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We report results of an experimental study of the changes in the alignment of the rotational angular momentum of diatomic molecules during elastic collisions. The experiment involved collisions of diatomic lithium molecules in the A1Σu+ excited electronic state with noble gas atoms (helium and argon) in a thermal gas phase sample. Polarized light for excitation was combined with the detection of polarization-specific fluorescence in order to achieve magnetic sublevel state selectivity. We also report results for rotationally inelastic collisions of Li2 in the lowest lying rotational levels of the A1Σu+v=5 vibrational state with noble gas atoms.

Using Infrared-Infrared Double Resonance (IIDR) high resolution spectroscopy, we have observed the 20 200–21 600 cm−1 energy range of the 4 1 Σ g + electronic state of Rb 2 . The absolute vibrational quantum number assignment is based on the isotope effect using 824 rovibrational levels assigned to the 85 Rb 85 Rb and 85 Rb 87 Rb isotopomers. In addition to perturbations between the 4 1 Σ g + and 3 1 Σ g + state, strong couplings between the 4 1 Σ g + and 2 3 Π g states were observed. Preliminary molecular constants and an RKR potential energy curve are given.

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.

Electromagnetically induced transparency has been observed in 39 K 2 two-photon transitions by fluorescence detection. The two-photon absorptions correspond to 2 3 Π g ← X 1 Σ g + transitions through A 1 Σ u + ∼ b 3 Π u mixed intermediate enhancing levels, which are coincidentally on resonance with the excitation laser frequency. Laser intensity dependence of this effect has been studied and different detection schemes have been applied.

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.

We report calculations of the spin–orbit energy as a function of internuclear distance R within the b 3∏u state of K2, and between the b 3∏0u and A 1∑u+ states, together with new spectroscopic data on the b state and previously unpublished data on the A state. Both the new data and previous data are fitted to Hamiltonian parameters using the discrete variable representation (DVR) method. The DVR matrix includes nonrelativistic Born–Oppenheimer potentials and spin–orbit interactions, which are scaled to match the known asymptotic limits and to best fit the experimental data. We report fitted Dunham coefficients that yield the A and b state potentials by means of the Rydberg–Klein–Rees method. These parameters thus take into account second-order spin–orbit perturbation shifts (from the vibrational levels of these two states) which are normally not considered in band-by-band fits to spectroscopic data.

In this work we demonstrate optical control of the singlet-triplet probability distribution in the outcome of a collisional process involving lithium dimers and argon atoms. The control is achieved using the Autler-Townes effect to manipulate the spin character of a spin-orbit coupled pair of levels serving as a ``gateway'' between the singlet and triplet electronic state manifolds.

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 repulsive a 3Σu+ state potential of the Na2 molecule is determined by applying the IPA (inverse perturbation approach) of V. S. Ivanov and V. B. Sovkov [Chem. Phys. 213, 295 (1996)] to the analysis of the Na2 2 2Σg+ (v=15, N=27, and v=5, N=39)→a 3Σu+ continua observed in the work of T. J. Whang et al. [J. Mol. Spectrosc. 160, 411 (1993)]. The resulting a 3Σu+ state potential is close to the ab initio potential within the experimental error, but its right branch deviates from the RKR–Le Roy–Bernstein potential function of the a 3Σu+ state shallow well reported in E.-J. Friedman-Hill and R. W. Field [J. Chem. Phys. 96, 2444 (1992)]. The transition moment function M(R) of the 2 3Σg+−a 3Σu+ transition is also obtained from the analysis of the spectra and compared to the ab initio one. The same 2 3Σg+ (v=15, N=27)→a 3Σu+ experimental spectrum is used for investigating abilities of the WKB nodes method, the FCF phase method, and the method of the accurate equation for the potential in terms of the transitio...

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.

Using the most accurate potential curves available for the $a{}^{3}{\ensuremath{\sum}}_{u}^{+}$ and $X{}^{1}{\ensuremath{\sum}}_{g}^{+}$ states of lithium molecules, we compute the positions of shape resonances. We also calculate the deexcitation probability from a bound level ${v}^{\ensuremath{'}}$ with rotational number ${N}^{\ensuremath{'}}$ to the continuum of the lower state, and conclude that a shape resonance should be measurable for the transition $2{}^{3}{\ensuremath{\prod}}_{g}\ensuremath{\rightarrow}a{}^{3}{\ensuremath{\sum}}_{u}^{+}$. Such a shape resonance has been identified from the spectra of the transition from the ${v}^{\ensuremath{'}}{=2,N}^{\ensuremath{'}}=4$ level of $2{}^{3}{\ensuremath{\prod}}_{g}$ into the ${N}^{\ensuremath{''}}=4$ continuum of $a{}^{3}{\ensuremath{\sum}}_{u}^{+}$. Its position is in good agreement with the theoretical prediction.

We present a review of Li 2 and Na 2 triplet states. We summarize experimental results by perturbation facilitated optical–optical double resonance (PFOODR) and all-optical triple resonance techniques as well as other laser spectroscopic results. We review the PFOODR singlet∼triplet mixed window levels, the hyperfine structure of the triplet states, their predissociation, bound-free transitions in the triplet manifold, and collisional energy transfer within triplet states and between singlet and triplet states.

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.

CW optical–optical double resonance has been employed to study the upper portion of the G 1Πg state of 7Li2. The use of fluorescence and ion detection enabled the observation of vibrational levels ranging from v=20 to 48 and rotational levels ranging from J=1 to 25. For optical–optical double resonance experiments the Franck–Condon factors between these levels and useful A 1Σu+ state levels (levels that can be reached from the thermally populated levels of the ground state) were exceedingly small. The sensitive ionization detection made possible observation of this upper, anharmonic region of the potential. From the data a Rydberg–Klein–Rees potential curve was constructed which represents over 99% of the potential well depth. A C5 coefficient has been calculated and represents the first experimental determination of a long range coefficient for a doubly excited state in diatomic lithium.

The Na2 3 3Πg state adiabatically dissociates to the 3s+4p atomic limit. The 3 3Πg levels below the 3s+3d atomic limit have been observed by perturbation facilitated optical–optical double resonance (PFOODR) fluorescence excitation spectroscopy. Energy levels above the 3s+3d atomic limit cannot be observed by detecting molecular fluorescence but are observable by detecting atomic 3d→3p fluorescence. The 3 3Πg state interacts with the 3s+3d 2 3Πg state. At lower energy this interaction is responsible for many perturbations between bound vibrational levels of these two states. Above the 3s+3d limit, as a result of this interaction, the 3 3Πg state is strongly predissociated and the linewidths of levels close to the 3s+3d limit are about 22 cm−1. The predissociation interaction is due to an avoided crossing between the adiabatic 2 3Πg and 3 3Πg states at R≈2.85 A. Weak predissociation of the 4 3Σg+ and 2 3Δg states are also observed and discussed.

This Letter reports on state to state collision energy transfer in the A1Σu+ and G(2)1πg states of both 7Li2 and 6Li7Li dimers. The molecules were electronically excited by a single laser excitation or by using optical-optical double resonance (OODR) technique. Either a fluorescence or an ionization signal was monitored. A breakdown of the symmetric antisymmetric (s ⇎ a) rotational level selection rule was observed for collisional transitions in the A1Σu+ state of th nearly homonuclear 6Li7Li molecule. However, no s ⇎ a radiative transition breakdown was detected when we attempted the X1Σg+ → A1Σu+ → C(1)1πg ungerade-ungerade electronic excitation. Propensities for rotational energy transfer in the G(2)1πg state are discussed.

We report new experimental data for the Rb2 a(3)Σu(+) and 2(3)Π0g states obtained using the Perturbation Facilitated Infrared-Infrared Double Resonance (PFIIDR) technique. The results include ro-vibrational term values of the 2(3)Π0g state and resolved fluorescence spectra of the 2(3)Π0g→a(3)Σu(+) transitions for a wide range of rotational and vibrational quantum numbers. An analysis of these data confirms the initial assignment of the transitions to the a(3)Σu(+) state reported in our earlier work [B. Beser, V. B. Sovkov, J. Bai, E. H. Ahmed, C. C. Tsai, F. Xie, L. Li, V. S. Ivanov, and A. M. Lyyra, J. Chem. Phys. 131, 094505 (2009)]. The potential energy functions of the Rb2 a(3)Σu(+) and 2(3)Π0g states are derived from a simultaneous fit of the available experimental data. The improved potential function of the Rb2 a(3)Σu(+) state spans both the attractive and repulsive regions starting with internuclear distance R ∼ 4.5 Å.

State‐to‐state collision energy transfer in the 2 3Πg, 3 3Πg, 3 3Σ+g, 1 3Σ−g, and 1 3Δg states and from singlet to triplet states of 7Li2 has been studied experimentally by continuous wave optical–optical double resonance (OODR) resolved fluorescence spectroscopy. Propensity rules of collision‐induced transitions within a triplet state have been observed. When a rovibrational (v,J) level of the F 1Σ+g or G 1Πg state was excited by OODR transition, fluorescence from high‐lying triplet gerade states to the a 3Σ+u and/or b 3Πu states was always observed. This indicates that population can transfer from F 1Σ+g and G 1Πg states to triplet states by collision. Irrespective of the J of the initially excited singlet level, the most intense fluorescence from the triplet state will occur at the N or J corresponding to that of the F 1Σ+g (and/or G 1Πg)∼3Λg mixed levels. Molecular population moves to the mixed levels and then transfers to the triplet state. This clearly indicates that singlet–triplet mixed levels pla...

Resolved fluorescence from the K2 43 Σ+g state to the a3 Σ+u state has been measured by the perturbation‐facilitated optical–optical double resonance (PFOODR) technique. Data have been fit to an improved set of molecular constants for the a3 Σ+u state. In particular, the new Te value for this state has been determined as 4197.935±0.047 cm−1, nearly 1.8 cm−1 higher than previously reported. By combining the new results for the a3 Σ+u state and the recent results for the ground X1 Σ+g state [J. Chem. Phys. 103, 3350 (1995)], we report in this paper an improved analysis of long‐range dispersion and exchange interactions between two K atoms and of the X1 Σ+g and a3 Σ+u state dissociation energies De of 4450.674±0.072 cm−1 and 252.74±0.12 cm−1, respectively.

The hyperfine structure of the b 3Πu, 2 3Πg, and 3 3Πg states of 7Li2 has been studied by continuous wave perturbation facilitated optical–optical double resonance fluorescence excitation spectroscopy. The b 3Πu state has case bβJ coupling scheme. The hyperfine splittings of the two perturbed b 3Πu v=19, N=10, J=11e, s, F1 and v=19, N=5, J=4e, a, F3 levels were resolved and hyperfine constants determined to be +9.90 MHz and −20.94 MHz, respectively. Fermi contact is the main source of the hyperfine interaction and bF(b 3Πu)=+107 MHz has been obtained. The coupling schemes of different 2 3Πg levels are different: N=4, 6 levels observed from the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=10 levels observed via the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level have case bβJ coupling; the N=5 levels observed via the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=9, 11 levels observed from the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level are closer to case bβS cou...

The A 1Σ+u state of 7Li2 has been studied using all optical triple resonance spectroscopy. Vibrational levels v=27–62 and rotational levels ranging from J=0 to 27 have been observed. This represents a region between previous data from single photon experiments and new data from cold atom photoassociative spectroscopy. Our data was fit to a Dunham expansion and the resulting molecular constants reproduce most observed energies to within 0.050 cm−1. A Rydberg–Klein–Rees potential curve has also been constructed and the calculated eigenvalues are in good agreement with observed energies.

The (2p+2p) 2 3Πg and (2s+3p) 3 3Πg states of 7Li2 have been studied both experimentally and theoretically. Vibrational levels v=0–41 of the 2 3Πg state and v=6–10 of the 3 3Πg state have been observed by perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. Our ab initio calculations show that the 2 3Πg state, although dissociating into 2p+2p atomic limit, is a Rydberg state and strongly mixed with the (2s+3p) 3 3Πg and (2s+3d) 4 3Πg Rydberg states. Our theoretical calculations show good agreement with our experimental results.

The 4 3Σ+g, 3 3Πg, and 2 3Δg states of K2 have been studied by perturbation facilitated optical–optical double resonance spectroscopy for the first time. Molecular constants of those states are derived and compared with theoretical calculations. Varying the trial vibrational quantum numbers of these upper states, absolute vibrational quantum number assignments are obtained by comparison between the observed resolved fluorescence intensities and the calculated Franck–Condon factors. The Rydberg–Klein–Rees potential curves are constructed and compared with theoretical calculations. Finally, the observation of the lowest ‘‘dark’’ vibrational levels of the b 3Πu state by resolved fluorescence from the 2 3Δg state confirmed the absolute vibrational numbering of this state and allowed refinement of the b 3Πu molecular constants.

This paper reports the experimental observation of the 2 3Σ+g, 3 3Σ+g, and 4 3Σ+g states of 7Li2 by cw perturbation facilitated optical–optical double resonance spectroscopy. Molecular constants and RKR potential curves have been obtained. Our experimental Te and Re for the 2 3Σ+g state are 27 297.45(16) cm−1 and 3.0797(18) A, respectively, and for the 3 3Σ+g state are 31 043.93(53) cm−1 and 3.0378(19) A, respectively. The above values are in very good agreement with theoretical calculations. Hyperfine splitting for both states has been resolved. Both states follow Hund’s case (bβS) hyperfine coupling scheme. The experimental Fermi contact parameter, bF, is approximately 96±2 MHz for the 2 3Σ+g state and 95.6±3 MHz for the 3 3Σ+g state. These values are in good agreement with the previously obtained value 98.6±4 MHz [Li et al., J. Chem. Phys. 96, 3342 (1992)]. One level of the 4 3Σ+g state has been observed and its hyperfine structure has been resolved and characterized with Hund’s coupling case (bβS).

This paper reports the first experimental observation of the doubly excited valence (2p+2p)3Σ−g state of 7Li2. We used cw perturbation‐facilitated optical–optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopic techniques. All the observed levels have been detected through perturbations by the 2 3Πg state. The deperturbed primary molecular constants of this 1 3Σ−g state are Te=34 045.354(43) cm−1, ωe=216.820(37) cm−1, Be=0.673 69(47) cm−1, Re=2.670 81(94) A, and De=4279.306(43) cm−1. The equilibrium internuclear distance of the 1 3Σ−g state is smaller than that of the X 1Σ+g ground state.

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.

State‐to‐state collision‐induced transitions within the Na2 b 3Πu state have been studied by a sub‐Doppler optical–optical double resonance (OODR) technique employing cw, single mode dye lasers for the PUMP and PROBE steps. The main experimental results are (1) strong Ω‐conservation is observed when a low‐J 3Π0 or 3Π1 parent level is initially prepared (we are unable to prepare low‐J 3Π2 levels). This Ω‐conservation relaxes as J increases. (2) e/f parity conservation (i.e., propensity for even ΔJ changes in homonuclear molecules) is observed at low‐J within the 3Π0 manifold. This propensity for e/f‐conservation relaxes rapidly as J increases. (3) The e/f parity conservation rule observed within the 3Π0 manifold is observed not to apply to the collision‐induced transitions within the 3Π1 manifold. At low‐J, ΔJ=±1, e→f transitions are even stronger than ΔJ=±2, e→e transitions. (4) At higher‐J, for example J=16, neither Ω‐conservation nor e/f‐conservation within the 3Π0 manifold are observed. These results a...

The changes in the hyperfine quantum number (F’) that accompany collision‐induced ΔJ, ΔΩ, and Δ(e/f‐parity) transitions in the Na2 b 3Πu‐state have been studied by sub‐Doppler, cw, perturbation‐facilitated optical–optical double resonance (PFOODR) spectroscopy. The Na2 is contained in a heat pipe oven at ∼1 Torr and the primary collision partner is Na(3s 2S). The PUMP laser selectively excites a single b 3Π0u v’=12, J’=43e, s or 44e, a rotational level, the parent level. All F’ hyperfine components of the parent J’ level are directly populated by the PUMP laser, but with different velocity projections relative to the laser propagation direction. Thus each parent hf component is labeled by its longitudinal velocity. As the PROBE laser is scanned through various 2 3ΠΩg v=2, J←b 3ΠΩ’u v’=12, J’ transitions, sub‐Doppler hyperfine structure can be resolved on each parent and daughter rotational line in the PFOODR fluorescence excitation spectrum. The collisional propensity rule ΔF=ΔJ is obeyed for (s, a permut...

We present an experimental study of electromagnetically induced transparency (EIT) in a $\ensuremath{\Lambda}$-type molecular lithium system. Copropagating beam geometry is utilized in order to minimize the residual Doppler width. A coupling laser power dependent study of the EIT feature is carried out. Our findings have been complemented by theoretical studies of open systems that trace the presence of EIT starting from the density-matrix equations. Numerical simulations have been performed and are in good agreement with the experimental results.

We present here the best qualitative and quantitative illustration to date of the perturbation ‘‘gateway’’ effect in collision‐induced transitions between two mutually perturbing electronic states. The gateway effect, as described by Gelbart and Freed [Chem. Phys. Lett. 18, 470 (1973)], is a suggestion that all collision‐induced transfer of population between two electronic states proceeds through a small number of isolated‐molecule eigenstates which are of mixed electronic character, the ‘‘gateway levels,’’ and that the rates for such gateway‐mediated processes are related to the mixing fractions in the gateway levels. The gateway levels here are the Na2 A 1Σu+ v’=26∼b 3Π2u v’=28 J’=16e,a‐symmetry levels which are significantly mixed owing to an extremely small spin–orbit perturbation matrix element (the neighboring J’=15 and 17e,s‐symmetry levels are essentially free of mixing). A cw optical–optical double resonance (OODR) scheme is used to PUMP a single parent level and PROBE single daughter and grandd...

The Na2 b 3Πu state has been studied by the continuous wave (cw) all‐optical triple resonance (AOTR) technique. The AOTR technique used here corresponds to a perturbation‐facilitated optical–optical double resonance (PFOODR) excitation through A 1Σu+∼b 3Πu mixed intermediate levels from the ground state to the 2 3Πg state and stimulated emission pumping (SEP) of the 2 3Πg→b 3Πu transition. This sub‐Doppler high‐resolution PFOODR‐SEP technique has allowed us to reach many b 3Πu levels (Ω=0, 1, 2, perturbed and unperturbed, including low v below the A 1Σu+ potential minimum and higher vibrational levels up to v=57). Based on these new high resolution data and previous results from high resolution spectroscopy, we have determined a new set of deperturbed molecular constants from the b 3Πu state up to v=57, the corresponding RKR potential energy curve and the A 1Σu+∼b 3Πu spin–orbit interaction constants. This represents an example of a powerful and general technique for observing a ‘‘dark’’ (e.g., triplet) p...

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.

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed A (1)Sigma(+)(u) and b (3)Pi(u) states of the rubidium dimer. The results are based on laser-induced fluorescence and optical-optical double-resonance polarization spectroscopy measurements combined with earlier laser-induced fluorescence data. We used an analytic potential (Hannover form) incorporated in a discrete variable representation of the Hamiltonian matrix for numerical energy-level calculation. A previous vibrational assignment of the A levels is confirmed, and very probable vibrational assignment for the b levels is also obtained. Currently, the rms residual of our fit is 0.053 cm(-1) as compared to the typical experimental uncertainties that are estimated to be 0.005 cm(-1). Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with ab initio calculations by all electrons and effective core pseudopotential methods. Analysis of the computational results yields an explanation for the ubiquitous single minima in these spin-orbit functions, which can be represented approximately by Morse-type functions. (Less)

International audience; We have observed the vibrational levels v(") = 0-40 of the Cs(2) a (3)Sigma(u)(+) state by perturbation facilitated infrared-infrared double resonance excitation and spectrally resolved fluorescence measurements, and derived a multiparameter Morse long range potential and molecular constants based on these data.

Complete understanding of processes involving large internuclear distances (e.g. , cold atom collisions) requires accurate knowledge of long-range potentials. Determination of these long-range potentials has been difficult due to the weakness of direct excitation to these levels from thermally populated ground-state levels near an equilibrium internuclear distance. In long-range molecular states most of the amplitude of the vibrational wave function is at large internuclear distances, leading to exceedingly small Franck-Condon factors with therfluorescence mally populated levels. Spin selection rules and the inversion selection rule (gerade ungerade) in homonuclear diatomic molecules impose additional restrictions. For example, unperturbed levels of the b H„state of alkali dimers cannot be reached in a single electronic transition from the ground state. In this paper we report a new continuous-wave high-resolution technique to overcome these difficulties. With regard to the Na2 X'Xg+ 2 'X, „+ system several cw techniques were previously developed to reach high vibrational excitation in the A 'X„+ state: hvl decay hv2 X'X~+(low thermal v) A 'Z„+(low v) X'Z~+(intermediate v) A 'Z„+(high v) .

Collisional energy transfer between 1 Δ g and 1 Σ + g Rydberg states of K 2 has been studied by optical-optical double resonance (OODR) resolved fluorescence spectroscopy. The collision-induced probability for transition from a 1 Δ g state to an adjacent 1 Σ + g state of K 2 depends much more strongly on Δ J than on Δ E in each case studied. Δ J = 0 collision transfer is more favorable than Δ J = ±2, … for 1 Δ g odd J e levels. For 1 Δ g even J f levels, Δ J = ± 1 transfers are most favorable. The measurements of intensities of 1 Δ g , 1 Σ + g ← B 1 Π u , υ′ = 2, J ′ = 14e transitions and fluorescence intensities show that the collision-induced transition probability of these 1 Δ g - 1 Σ + g systems is quite large.

We have investigated the effects of inhomogeneous Doppler line broadening on the Autler-Townes (AT) splitting in a three-level open molecular cascade system. For moderate Rabi frequencies in the range of $300--600\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, the fluorescence line shape from the uppermost level \ensuremath{\mid}3⟩ in this system depends strongly on the wave-number ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level \ensuremath{\mid}2⟩ appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the ratio of the probe and coupling laser wave numbers, and the laser propagation geometry based on our theoretical analysis of the Doppler integral. The low threshold Rabi frequency region for Autler-Townes splitting is important for high-resolution Autler-Townes spectroscopy since the laser E-field amplitudes are modest in continuous-wave laser experiments.

Rydberg states of the potassium dimer in the 28 430–29 080 cm−1 and 30 030–30 500 cm−1 regions above the ground state X1Σ+g minimum have been studied using the perturbation facilitated optical–optical double resonance technique (PFOODR). Energy levels in these energy regions have been assigned to both triplet and singlet gerade states based on excitation pattern information as well as intensity considerations. Resolved fluorescence from a mixed triplet–singlet 43Πg ∼1Πg upper state to the ground triplet state a 3Σ+u has been used to construct a potential energy curve for the a 3Σ+u state which is in excellent agreement with recent theoretical results. Since this electronic state and the ground singlet state X1Σ+g share the same dissociation limit, we have determined the dissociation energy for the potassium dimer to be De=4450±2 cm−1.

Using resolved fluorescence from a 1Σ+g Rydberg state to the A 1Σ+u state of K2, we have observed the lowest vibrational levels (v’≤12) of the A 1Σ+u state. Levels v’=21 to 62 (well beyond the previously known v’=12 to 18 region) were observed using the polarization optical–optical double resonance technique. Molecular constants and a Rydberg–Klein–Rees (RKR) potential energy curve based on these constants are given. Franck–Condon factors for the K2, A 1∑+u–X 1∑+g system based on this new A 1Σ+u potential are also given.

Theoretical analysis of the Autler-Townes splitting pattern in a three-level cascade excitation of a Doppler-broadened sample reveals that the observed Autler-Townes splitting is not only a function of the coupling-laser Rabi frequency, as in the homogeneously broadened case, but can also strongly depend on the wavenumber ratio of the coupling and probe lasers. Utilizing a steady-state density matrix formalism, we derive exact expressions for the populations of the intermediate and upper levels for a homogeneously broadened system. In the limit of a weak probe field, analytical expressions for Doppler-broadened excitation spectra from the intermediate and upper levels are derived. Using these expressions, we investigate the critical role of Doppler broadening on the observation of Autler-Townes splitting and its asymptotic behavior as a function of the coupling Rabi frequency for counterpropagating and copropagating configurations for different wavenumber ratios of the lasers.