions areproduced solely by photodissociation. Furthermore, dueto an occasional reaction between trapped Sr + fragmentsand background gas, SrOH + peaks are also included inthe photodissociation fraction, similar to a reaction in-volving Ba + previously observed in Ref. 39.By measuring the amount of Sr + relative to the ini-tial amount of SrCl + , a photodissociation fraction, η canbe extracted and used to calculate the photodissociationcross-section, σ , at wavenumber K , as: σ = hcK ¯ It ln 1(1 − η ) (1)where h is Planck’s constant, c is the speed of light,and I is the effective PDL intensity given by ( E × r ) /A ,where A is the beam area. By repeating the process ateach wavenumber K the photodissociation cross-sectionis measured in steps of 50 cm − as shown in Figure 3.Each point in this data set represents the average often experimental cycles, each ∼ (cid:46)
6% foreach data point. Long timescale drifts in the PDL beamshape and intensity makes it necessary to take data in in-tervals of ∼ − . To calibrate each interval, cross-section values are remeasured and normalized to those ofpreviously measured intervals. This normalization factoris typically found to be between 0 . +4 (shown in Figure 3), which we also measure withthis apparatus. This normalization factor is found to be2 .
65, and along with the interval normalization, is thedominant source of systematic error, which is estimatedto be ≤ × . IV. THEORY
To identify this photodissociation pathway, wehave calculated the Σ and Π non-relativistic elec-tronic potentials of the SrCl + molecule dissociat-ing to the Sr + ( S )+Cl( P ), Sr + ( D )+Cl( P ), andSr + ( P )+Cl( P ) limits, shown in Figure 4a. The poten-tial energies, transition and permanent dipole momentsfor the X Σ + and A Π potentials, which are relevantfor our experimental measurements, have been calcu-lated using the coupled cluster method with single, dou-ble, and perturbative triple excitations (CCSD(T)) forthe ground X state and coupled cluster equation of mo- -1 )0 (cid:31)(cid:31)(cid:31) P ho t od i ss o c i a ti on C r o ss S ec ti on ( Å ) K TheorySrCl + BaCl + FIG. 3. Cross-section of the A Π ← X Σ + photodissociationtransition in SrCl + at 300 K. The 300 K theoretical cross-section is also presented as a dashed line. A peak value of0 . is measured at 40481 cm − For comparison, boththe experimental and the theoretical 300 K cross-sections forthe A Π ← X Σ + photodissociation transition in BaCl + arealso displayed . (Color online) tion (EOM-CCSD) for the excited A state. The def2-QZVPP basis sets for Cl:(20s14p4d2f1g)/[9s6p4d2f1g]and Sr:(8s8p5d3f)/[7s5p4d3f] with the StuttgartECP28MDF relativistic effective core potential areused.For completeness, higher excited states have been cal-culated based on the multi-reference configuration inter-action (MRCI) method in the MOLPRO software suite.The Gaussian basis set aug-cc-pVTZ [6s,5p,3d,2f] for Cl and the correlation consistent [8s8p5d4f] withECP28MDF pseudo-potential for Sr are applied. Ref-erence configurations are obtained in a complete activespace self-consistent field calculation with 5 s, p, d or-bitals for Sr and 3 p, d orbitals for Cl. The core electrons4 s p for Sr and 1 s s p for Cl are not correlated inthe MRCI calculation. The potential curves that are rele-vant to the experimental observation have solid lines andare labeled as X Σ + and A Π for the ground and firstexcited state, respectively.Using the CCSD(T) and EOM-CSSD methods de-scribed above, the electronic dipole matrix element asa function of internuclear separation R for the A Π ← X Σ + transition is also calculated and shown in Fig-ure 4b. With this dipole moment function and the molec-ular potentials for these states, LeRoy (cid:48) s BCONT pro-gram is used to calculate a thermally-averaged theo-retical photodissociation cross-section shown in Fig. 3.For this calculation, it is assumed that the SrCl + rovi-brational degrees of freedom are in equilibrium with the300 K blackbody radiation of the vacuum chamber. Asseen in Fig. 3, the agreement between the measured -30-20-100102030 V / ( h c ) ( c m - ) R (units of a ) d ( un it s o f ea ) X Σ + A Π d = 0.19 a.u. a)b) Sr + ( P) + Cl( P)Sr + ( S) + Cl( P)Sr + ( D) + Cl( P) FIG. 4. Panel a): Molecular potentials of the SrCl + moleculeas a function of internuclear separation R . Solid curves indi-cate potentials that are involved in the photodissociation andare labeled by their X Σ + and A Π symmetry. Other po-tentials are shown by dashed and dashed–dotted lines for the Σ + (black) and Π (blue) symmetries, respectively. The ver-tical line indicates a transition from the lowest rovibrationallevel of the ground-state potential to a continuum state ofthe A Π potential driven by one-color laser radiation. Panelb): The X Σ + to A Π electronic transition dipole moment asa function of internuclear separation R . The dipole momentat the equilibrium separation of the X Σ + state is indicated.(Color online) and predicted cross-section is good. Given that we es-timate a systematic error in the absolute cross-sectionmeasurement of ≤ × , the similarity of the measuredand calculated magnitudes of the cross-section may in-dicate that error estimates are overly conservative. Theslight horizontal shift between the measured and calcu-lated cross-sections could be attributed to inaccuraciesof either the ab initio molecular potentials or the dipolemoment function. Given that the current calculation isnon-relativistic this shift is not surprising.The spectroscopic constants for the states relevant tothis work are give in Table I; constants for the same states in BaCl + are also presented for comparison. Theequillibrium bond lengths for these molecules, and there-fore the rotational constants, are very similiar. How-ever, we observe that the ground and first excited statepotentials of SrCl + are less deep than those of BaCl + .To understand this relationship, we analyze the perma-nent dipole moments and the charge distributions for theground state of both molecules. Figure 5 shows the per-manent dipole moment of the X state of BaCl + and SrCl + as a function of internuclear separation R defined relativeto the center of mass of each molecule, i.e. its center ofrotation. The two dashed lines in either panel correspondto the dipole moment of two limiting charge distributions.The ones labeled by Ba + Cl and Sr + Cl correspond to adipole moment for a singly charged barium or strontiumion and a neutral chlorine atom. The other dashed linein either panel corresponds to the dipole moment for adoubly charged barium or strontium ion and a negativelycharged chlorine anion.Our calculations show that for R ≤ a for SrCl + andR ≤ a for BaCl + , the electronic wavefunction is “ionic”in character, dominated by configurations that containthe closed shell Sr and Cl − and Ba and Cl − ions,respectively. At separations larger than 8 a or 9 a , re-spectively, the electronic wavefunctions rapidly change toa covalently bonded state with neutral chlorine and ionicstrontium and barium. The numerical dipole momentstend to the dipole moments predicted by the correspond-ing limiting charge distributions. Because the double ion-ization potential of Sr is larger than that of Ba, we ex-pect the ionic coupling of BaCl + to be stronger than thatof SrCl + , which is supported by the relative difference inphotodissociation energies of these molecules. V. SUMMARY
We have described the use of an integrated linear iontrap and time-of-flight mass spectrometer to record thephotodissociation cross-section of SrCl + in the spectralrange of 36000 – 46000 cm − . Ab initio molecular po-tentials and transition moments were calculated. Thesecalculations indicate that the A Π ← X Σ + transition isresponsible for the observed photodissociation signal andshow good agreement with the measurement. Based onthese calculations spectroscopic constants for the lowesttwo electronic states of SrCl + were reported. TABLE I. Spectroscopic molecular constants for the X Σ + and A Π potentials of both SrCl + and BaCl + . Ion State R e D e / ( hc ) ω e / ( hc ) B e / ( hc )( a ) (cm − ) (cm − ) (cm − )SrCl + X Σ + Π 6.32 1658 77 0.0603BaCl + X Σ + Π 6.38 2083 96 0.0528 )-10-50-10-50 Sr Cl - a)b) d ( un it s o f ea ) Ba Cl - Sr + ClBa + Cl FIG. 5. The permanent electric dipole moment (solid lines)of the X Σ + state as a function of internuclear separation forSrCl + (panel a) and BaCl + (panel b). The dipole momentis given relative to the center of mass. The top dashed linein each panel corresponds to the classical dipole moment fora single positive charge placed at the position of the bariumor strontium ion, respectively. The bottom dashed line cor-responds to the classical dipole moment for a doubly chargedbarium or strontium ion and a negatively charged chlorineanion As outlined in the introduction, a new effort for pro-ducing and studying ultracold molecular ions is rapidlyemerging in physics and chemistry. This effort, de-spite notable results, is hampered by a significant lackof small molecular ion spectroscopic data. The workpresented here provides the first spectroscopic data forSrCl + , an interesting candidate for these studies. Italso outlines the design and use of an apparatus whichovercomes many of the challenges of molecular ion spec-troscopy and should be applicable to higher resolutionspectroscopic studies, e.g pre- and multi-photon dissoci-ation spectroscopy. Nonetheless, for the field of ultracoldmolecular ions to reach its full potential a renewed effortfrom the community in small molecular ion spectroscopyis required. VI. ACKNOWLEDGMENTS
The authors thank Shylo Stiteler for his assistance withthe machining of the stainless steel TOF-MS device; theinstrument could not have been constructed without hishard work and mettle. P.P. thanks the U.S. Army Re-search Office (ARO) Undergraduate Research Appren-ticeship Program (URAP) for their support. This workwas supported by National Science Foundation (NSF)and ARO grants (Grant Nos. PHY-0855683, PHY-1308573, W911NF-12-1-0476 and W911NF-10-1-0505).
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BCONT 2.0 Computer Pro-gram for Calculating Absorption Coefficients, Emission Intensi-ties or (Golden Rule) Predissociation Rates,
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