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New observations of the 39K2 a 3 Σ u + state are reported. The results include ro-vibrational term values and intensity distributions of the transitions from excited triplet states to this lowest triplet state. The new and previous experimental data are analyzed to obtain the multi-parameter [modified Lennard-Jones] description of the a 3 Σ u + state potential function in a range including both attractive and repulsive limbs. The same description is applied to the K2 33Πg and 4 3 Σ g + states.

New bound-free spectra of the K2 3 3 Π g ( v , J ) → a 3 Σ u + and 4 3 Σ g + ( v , N ) → a 3 Σ u + transitions have been observed with the perturbation facilitated optical–optical double resonance experimental technique. Our analysis has led to a conclusion that the vibrational assignments of the 33Πg and 4 3 Σ g + ro-vibrational terms observed in Kim et al. [J. Chem. Phys. 102 (1995) 6646] have to be corrected. New potential energy functions of the K2 33Πg state, the 4 3 Σ g + state, and of the a 3 Σ u + state repulsive branch are proposed.

The RKR potential function of the Na 2 4 3 Π g state determined by Y. Liu, H. Chen, J. Li, D. Chen, Li Li, and R. W. Field ( J. Mol. Spectrosc. 192, 32 (1998)) is checked for its ability to reproduce the experimental continuum of the Na 2 4 3 Π g ( v =12, N =23)→ a 3 Σ + u bound–free transition observed by G. Lazarov, A. M. Lyyra, Li Li, and J. Huennekens ( J. Mol. Spectrosc. 196, 259 (1999)). A significant difference between the experimental and simulated bound–free spectra is found even though about 300 rovibrational term values spanning the range of v =2–25 vibrational quantum numbers and N =6–15 rotational quantum numbers were used for the construction of this RKR potential. The new potential curve of the Na 2 4 3 Π g state was determined by applying the two-step global fit procedure of V. S. Ivanov, V. B. Sovkov, Li Li, A. M. Lyyra, G. Lazarov, and J. Huennekens ( J. Mol. Spectrosc. 194, 147 (1999)) to a set of all the available spectroscopic data on the Na 2 4 3 Π g state. This 4 3 Π g state is perturbed by the 6 3 Σ g + state through L -uncoupling. The “nonperturbed” RKR potential is constructed from a subset of the nonperturbed rovibrational term values solely. The potential curve constructed from the nonperturbed levels only is very close to the potential curve obtained by the two-step global fit and reproduces the term values and the bound–free continuum with the same accuracy.

The hyperfine spectra of the Na2 1 3Δg state have been recorded with sub-Doppler continuous wave (CW) perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy via A 1∑u+∼b 3∏u mixed intermediate levels. The rotational lines into the N=14–51 levels of the 1 3Δg state observed previously [J. Mol. Spectrosc. 134, 50 (1989)] have four components for transitions between symmetric rotational levels or five components for transitions between antisymmetric rotational levels and the hyperfine coupling belongs to Hund’s case bβS. For the low-N levels observed later, however, the hyperfine spectra are much more complicated. We have worked out the matrix elements of the molecular Hamiltonian in the case bβS basis. After taking into consideration spin–orbit, spin–spin, and spin–rotation interactions, we obtained a set of molecular constants for the Na2 1 3Δg state, with which we can reproduce the hyperfine spectra of both high- and low-N rotational levels.

The predissociation of the 1(3)Sigma(-)(g) v >/= 10 levels of (7)Li(2) has been observed by pulsed and continuous-wave perturbation-facilitated optical-optical double-resonance spectroscopy (PFOODR). Our ab initio calculation shows that the inner wall of the 1(3)Sigma(-)(g) potential intersects the 1(3)Pi(g) repulsive potential at internuclear distance R = 2.00 A. The predissociation is due to a DeltaS = 0, DeltaLambda = +/-1 rotational-electronic interaction with the repulsive 1(3)Pi(g) state. Copyright 2001 Academic Press.

An experimental study of the 3(3)Pig electronic state of 7Li2, using the Perturbation-Facilitated Optical-Optical Double Resonance (PFOODR) technique, was recently reported [A. Yiannopoulou et al., J. Chem. Phys. 103, 5898, (1995)]. However, due to the very small number of known 7Li2 A1Sigma+u approximately b3Piu window levels, only 13 ro-vibrational levels (spanning a range of vibrational levels designated upsilonx - 1 to upsilonx + 3 in that reference) could be observed. Dunham coefficients, based on the assignment upsilonx = 7, were found to fit the observed term values and give a qualitative fit to the intensities of the first six lines of the 3(3)Pig (upsilon = upsilonx, N = 11) --b3Piu emission spectrum. However, due to the limited number of levels used in the fit, both the absolute vibrational numbering and the 3(3)Pig RKR potential curve obtained from the Dunham coefficients, must be considered to be uncertain. In the present work, we show that the previously reported 3(3)Pig RKR curve is unable to reproduce the experimental intensity distribution in the 7Li2 3(3)Pig (upsilonx = 7, N = 11) --a3Sigma+u emission continuum. We report new experimental data for the 7Li2 3(3)Pig (upsilonx + 1, N = 11) --a3Sigma+u bound-free continuum and discrete 3(3)Pig (upsilonx +/- 1, N = 11) --b3Piu spectra obtained using the PFOODR experimental technique. We demonstrate that the correct vibrational numbering and an improved RKR potential curve can be obtained by analyzing the experimental term values in combination with all observed bound-free and discrete spectra. Finally, term values for four 6Li2 3(3)Pig ro-vibrational levels were obtained using PFOODR spectroscopy. The measured isotope shifts confirm the absolute vibrational numbering obtained from the present analysis. Copyright 1999 Academic Press.

We have demonstrated quantum control of the spin-orbit interaction based on the Autler-Townes (ac-Stark) effect in a molecular system using a cw optical field. We show that the enhancement of the spinorbit interaction between a pair of weakly interacting singlet-triplet rovibrational levels, G 1 � gðv ¼ 12; J ¼ 21 ;f Þ‐1 3 � � ðv ¼ 1 ;N ¼ 21 ;f Þ, separated by 750 MHz in the lithium dimer, depends on the Rabi frequency (laser power) of the control laser. The increase in the spin-orbit interaction due to the control field is observed as a change in the spin character of the individual components of the perturbed pair. DOI: 10.1103/PhysRevLett.107.163601 PACS numbers: 42.50.Hz, 31.15.aj, 33.40.+f The interaction between the spin and the orbital angular momenta (spin-orbit interaction) of the electron in an atom or a molecule often can be neglected or treated as a perturbation. However, when relativistic effects are not negligible, the spin-orbit interaction must be taken into account. It can cause mixing of electronic states of different spin multiplicity, with the degree of mixing dependent on the strength of the spin-orbit interaction as well as the energy separation between the interacting states. It is also well known that, in the presence of strong electromagnetic fields, the energy levels in atoms or molecules experience shifts in their positions due to the Autler-Townes (AT) effect [1]. Thus control of the spin-orbit interaction can be realized by using resonant or nonresonant laser fields as an external control mechanism. Several recent theoretical studies have been devoted to this subject [2‐5]. Specific possible applications of quantum control of the spin-orbit interaction include enhancing the rate of population transfer to otherwise ‘‘dark’’ states, either by increasing the mixing between existing perturbed pairs of levels or by creating mixed levels out of previously unmixed ones. In alkali-metal molecules, states with mixed character (i.e., singlet and triplet) have been used as ‘‘gateways’’ or ‘‘windows’’ for accessing states with different spin character than the ground state [6‐9]. Such perturbed levels have also been used as intermediate levels in the transfer of cold molecules formed at long range in the triplet a 3 � þ state to deeply bound levels of the singlet X 1 � þ ground state [10‐14]. Thus, the ability to enhance the mixing of the spin character of singlet-triplet pairs of states could be used to improve the transfer rates in such schemes. Also, there is a great deal of interest in controlling photochemical reactions and intersystem crossings by means of optical fields. For example, control of the chemical reaction potential energy surface using the nonresonant dynamic Stark effect has been demonstrated [15]. In principle, this control scheme could also be used in experiments that investigate the role of electron spin in entrance-channel controlled and excited state reactive collisions. Another possible application of control of the spin-orbit interaction with external fields is preparation of optical spin switches [3,16,17]. In this work, we demonstrate all-optical control of the spin-orbit interaction using the lithium dimer ( 7 Li 2 ) and a narrow band cw laser as the control field. The small linewidth (0.5 MHz) of the cw control laser allows the experiments to be performed state selectively by using a specific singlet-triplet pair of rovibrational levels mixed by the spin-orbit interaction. We chose to work with 7 Li 2 , since for molecules with light nuclei the spin and orbital angular momenta are weakly coupled, and therefore the spin-orbit interaction is small. Thus the interacting levels can lie very close in energy without being

We report the experimental observation of electromagnetically induced transparency (EIT) in an inhomogeneously broadened V-type Na2 molecular system. The experiment is performed with both co- and counterpropagating arrangements for the propagation directions of the coupling and probe laser beams. In our theoretical model we employ the density matrix formalism, as well as perturbative methods for obtaining the probe field absorption profile for both open and closed systems. Simulations of the experimental data show excellent agreement with the predictions derived from the basic theory. Our fluorescent intensity measurements show that, in the copropagating configuration, the EIT plus saturation window depth is about 95%, while under similar conditions in the counterpropagating geometry we observed 40%‐45% reduction in the fluorescence signal around the line center. To separate the two simultaneously occurring mechanisms in a V-type system (i.e., EIT and saturation) that are induced by the coupling field, we have carried out theoretical calculations which show that, in the copropagating case, a significant fraction of the depth of the dip is due to the coherent effect of EIT. When the coupling and probe beams are in the counterpropagating configuration, the dip is mostly due to saturation effects alone.

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed A {sup 1{Sigma}}{sub u}{sup +} and b {sup 3{Pi}}{sub u} states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aime Cotton primarily to study the X {sup 1{Sigma}}{sub g}{sup +} state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the b {sup 3{Pi}}{sub 0u}{sup {+-}} state as well as additional high-resolution data. From Innsbruck University, we have precision data obtained with cold Cs{sub 2} molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the expanded Morse oscillator form) with both finite-difference (FD) coupled-channel and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with ab initio results from Temple and Moscow State universities.

The Na2(3sσg)(4sσg) 23Σ+g state of Na2 has been observed and studied by cw perturbation-facilitated optical-optical double-resonance (PFOODR) spectroscopy for the first time. A single-mode dye laser and a Ti-sapphire laser served as the pump and the probe lasers, respectively. A total of 543 PFOODR excitation signals have been assigned to the 23Σ+g ← b3Π1u transitions. Absolute vibrational numbering was determined by counting nodes in the 23Σ+g → a3Σ+u bound-free spectra. Spectroscopic constants and the corresponding RKR potential energy curve are presented in this vsork. The values of Te, Re, and De, are found to be 25 551.237(49) cm−1, 3.53463(35) A, and 6211.5(1) cm−1 respectively.

The 3(3d)3Σg+ state of the Na2 molecule has been observed for the first time by perturbation-facilitated optical-optical double-resonance (PFOODR) excitation spectroscopy through A1Σu+ ∼ b3Πu mixed intermediate levels. The rotational structure and the fine-hyperfine splittings of the 33Σg+ ← b3Πu transitions are similar to the 43Σg+ ← b3Πu transitions of Na2. Absolute vibrational numbering of the 33Σg+ state was determined by comparing the experimental excitation intensities with the calculated Franck-Condon factors. Molecular constants and the RKR potential curve are also reported. A comparison of the molecular constants of all eight observed states dissociating to the same 3s + 3d asymptote with ab initio theory shows remarkably good agreement.

The lowest vibrational levels v = 0 to 12 of the A1Σu+ state of K2, which are perturbed by the b3Πu state (13 ≤ v ≤ 24), were reexamined using all-optical triple-resonance (AOTR) spectroscopy. The experimental data were fitted by a nonlinear least-squares fit program to obtain deperturbed molecular constants for both the A1Σu+ and b3Πu states. Improved Dunham coefficients of the A1Σu+ state in the range 0 ≤ v ≤ 62 are determined from the deperturbed Tv and Bv values including the v ≤ 12 region of this work, the v = 12–18 region in the work of Ross et al. [J. Phys. B.20, 6225–6231 (1987)], and the v = 21–62 region in the work of Lyyra et al. [J. Chem. Phys.92, 43–50 (1990)]. The electronic matrix element for the A1Σu+ ∼ b3Πu interaction is Hel = 18.64(9) cm−1, in good agreement with the value of 18.4 (2) cm−1 found by Ross et al.

Three intermediate-lying Rydberg 1Δg states of 39K2 were studied by CW optical-optical double-resonance (OODR) spectroscopy. The absolute vibrational numbering, the Dunham coefficients, the Rydberg-Klein-Rees (RKR) potential curves, and the Franck-Condon factors (FCF) of three (nd)1Δg-B1Πu systems are given. The variation with the principal quantum number n of the contribution of the ndδg Rydberg electron to the binding energy is discussed. In addition, five observed successive (nd)1Δg states included in this work (n = 8, 9, and 10) and the work of Wang et al. (J. Chem. Phys., in press) (n = 6 and 7) are assigned absolute electronic state numbering based on the molecular building-up principle. Furthermore, the dissociation limits, the dissociation energies, and the quantum defects of those (nd)1Δg states are compared with respect to the asymptotic assignments made by Broyer et al. (Chem. Phys. Lett. 99, 206–212, 1983) and by Kowalczyk et al. (Z. Phys. D. 13, 231–240, 1989); our work supports the assignment of Broyer et al.

Two examples of the 41Σg+ ∼ 23Πg ∼ 13Δg triple perturbation were observed by cw dye laser optical-optical double resonance spectroscopy via the A1Σu+ v′ = 5 intermediate state. The (vΣ, vΠ, vΔ) = (6, 2, 7) and (7, 3, 8) perturbation complexes were deperturbed, yielding the following molecular constants: T2 (23Πg) = 29027.102 (10) cm−1 , ΔG52 (23Πg) = 92.206 (10) cm−1 , A (23Πg) = 4.06 (1) cm−1 , B2 (23Πg) = 0.073740 (16) cm−1 , T7 (13Δg) = 28979.385 (15) cm−1 , ΔG152 (13Δg) = 122.450 (25) cm−1 , B7 (13Δg) = 0.117243 (20) cm−1 , T6 (41∑+g) = 29010.357 (31) cm−1 , ΔG132(41∑+g) = 101.096 (44) cm−1 , B6 (41∑+g) = 0.087626 (19)cm−1 and perturbation parameters: ζ(41∑+g ∼ 23Πg〈 υ∑ | υπ〉 = 1.459 (16) cm− 1 at Rc = 4.64 A: , α(23∑+g ∼ 13Πg〈 υπ | υδ〉 = 0.16 (7) cm− 1 at Rc = 4.12 A: , β(2(3Πg ∼ 13 Δg)lang;υπ | B (R) | υ δ〉 = 0.648 (20) A: In addition, the hyperfine structure of the 23Πgv = 2 level was sampled for all three Ω-components and many J-values. The hyperfine structure of the case aβ23Πg state is very similar to that in the b3Πu state and, like all singly excited triplet states of Na2, is dominated by the Fermi contact contribution from the singly occupied σg(3s) valence orbital.

The Na(2) 4(3)Pi(g) state has been studied by continuous-wave (cw) perturbation-facilitated optical-optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopy. The absolute vibrational numbering was determined by resolved fluorescence to the a(3)Sigma(+)(u) state. The OODR excitation lines of the 4(3)Pi(g) (Kv, N)

Perturbation-facilitated optical–optical double resonance (PFOODR) has been used to access the 2 3 Π g state of 7 Li 2 via the excitation scheme using two single-mode tunable lasers. The selected () mixed level provides a gateway through which the triplet manifold can be accessed. Fluorescence from single rovibrational levels of 2 3 Π g to the state was detected at high resolution using a Fourier transform spectrometer. Transitions to v = 0–9 in the state were observed, covering the potential well almost to the dissociation limit. The data were analyzed using a near dissociation expansion (NDE) technique and the resulting vibrational and rotational parameters were used to calculate a new RKR potential curve which reproduced the observed energy levels to within a rms error of 0.02 cm −1 . The following parameters were obtained for the state: D 0 = 301.829 ± 0.015 cm −1 , D e = 333.69 ± 0.10 cm −1 , T e = 8183.12 ± 0.12 cm −1 .

Collisional satellite lines with |ΔJ| ≤ 58 have been identified in recent polarization spectroscopy V-type optical-optical double resonance (OODR) excitation spectra of the Rb(2) molecule [H. Salami et al., Phys. Rev. A 80, 022515 (2009)]. Observation of these satellite lines clearly requires a transfer of population from the rotational level directly excited by the pump laser to a neighboring level in a collision of the molecule with an atomic perturber. However to be observed in polarization spectroscopy, the collision must also partially preserve the angular momentum orientation, which is at least somewhat surprising given the extremely large values of ΔJ that were observed. In the present work, we used the two-step OODR fluorescence and polarization spectroscopy techniques to obtain quantitative information on the transfer of population and orientation in rotationally inelastic collisions of the NaK molecules prepared in the 2(A)(1)Σ(+)(v' = 16, J' = 30) rovibrational level with argon and potassium perturbers. A rate equation model was used to study the intensities of these satellite lines as a function of argon pressure and heat pipe oven temperature, in order to separate the collisional effects of argon and potassium atoms. Using a fit of this rate equation model to the data, we found that collisions of NaK molecules with potassium atoms are more likely to transfer population and destroy orientation than collisions with argon atoms. Collisions with argon atoms show a strong propensity for population transfer with ΔJ = even. Conversely, collisions with potassium atoms do not show this ΔJ = even propensity, but do show a propensity for ΔJ = positive compared to ΔJ = negative, for this particular initial state. The density matrix equations of motion have also been solved numerically in order to test the approximations used in the rate equation model and to calculate fluorescence and polarization spectroscopy line shapes. In addition, we have measured rate coefficients for broadening of NaK 3(1)Π ← 2(A)(1)Σ(+)spectral lines due to collisions with argon and potassium atoms. Additional broadening, due to velocity changes occurring in rotationally inelastic collisions, has also been observed.

Five lower vibrational levels of the 1 3 Δ g state of Na 2 have been observed using the perturbation facilitated optical-optical double resonance technique (PFOODR). Absolute vibrational numbering has been established from a comparison of calculated Franck-Condon factors and the resolved fluorescence spectra of the 1 3 Δ g → b 3 Π u system. Molecular constants and a RKR potential energy curve based on these constants are given.

Extensive laser excitation spectra and rotationally resolved laser-induced fluorescence spectra have been recorded for the “orange system” of gaseous FeO in the wavelength regions 5790–6140 and 5580–5640 A. Detailed rotational analyses have been performed for about 20 Ω ′ substates lying between 16 350 and 18 550 cm−1. These are found to comprise a very severely perturbed 5Δi excited electronic state with a bond length of about 1.69 A (which is responsible for the parallel polarization of the electronic transition from the 5Δi ground electronic state) and a large number of “extra” Ω substates with B′ values ranging from 0.38 to 0.50 cm−1, which almost certainly belong to high vibrational levels of lower-lying electronic states. Evidence about the natures of the “extra” states is confusing, however, with the 54FeO56FeO isotope shifts apparently being in conflict with the patterns of vibrationally resolved laser-induced fluorescence. Every single Ω substate that has been analyzed shows rotational perturbations of varying severity. The density and magnitude of the rotational perturbations are quite exceptional for a diatomic molecule, and result in a new type of totally chaotic diatomic spectrum. There is a remarkable similarity to the visible spectrum of NO2: in NO2 the complications arise from the high density of perturbing ground state vibrational levels; in FeO there is a correspondingly high density of perturbing electronic states at lower energy. The great complexity of the FeO spectrum arises because the states are in an awkward intermediate spin-coupling case which still resembles Hund's case (a) but shows strong tendencies toward Hund's case (c) coupling.

One 1 Δ g state, one 1 Π g state, and several 1 Σ g + states of 39 K 2 in the energy region 28 522–30 050 cm −1 have been observed by cw optical-optical double-resonance (OODR) fluorescence excitation techniques. Absolute vibrational numberings of the 1 Δ g state, the 1 Π g state, and one of the 1 Σ g + states have been assigned and major molecular constants for these three states have been determined.

The hyperfine structure of the level N = 37, J = 38 1 2 in the C 4 Σ − , v = 0 state of VO is anomalous as a result of an electronic perturbation. Because of the high nuclear spin of 51 V ( I = 7 2 ), the hyperfine pattern has a sufficient number of lines that it can be analyzed in detail just as if it were a rotational branch fragment containing an avoided crossing. It is shown how the coefficient of F ( F + 1) in the hyperfine energy expression for the perturbing state and the perturbation matrix element can be obtained very accurately, though because the nature of the perturbing state is unknown it has not been possible to interpret the coefficient in terms of conventional hyperfine parameters in this case. The conditions for the appearance of perturbations of this type and the results to be obtained from them are discussed.

Laser-induced fluorescence studies of the “orange” system of gaseous FeO were combined with analyses of the discharge emission spectrum of FeO near 1 μm (recorded at high resolution by Fourier transform spectrometry) to give spectroscopic constants for the levels v = 0–3 of the ground state of FeO. FeO is shown to have a 5Δi ground state with r e = 1.616 A and a spin-orbit coupling constant A = −94.9 cm−1; the 5Δ0 component shows a small Λ doubling of about 0.3 cm−1. In contrast to all the known excited states of FeO the ground state is well behaved and no local rotational perturbations were detected. Predictions are given for transition frequencies of interest in astrophysical studies of FeO.