Experimental study of the 39 K g state by perturbation facilitated infrared-infrared double resonance and two-photon excitation spectroscopy

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1 THE JOURNAL OF CHEMICAL PHYSICS 122, Experimental study of the 39 K g state by perturbation facilitated infrared-infrared double resonance and two-photon excitation spectroscopy Yizhuo Chu, Feng Xie, Dan Li, and Li Li a Department of Physics and Key Lab of Atomic and Molecular Nanosciences, Tsinghua University, Beijing , China V. B. Sovkov and V. S. Ivanov V. A. Fock Institute of Physics, St. Petersburg State University, 1 Ulyanovskaya Street, Petrodvorets, St. Petersburg , Russia A. M. Lyyra Department of Physics, Temple University, Philadelphia, Pennsylvania Received 21 October 2004; accepted 11 November 2004; published online 4 February 2005 The 39 K g state has been observed by perturbation facilitated infrared-infrared double resonance and two-photon excitations. The vibrational numbering of the 2 3 g levels was determined by resolved fluorescence into the bound levels as well as to the continuum of the a 3 + state. The rotational assignment of the 2 3 g levels excited by two-photon transitions was determined from excitation frequencies and resolved fluorescence into the bound levels of the a 3 + and b 3 states. Molecular constants obtained from these observed levels agree with theoretical constants American Institute of Physics. DOI: / I. INTRODUCTION The K 2 electronic states have been studied both theoretically and experimentally. Potential energy curves of 98 electronic states below the 4s+5d atomic limit have been calculated with high accuracy. 1,2 While many singlet states have been observed, much less is known about triplet states because the ground state has 1 + g symmetry and transitions from the singlet ground state into triplet states are spin forbidden. In order to observe triplet states of K 2, perturbation facilitated optical-optical double resonance PFOODR spectroscopy, 3,4 which has been used to study the triplet states of Na 2 and Li 2 successfully, has been applied to K The key of this PFOODR technique is to use A 1 + u b 3 mixed levels as the intermediate window levels in the twostep excitation. Resolved fluorescence from triplet Rydberg states gives information about the a 3 + u and b 3 states. With this technique, several triplet Rydberg states and the a 3 + u and b 3 states of 39 K 2 have been studied One two-photon transition into a high-v, J=67 level of the 39 K g state has been observed. 13 Fluorescence from this level into the b 3 state has been resolved by Fourier transform FT spectrometer. With these FT data and all available data, very accurate molecular constants of the b 3 state have been reported. 13 Recently we carried out perturbation facilitated infrared-infrared double resonance and two-photon excitations of K 2 and observed v=0 14 and several high-v levels of the 2 3 g state. This paper reports our experimental observation and simulation. a Author to whom correspondence should be addressed. II. EXPERIMENT Figure 1 is the experimental setup of our double resonance excitation and resolved fluorescence spectroscopy. Potassium vapor was generated in a crossing heatpipe oven with 1 Torr Ar buffer gas. At equilibrium condition, the temperature of the potassium vapor is about 500 K. A Toptica DL 100 single mode tunable diode laser center wavelength 850 nm, 40 mw output was used as the pump laser; another Toptica DL 100 diode laser 980 nm central wavelength, 100 mw output was used as the probe laser. The laser frequencies were measured by Burleigh WA-1600 wavemeters with accuracy of cm 1. The pump laser was modulated with a mechanical chopper and its frequency was held fixed to excite an A 1 + u b 3 mixed intermediate level from the ground state. The probe laser was scanned and transitions into the 2 3 g state were detected by monitoring the 2 3 g a 3 + u yellow-green fluorescence with filters and photomultiplier PMT. When the two diode laser frequencies were held fixed to excite a 2 3 g level, resolved fluorescence was recorded by scanning a Spex 1404 monochromator. Two-photon excitations into the 2 3 g state were carried out by using only one of the two diode lasers at a time. A Coherent Ti:Sapphire laser 600 mw output is also used to excite two-photon transitions into high-v levels of the 2 3 g state. While the laser frequency was scanned, twophoton transitions were monitored by detecting the 2 3 g a 3 + u yellow-green fluorescence with filters and PMT. Fluorescence from the two-photon excited upper 2 3 g levels to the a 3 + u and b 3 states is resolved by a Spex 1404 monochromator. When the two photons of the two-photon absorption are propagating in the same direction, the two-photon excitation lines are Doppler limited. We also carried out Doppler-free two-photon excitations by reflecting the laser beam back. In this case, narrow Doppler-free lines appeared on top of the Doppler broadened background /2005/122 7 /074302/8/$ , American Institute of Physics

2 Chu et al. J. Chem. Phys. 122, FIG. 1. Experimental setup. III. RESULTS A. IR-IR double resonance excitation Accurate molecular constants of the ground state X 1 + g of K 2 are available. 14,15 The intermediate A 1 + u state and the b state e-parity strongly perturb each other and a global deperturbation has been performed. 13 With the deperturbed constants and perturbation parameters term values of the A 1 + u and b 3 levels, unperturbed as well as perturbed levels, can be calculated very accurately. In our IR-IR double resonance excitation, the intermediate mixed e-parity window levels used are the b 3 1u v=18, J=36, 38, 40 levels perturbed by the A 1 + u v=7, J=36, 38, 40 levels, respectively, the b 3 0u v=20, J=24, 26, 28, 30, 32, 34, 36 levels perturbed by the A 1 + u v=8, J=24, 26, 28, 30, 32, 34, 36 levels, respectively, the b 3 0u v=21, J=20, 22, 24 levels perturbed by the A 1 + u v=9, J=20, 22, 24 levels, respectively, the b 3 1u v=23, J=22, 24 levels perturbed by the A 1 + u v=12, J=22, 24 levels, respectively, and the b 3 0u v=24, J=22 level perturbed by the A 1 + u v=13, J=22 level. Because the energy level density of K 2 is high, even a single mode laser could excite more than one intermediate levels when its frequency was held fixed. Thus the IR-IR double resonance excitation lines in the excitation spectra may not all originate from the selected intermediate window level. In order to distinguish the IR-IR double resonance transitions via the selected intermediate window level from those via other intermediate levels that were excited coincidentally by the pump laser, we first excited this selected intermediate b 3 v, J window level with b 3 v, J X 1 + g v J =J +1 transition and scanned the probe laser frequency, then excited this intermediate level with b 3 v, J X 1 + g v J =J 1 transition and repeated the probe scan. Only those signals that appeared at the same frequency with the same intensity in both scans were confirmed to be the signals via the selected intermediate level. Since both b 3 0u and b 3 1u levels were used as the intermediate window levels, different spin components F 1 /F 2 for case b or =0/ =1 for case a could have been observed. Our data show that the 2 3 g state belongs to intermediate case between Hund s case a and case b. The 2 3 g v b 3 0u v, J transition of K 2 contains two J =±1 R and P rotational lines into the =0 component and two much weaker J= ±1 lines into the =1 component. The 2 3 g v b 3 1u v, J transition contains J= ±1 rotational lines into the =1 component and weak lines into the =0 component. Since the A 1 + u b 3 2u mixing is very weak, no mixing levels could be used as the intermediate window levels, and the weak lines into the =2 component could not be assigned unambiguously. The rotational quantum numbers J of the 2 3 g levels were confirmed by observing the same J level via both J =J+1 and J =J 1 intermediate levels for example, the 2 3 0g v=6, J=27 level was observed both via b 3 0u J =26 and J =28 intermediate levels. Table I gives the IR-IR double resonance excitation data. The vibrational numbering of the 2 3 g levels observed by IR-IR double resonance excitation was determined by resolved fluorescence to the a 3 + u state. Figure 2 gives resolved fluorescence spectra of the 2 3 g v=4 8 levels. The spectra contain discrete bound-bound lines into the bound levels in the shallow well of the a 3 + u state, as well as bound-free fluorescence to the repulsive part of the a 3 + state. From the node counting, upper vibrational quantum numbers can be determined. Figure 3 gives the comparison between the observed spectrum upper and calculations lower of the 2 3 g v=8, J=27 a 3 + u transition. In the calculation ab initio potential curves of the 2 3 g and a 3 + states were used. 2 Although the calculated positions of the bound-bound lines all shifted to the longer wavelength, the relative intensities agree with the observed lines. The boundfree part also agrees with the observed spectrum. If the vibrational quantum number of the upper state changes by ±1, the calculated spectrum will be quite different from the observed spectrum. B. Two-photon transitions The laser frequency in this experiment was in the frequency range of the A 1 + u X 1 + g transition. Since many vibrational rotational levels of the A 1 + u state are perturbed by the b 3 state, two-photon transitions into triplet states are also possible. In order to discriminate against transitions into other states and in favor of the transitions into the 2 3 g state, yellow-green 2 3 g a 3 + u fluorescence was selectively detected when laser frequency is scanned. Two-photon transitions appeared in every wave number in our fluorescence excitation spectra. In order to determine the electronic symmetry and vibrational and rotational quantum numbers of the two-photon excited upper levels, resolved fluorescence spectra have been recorded from the upper levels. Many transitions have been assigned to transitions into the 2 3 g state. Figure 4 shows several resolved fluorescence spectra into the a 3 + u state. All spectra in Fig. 4, except Fig. 4 d, contain sharp discrete lines, which correspond

3 Study of the 39 K g state J. Chem. Phys. 122, TABLE I. IR-IR double resonance excitation data. Intermediate b 3 levels Probe laser 2 3 g levels frequencies v J cm 1 Term value cm 1 v J

4 Chu et al. J. Chem. Phys. 122, TABLE I. Continued. Intermediate b 3 levels Probe laser 2 3 g levels frequencies v J cm 1 Term value cm 1 v J to transitions into the bound levels of the shallow well of the a 3 + state. The spectra also have continua, which correspond to transitions into the repulsive wall of the a 3 + state. The 2 3 g state can also fluoresce to the b 3 state, but the fluorescence is too red from these low-v upper levels for our monochromator detection. The upper level assignment is based on the fluorescence to the a 3 + state as well as the excitation frequency. The procedures of our assignment are as follows: 1 From the bound-bound lines into the a 3 + state, we determine the upper rotational quantum number. The a 3 + state has been observed and molecular constants of the well

5 Study of the 39 K g state J. Chem. Phys. 122, FIG. 2. Resolved fluorescence spectra of the transitions. The sharp lines correspond to transitions into the bound and quasibound levels of the shallow well of the state, and the continua in the spectra correspond to transitions to the repulsive wall of the state. have been reported. 5 From the vibrational spacings and P-R splittings, upper rotational quantum number J can be determined with an uncertainty of ±2. 2 From the fluorescence wavelengths and the term values of the a 3 + u state, the term value of the upper level can be estimated with an uncertainty of 5 cm 1. The accuracy of the fluorescence wavelength was limited by the monochromator and was much less than the accuracy of the laser frequency measurement. 3 After the term value of the upper level is estimated from fluorescence spectrum, we can find out the initial X 1 + g level, the intermediate enhancing A 1 + u b 3 mixed level, and then determine the accurate term value of the upper 2 3 g level. Although many transitions might match the laser frequency within a small difference, only one transition FIG. 3. Comparison of the experimental and calculated spectra of the 2 3 g v=8, J=26, transition. Relative intensities of the bound-bound and bound-quasibound lines in the calculated spectrum are given by the Franck Condon factors. FIG. 4. Resolved fluorescence spectra from the 2 3 g levels excited by two-photon transitions to the state with excitation frequencies: a ; b ; c ; d ; e ; f ; g cm 1. The sharp lines correspond to transitions into the bound and quasibound levels of the shallow well of the a 3 + state, the continua in the spectra correspond to transitions to the repulsive wall of the state. matches the upper rotational quantum number determined from the fluorescence. The accurate term value of the upper level then can be determined and equals to the sum of the term value of the ground state and the energy of the two photons. The term value determined from fluorescence should agree with that determined from excitation within the error of measurement. 4 From the global fluorescence spectra into the a 3 + state bound-bound as well as bound-free parts, we determine the upper vibrational quantum number of the 2 3 g levels by node counting and simulation. The upper vibrational quantum numbers of Figs. 4 a 4 f are v=0,1,2,2, 3, and 6 levels, respectively. Figure 4 d is also from a 2 3 g v=2 level as Fig. 4 c but no bound-bound lines appeared in the spectrum. This upper level may be a high-j level such that the effective potential curve of the high-n a 3 + u state has no potential well. Quantum interference appears in the 2 3 g a 3 + u fluorescence spectra when the vibrational quantum number is high. In this case node counting will not be possible to determine the vibrational quantum numbers and comparing the observed and calculated spectra is useful. Figure 5 a is the enlargement of Fig. 4 c. The fluorescence has two nodes, indicating that the upper level has a vibrational quantum number of v = 2. From the vibrational spacing and P-R separations, we estimate the upper J is around 71±2. Only the b 3 0u v =16, J =72 mixed with A 1 + u v=0, J=72 X 1 + g v =12, J =71 transition matches both in frequency and the selection rules for rotational quantum numbers. Figure 5 b is the energy level diagram of the assignment. The upper level has been assigned to the 2 3 g v=2, J=71 level with term value of cm 1. Table II gives the full assignment of two-

6 Chu et al. J. Chem. Phys. 122, C. Molecular constants and conclusion Because the A 1 + b 3 perturbation is due to spinorbit interaction, the b 3 0u levels are strongly mixed. Most of the 2 3 g levels were observed via the b 3 0u intermediate levels in this experiment. Only a few b 3 1u levels have proper singlet character and can be used as intermediate window levels. The levels of the 2 3 g state have intermediate coupling between case a and case b. The 2 3 1g levels are observed to be 14 cm 1 higher than the 2 3 0g levels with same rotational quantum numbers within our J range. Using the 3 0, 3 1, 3 2 case a basis, the effective Hamiltonian matrix elements are as follows: 3 0 H 3 0 = T v + B v X +1 D v X 2 +4X +1 A v, 3 1 H 3 1 = T v + B v X +1 D v X 2 +6X 3, 3 2 H 3 2 = T v + B v X 3 D v X 2 4X +5 + A v, 3 0 H 3 1 = 2X 1/2 B v 2D v X +1, 3 0 H 3 2 =2D v X X 2 1/2, FIG. 5. a Resolved fluorescence spectrum from the 2 3 g v=2 level excited by two cm 1 photons. b Energy level diagram of the assignment of the 2 3 g v=2, J=71 level excited by two cm 1 photons. photon transitions into the 2 3 g state. Table III gives the partial upper vibrational level assignment of two-photon transitions. We could only assign the vibrational quantum numbers from the global spectra for the 21 transitions since there were no bound-bound lines in the resolved fluorescence spectra. 3 1 H 3 2 = 2X 4 1/2 B v 2D v X 1, where X=J J+1. Numerically diagonalizing the resulting matrix for each J and performing a nonlinear least-squares fit to the observed term values by double resonance, molecular constants are obtained and given in Table IV. An iterative semiclassical estimate of Y 02 is calculated and held fixed in the fit. The v=9 levels are perturbed and not included in the fit. The levels observed by two-photon transitions show bigger deviations, which might be due to big gaps in rotational or/and vibrational quantum numbers. The perturbation of the high-j levels due to L-uncoupling could be stronger than the perturbation of low-j levels. Table IV also gives the ab initio molecular constants by Magnier, Aubert-Frecon, and Allouche. 1 The agreement is quite good. We calculated the fluorescence spectra of the 2 3 g v=8, J=27 a 3 + transitions Fig. 2sing the Rydberg Klein Rees RKR potential curve of the 2 3 g state calculated from the constants in Table IV and the ab initio potential curve of the a 3 + state and both bound-bound and bound-free spectra agree with the observed spectra. TABLE II. Full assignment of the two-photon transitions. X 1 g + level Intermediate enhancing level 2 3 g state laser cm 1 v J T cm 1 A/b v J E a cm 1 v J T cm 1 b A b A A A b b a E is the difference between the intermediate enhancing level and the half energy between the upper and ground levels E=T X 1 g + v,j + laser T A 1 + /b 3 u v,j. b T 2 3 g v,j =T X 1 g + v,j +2 laser.

7 Study of the 39 K g state J. Chem. Phys. 122, TABLE III. Partial assignment of the two-photon transitions. X 1 g + level Intermediate enhancing level 2 3 g state laser cm 1 v J T cm 1 A/b v J E a cm 1 v J T cm 1 b b b A b b b A b a E is the difference between the intermediate enhancing level and the half energy between the upper and ground levels E=T X 1 g + v,j + laser T A 1 + /b 3 u v,j. b T 2 3 g v,j =T X 1 g + v,j +2 laser. The results show that the 2 3 g state has a spin-orbit splitting A, 14 cm 1. The 2 3 g state dissociates to the 4s +3d atomic limit. The 3d atom has a small fine structure splitting 2.23 cm 1. However, the 2 3 g state may interact with other states to give rise to such a large spin-orbit splitting. To conclude, the 39 K g state has been probed by TABLE IV. Molecular constants. All quantities are in cm 1, except R e, which is in Ångstrom. This work Ab initio a T e +Y Y 1, Y 2, Y 3, Y 0, Y 1, Y 0, b A e R e a Reference 1. b Y 02 is calculated and held fixed in the fit. IR-IR double resonance and two-photon excitations with single mode diode lasers. In the double resonance excitation, A 1 + b 3 mixed levels were used as the intermediates. Eleven vibrational levels, v=4 14, have been observed by IR-IR double resonance and molecular constants are obtained. These experimental constants agree very well with ab initio calculation results. Two-photon transitions into the 2 3 g state were also observed. ACKNOWLEDGMENTS The authors thank Professor Yikang Pu for lending them a wavemeter, a chopper, and for other additional support, Professor T. Bergeman for calculating the term values of the A 1 + and b 3 states, Dr. Y. Liu and Professor J. Huenneckens for calculating the rotational line intensities, Professor S. Magnier and E. Ahmed for sending them unpublished results, and Professor Y. Mo and W. Han for technical assistance. Support from the NNSF Grant Nos and and NKBRSF of China, from the U.S. National Science Foundation, and from RFBR Grant No of Russia is gratefully acknowledged.

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