The effect of collisions on the rotational angular momentum of diatomic molecules studied using polarized light.

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.

Rotationally inelastic collisions of excited NaK and NaCs molecules with noble gas and alkali atom perturbers.

We report measurements of rate coefficients at T ≈ 600 K for rotationally inelastic collisions of NaK molecules in the 2(A)1Σ+ electronic state with helium, argon, and potassium atom perturbers. Several initial rotational levels J between 14 and 44 were investigated. Collisions involving molecules in low-lying vibrational levels (v = 0, 1, and 2) of the 2(A)1Σ+ state were studied using Fourier-transform spectroscopy. Collisions involving molecules in a higher vibrational level, v = 16, were studied using pump/probe, optical-optical double resonance spectroscopy. In addition, polarization spectroscopy measurements were carried out to study the transfer of orientation in these collisions. Many, but not all, of the measurements were carried out in the "single-collision regime" where more than one collision is unlikely to occur within the lifetime of the excited molecule. The analysis of the experimental data, which is described in detail, includes an estimate of effects of multiple collisions on the reported rate coefficients. The most significant result of these experiments is the observation of a strong propensity for ΔJ = even transitions in collisions involving either helium or argon atoms; the propensity is much stronger for helium than for argon. For the initial rotational levels studied experimentally, almost all initial orientation is preserved in collisions of NaK 2(A)1Σ+ molecules with helium. Roughly between 1/3 and 2/3 of the orientation is preserved in collisions with argon, and almost all orientation is destroyed in collisions with potassium atoms. Complementary measurements on rotationally inelastic collisions of NaCs 2(A)1Σ+ with argon do not show a ΔJ = even propensity. The experimental results are compared with new theoretical calculations of collisions of NaK 2(A)1Σ+ with helium and argon. The calculations are in good agreement with the absolute magnitudes of the experimentally determined rate coefficients and accurately reproduce the very strong propensity for ΔJ = even transitions in helium collisions and the less strong propensity for ΔJ = even transitions in argon collisions. The calculations also show that collisions with helium are less likely to destroy orientation than collisions with argon, in agreement with the experimental results.

Experimental studies of the NaCs 12(0+) [71Σ+] state: Spin-orbit and non-adiabatic interactions and quantum interference in the 12(0+) [71Σ+] and 11(0+) [53Π0] emission spectra.

We present results from experimental studies of the 11(0+) and 12(0+) electronic states of the NaCs molecule. An optical-optical double resonance method is used to obtain Doppler-free excitation spectra. Selected data from the 11(0+) and 12(0+) high-lying electronic states are used to obtain Rydberg-Klein-Rees and Inverse Perturbation Approach potential energy curves. Interactions between these two electronic states are evident in the patterns observed in the bound-bound and bound-free fluorescence spectra. A model, based on two separate interaction mechanisms, is presented to describe how the wavefunctions of the two states mix. The electronic parts of the wavefunctions interact via spin-orbit coupling, while the individual rotation-vibration levels interact via a second mechanism, which is likely to be non-adiabatic coupling. A modified version of the BCONT program was used to simulate resolved fluorescence from both upper states. Parameters of the model that describe the two interaction mechanisms were varied until simulations were able to adequately reproduce experimental spectra.

Experimental studies of the NaCs 5(3)Π0 and 1(a)3Σ+ states.

We report high resolution measurements of 372 NaCs 5(3)Π(0)(v, J) ro-vibrational level energies in the range 0 ≤ v ≤ 22. The data have been used to construct NaCs 5(3)Π(0) potential energy curves using the Rydberg-Klein-Rees and inverted perturbation approximation methods. Bound-free 5(3)Π(0)(v, J) → 1(a)(3)Σ(+) emission has also been measured, and is used to determine the repulsive wall of the 1(a)(3)Σ(+) state and the 5(3)Π(0) → 1(a)(3)Σ(+) relative transition dipole moment function. Hyperfine structure in the 5(3)Π(0) state has not been observed in this experiment. This null result is explained using a simple vector coupling model.

Quantum control of the spin-orbit interaction using the Autler-Townes effect.

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 spin-orbit interaction between a pair of weakly interacting singlet-triplet rovibrational levels, G (1)Π(g)(v=12,J=21,f)-1 (3)Σ(g)(-)(v=1,N=21,f), 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.

Collisional transfer of population and orientation in NaK.

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 â† 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.

Measurement of absolute transition dipole moment functions of the 3 (1)Pi --> 1(X) (1)Sigma+ and 3 (1)Pi --> 2(A) (1)Sigma+ transitions in NaK using Autler-Townes spectroscopy and calibrated fluorescence.

We describe a two-laser experiment using optical-optical double resonance fluorescence and Autler-Townes (AT) splittings to determine the NaK 3 (1)Pi-->1(X)(1)Sigma(+), 2(A)(1)Sigma(+) absolute transition dipole moment functions. Resolved 3 (1)Pi-->A (1)Sigma(+) and 3 (1)Pi-->X (1)Sigma(+) fluorescence was recorded with the frequencies of a titanium-sapphire laser (L1) and a ring dye laser (L2) fixed to excite particular 3 (1)Pi(upsilon = 19,J = 11,f)<--A (1)Sigma(+)(upsilon('),J(') = J = 11,e)<--X (1)Sigma(+)(upsilon("),J(") = J(')+/-1,e) double resonance transitions. The coefficients of a trial transition dipole moment function mu(e)(R) = a(0)+a(1)(R(eq)/R)(2)+a(2)(R(eq)/R)(4)+... were adjusted to match the relative intensities of resolved spectral lines terminating on the lower A (1)Sigma(+)(upsilon('),11,e) and X (1)Sigma(+)(upsilon("),11,e) levels. These data provide a relative measure of the functions mu(e)(R) over a broad range of R. Next, L2 was tuned to either the 3 (1)Pi(19,11,f)<--A (1)Sigma(+)(10,11,e) or 3 (1)Pi(19,11,f)<--A (1)Sigma(+)(9,11,e) transition and focused to an intensity large enough to split the levels via the AT effect. L1 was scanned over the A (1)Sigma(+)(10,11,e)<--X (1)Sigma(+)(1,10,e) or A (1)Sigma(+)(9,11,e)<--X (1)Sigma(+)(0,12,e) transition to probe the AT line shape, which was fit using density matrix equations to yield an absolute value for mu(ik) = integral psi(vib) (i)(R)mu(e)(R)psi(vib)(k)(R)dR, where i and k represent the upper and lower levels, respectively, of the coupling laser (L2) transition. Finally, the values of mu(ik) were used to place the relative mu(e)(R) functions obtained with resolved fluorescence onto an absolute scale. We compare our experimental transition dipole moment functions to the theoretical work of Magnier et al. [J. Mol. Spectrosc. 200, 96 (2000)].

Nonadiabatic coupling in the 3 3Pi and 4 3Pi states of NaK.

The excited 3 (3)Pi and 4 (3)Pi electronic states of the NaK molecule exhibit an avoided crossing, leading to the anomalous behavior of many features of the rovibrational energy levels belonging to each state. A joint experimental and theoretical investigation of these states has been carried out. Experimental measurements of the vibrational, rotational, and hyperfine structure of numerous levels of the 3 (3)Pi state were recently obtained using the Doppler-free, perturbation-facilitated optical-optical double resonance technique. Additional measurements for the 4 (3)Pi state as well as bound-free emission spectra from selected 3 (3)Pi, 4 (3)Pi, and mixed 3 (3)Pi to approximately 4 (3)Pi rovibrational levels are reported here. A model is also presented for calculating the mixed rovibrational level energies of the coupled 3 (3)Pi-4 (3)Pi system, starting from a 2x2 diabatic electronic Hamiltonian. The 3 (3)Pi and 4 (3)Pi potential curves and the coupling between them are simultaneously adjusted to fit the observed rovibrational levels of both states. The energy levels of the potential curves determined by the fit are in excellent agreement with experiment. The nonadiabatic coupling is sufficiently strong to cause an overall shift of 2-3 cm(-1) for many rovibrational levels as well as somewhat larger shifts for certain pairs of 3 (3)Pi to approximately 4 (3)Pi levels that would otherwise be very close together.

Experimental study of the NaK 3 3Pi double minimum state.

We have used the Doppler-free, perturbation-facilitated optical-optical double-resonance technique to investigate the vibrational, rotational, and hyperfine structure of the 3 (3)Pi double minimum state of NaK. Since this electronic state arises from an avoided crossing with the nearby 4 (3)Pi state, we observe striking patterns in the data that provide a sensitive probe of the electronic wave function in the various regions of the double well potential. A single-mode cw dye laser excites 2(A) (1)Sigma(+)(v(A),J) approximately 1(b) (3)Pi(Omega=0)(v(b),J) mixed singlet-triplet "window" levels from thermally populated rovibrational ground state levels, 1(X) (1)Sigma(+)(v(X),J+/-1). Further excitation by a single-mode cw Ti:sapphire laser selects various 3 (3)Pi(0)(v(Pi),J(Pi)) rovibrational levels, which are detected by observing direct 3 (3)Pi(0)-->1(a) (3)Sigma(+) fluorescence in the green spectral region. Using the inverse perturbation approximation method, we have determined a 3 (3)Pi(0) potential curve that reproduces the measured energies to approximately 0.24 cm(-1). In addition, the hyperfine and spin-orbit constants, b(F) and A(v), have been determined for each region of the potential curve.

The NaK 1(b) 3Pi(Omega=0) state hyperfine structure and the 1(b) 3Pi(Omega=0) approximately 2(A) 1Sigma+ spin-orbit interaction.

We have measured the hyperfine structure of mutually perturbing rovibrational levels of the 1(b) 3Pi0 and 2(A) 1Sigma+ states of the NaK molecule, using the perturbation-facilitated optical-optical double resonance method with copropagating lasers. The unperturbed 1(b) 3Pi0 levels are split into four hyperfine components by the Fermi contact interaction bFIS. Mixing between the 1(b) 3Pi0 and 2(A) 1Sigma+ levels imparts hyperfine structure to the nominally singlet component of the perturbed levels and reduces the hyperfine splitting of the nominally triplet component. Theoretical analysis relates these observations to the hyperfine splitting that each 1(b) 3Pi0 level would have if it were not perturbed by a 2(A) 1Sigma+ level. Using this analysis, we demonstrate that significant hyperfine splitting arises because the 1(b) 3Pi0 state cannot be described as pure Hund's case (a). We determine bF for the 1(b) 3Pi0 levels and also a more accurate value for the magnitude of the singlet-triplet spin-orbit coupling HSO=[1(b) 3Pi0(vb,J)(H(SO))2(A) 1Sigma+(vA,J). Using the known spectroscopic constants of the 1(b) 3Pi state, we obtain bF=0.009 89+/-0.000 27 cm(-1). The values of (H(SO)) are found to be between 2 and 3 cm(-1), depending on vb, vA, and J. Dividing (H(SO)) by calculated vibrational overlap integrals, and taking account of the 1(b) 3Pi(Omega) rotational mixing, we can determine the magnitude of the electronic part H(el) of H(SO). Our results yield (H(el))=(16.33+/-0.15) cm(-1), consistent with our previous determinations using different techniques.

The NaK 1 1,3delta states: theoretical and experimental studies of fine and hyperfine structure of rovibrational levels near the dissociation limit.

Earlier high-resolution spectroscopic studies of the fine and hyperfine structure of rovibrational levels of the 1 3delta state of NaK have been extended to include high lying rovibrational levels with v < or = 59, of which the highest levels lie within approximately 4 cm(-1) of the dissociation limit. A potential curve is determined using the inverted perturbation approximation method that reproduces these levels to an accuracy of approximately 0.026 cm(-1). For the largest values of v, the outer turning points occur near R approximately 12.7 angstroms, which is sufficiently large to permit the estimation of the C6 coefficient for this state. The fine and hyperfine structure of the 1 3delta rovibrational levels has been fit using the matrix diagonalization method that has been applied to other states of NaK, leading to values of the spin-orbit coupling constant A(v) and the Fermi contact constant b(F). New values determined for v < or = 33 are consistent with values determined by a simpler method and reported earlier. The measured fine and hyperfine structure for v in the range 44 < or = v < or = 49 exhibits anomalous behavior whose origin is believed to be the mixing between the 1 3delta and 1 1delta states. The matrix diagonalization method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. The analysis leads to accurate values for A(v) and b(F) for all values of v < or = 49. For higher v (50 < or = v < or = 59), several rovibrational levels have been assigned, but the pattern of fine and hyperfine structure is difficult to interpret. Some of the observed features may arise from effects not included in the current model.

Rotational Pattern Difference in Resolved Fluorescence Spectra with Different Detection Schemes.

The relative intensities of rotational lines in resolved fluorescence spectra are dependent on the detection direction and the choice of the detection scheme when a grating monochromator is used. These differences arise from the spatially anisotropic distribution of the fluorescence, the rotational branch dependence of the fluorescence polarization, and the polarization dependence of the monochromator grating efficiency. Both the anisotropy of the emission and the rotational branch dependence of the fluorescence polarization are enhanced in double-resonance excitation schemes. In the present work, we analyze the relative intensities in the (7)Li(2) 1(3)Sigma(-)(g) --> 1(b)(3)Pi(u) and 1(3)Delta(g) --> 1(b)(3)Pi(u) resolved fluorescence spectra, observed following double-resonance excitation, for three different detection schemes. Copyright 1999 Academic Press.

The 4(3)Pi(g) State of Na(2): Vibrational Numbering and Hyperfine Structure.

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) <-- b(3)Pi(u) (Kv(b)('), J') approximately A(1)Sigma(+)(u) (Kv(A)('), J') <-- X(1)Sigma(+)(g) (Kv", J") transitions show hyperfine splittings, and the hyperfine coupling scheme of the upper 4(3)Pi(g) levels is case b(betaS). Although this 4(3)Pi(g) state dissociates to the 3p + 3p atomic limit, it is a Rydberg state at a small internuclear distance, and the hyperfine splitting is caused mainly by the Fermi contact interaction of the varsigma(g)3s valence electron with the nuclei. The Fermi contact constant was determined to be b(F) = 218.3 +/- 3.9 MHz. Copyright 1999 Academic Press.

Experimental Study of the NaK 3(1)Pi State.

We report the results of an optical-optical double resonance experiment to determine the NaK 3(1)Pi state potential energy curve. In the first step, a narrow band cw dye laser (PUMP) is tuned to line center of a particular 2(A)1Sigma+(v', J') <-- 1(X)1Sigma+(v", J") transition, and its frequency is then fixed. A second narrowband tunable cw Ti:Sapphirelaser (PROBE) is then scanned, while 3(1)Pi --> 1(X)1Sigma+ violet fluorescence is monitored. The Doppler-free signals accurately map the 3(1)Pi(v, J) ro-vibrational energy levels. These energy levels are then fit to a Dunham expansion to provide a set of molecular constants. The Dunham constants, in turn, are used to construct an RKR potential curve. Resolved 3(1)Pi(v, J) --> 1(X)1Sigma+(v", J") fluorescence scans are also recorded with both PUMP and PROBE laser frequencies fixed. Comparison between observed and calculated Franck-Condon factors is used to determine the absolute vibrational numbering of the 3(1)Pi state levels and to determine the variation of the 3(1)Pi --> 1(X)1Sigma+ transitiondipole moment with internuclear separation. The recent theoretical calculation of the NaK 3(1)Pi state potential reported by Magnier and Millié (1996, Phys. Rev. A 54, 204) is in excellent agreement with the present experimental RKR curve. Copyright 1999 Academic Press.

New Vibrational Numbering and Potential Energy Curve for the 3(3)Pig Electronic State of the Li2 Molecule.

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.