Hyperfine structures of the 7Li2 b3Πu, 23Πg, and 33Πg states: Continuous wave perturbation facilitated optical–optical double resonance spectroscopy

Characteristic footprints of an exceptional point in the dynamics of Li dimer under a laser field

Non-hermitian quantum mechanics is a formalism that excels in describing time-dependent states such as resonances. As one, it opens up a window to explore new and undiscovered phenomena. Under this formalism coalescence of two eigenstates and a deficient spectrum are a possible situation. These situations are unique and can occur solely in specific conditions known as Exceptional Points (EPs). An EP holds unique characteristics. One of which is a switch-like behavior: upon adiabatically changing the conditions in a closed loop around the EP, the population of one resonance can be transferred completely to another resonance. The phenomenon was not experimentally observed in an atomic or molecular system so far, although experiments involving nonlinear PT symmetry optics and microwave cavities have already indicated its existence. In this work, we demonstrate and confirm that the switch-like behavior exists in the spectrum of a lithium dimer taking into account both the rotations and the vibrations of the system. Moreover, a footprint of the EP is also shown to exist in the photo-association process of the lithium dimer. In this process, the EP's resonances serve as the mean to associate two free lithium atoms into a dimer. Based on this, we suggest a corresponding experiment to demonstrate for the first time the EP phenomenon in a molecular system.

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.

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.

The Na2 2 3pi(g) state: new observations and hyperfine structure

Many more Na2 2 3pi(g) v = 0-43, omega = 0, 1, 2 levels have been observed by sub-Doppler continuous wave perturbation facilitated optical-optical double resonance fluorescence excitation spectroscopy and the hyperfine structure of the omega = 0 and 2 levels has been resolved. New molecular constants for the less perturbed v = 0-43 levels have been obtained with these new and the previously reported data. The hyperfine coupling scheme of the observed 2 3pi(g) levels is close to Hund's case a(beta) with a Fermi contact constant b(F) = 160+/-5 MHz, which is smaller than the Fermi contact constants of other Na2 triplet Rydberg states, b(F) = 200-245 MHz.

Ab initio study of low-lying triplet states of the lithium dimer

Observation of Bose-Einstein condensation in Li27 initiated the interest in the scattering length of two ground state lithium atoms when they approach each other as a radical pair triplet aSigmau+3 state. But some properties of this state are still unknown. In present work, a number of low-lying triplet states of lithium molecule are calculated by multi-configuration self-consistent field (MCSCF) and response techniques with account of spin-orbit coupling, spin-spin coupling and some other magnetic perturbations. The singlet-triplet transition probabilities to the ground state are also presented. Most results are connected with the weakly bound lowest triplet a3Sigmau+ state, whose radiative lifetime and spin-splitting are unknown so far in spite of its great importance in Bose-Einstein condensation. Calculations indicate that this state has a very small spin-splitting, lambdass=-0.01 cm-1, which is negligible in comparison with the line-width in experimental Fourier transform spectra published so far. Similar splitting is obtained for the upper state of the 1(3)Sigmag+--a3Sigmau+ transition. This is in agreement with experimental rovibronic analysis of the 1(3)Sigmag+--a3Sigmau+ band system in which the triplet structure was not resolved. The radiative lifetime of the a3Sigmau+ state is predicted to exceed 10 h.

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.

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.

Hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2)

The hyperfine structures of the 2 (3)Sigma(g) (+), 3 (3)Sigma(g) (+), and 4 (3)Sigma(g) (+) states of Na(2) have been resolved with sub-Doppler continuous wave perturbation facilitated optical-optical double resonance spectroscopy via A (1)Sigma(u) (+) approximately b (3)Pi(u) mixed intermediate levels. The hyperfine patterns of these three states are similar. The hyperfine splittings of the low rotational levels are all very close to the case b(betaS) limit. As the rotational quantum number increases, the hyperfine splittings become more complicated and the coupling cases become intermediate between cases b(betaS) and b(beta J) due to spin-rotation interaction. We present a detailed analysis of the hyperfine structures of these three (3)Sigma(g) (+) states, employing both case b(betaS) and b(beta J) coupling basis sets. The results show that the hyperfine splittings of the (3)Sigma(g) (+) states are mainly due to the Fermi-contact interaction. The Fermi contact constants for the two d sigma Rydberg states, the 2 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+), are 245+/-5 MHz and 225+/-5 MHz, respectively, while the Fermi contact constant of the s sigma 3 (3)Sigma(g) (+) Rydberg state is 210+/-5 MHz. The diagonal spin-spin and spin-rotation constants, and nuclear spin-electronic spin dipolar interaction parameters of the 3 (3)Sigma(g) (+) and 4 (3)Sigma(g) (+) states are also obtained.

Observation of the 3 3Σ+–X 1Σ+ transition of KRb by resonance enhanced two-photon ionization in a pulsed molecular beam: Hyperfine structures of 39K85Rb and 39K87Rb isotopomers

The 3(3)Sigma(+)-X1Sigma+ transition of KRb is observed by resonance enhanced two-photon ionization in a pulsed molecular beam. Hyperfine splittings of 39K85Rb and 39K87Rb isotopomers are observed. From the magnitude of hyperfine splittings, we found that the main hyperfine structure was dominated by the Fermi contact interaction between the Rb nuclear spin and the unpaired electron spin. The Fermi contact interaction constants were determined to be 291 MHz for 39K85Rb and 665 MHz for 39K87Rb. In the KRb 3(3)Sigma+ state the electron spin couples more strongly with the Rb nuclear spin than with other angular momenta, and the energy level structure is well described by the hyperfine angular momentum coupling scheme of the b(betaS) case. The molecular constants and the Rydberg-Klein-Rees potential energy curve of the 3(3)Sigma+ state were determined.

The Predissociation of the 1(3)Sigma(-)(g) State of (7)Li(2)

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 Å. 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.

The 2(3)Delta(g) State of (7)Li(2)

Using pulsed perturbation-facilitated optical-optical double resonance (PFOODR) spectroscopy, the 2(3)Delta(g) state of (7)Li(2) (electronic configuration (varsigma(g)2s) (4ddelta(g)), effective principal quantum number n* = 4.101) has been observed and assigned. Molecular constants and a RKR potential energy curve were obtained. The major molecular constants are Copyright 2000 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.