The NaK 1(b)ΠΩ=3 state hyperfine structure and the 1(b)ΠΩ=3∼2(A)Σ+1 spin–orbit interaction

Abstract

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.

Spin–orbit coupling of the NaK 33Π and 31Π states: Determination of the coupling constant and observation of quantum interference effects

“…(13), the factor cos 2 u/sin 2 u multiplies the cos 2 u/sin 2 u from the excitation step to yield the cos 4 u/sin 4 u appearing in Eq. (14). The upper state mixing angle is easily obtained from the ratio of these ratios:…”

“…We use a single-mode cw dye laser (the ''pump'' laserCoherent model 699-29) to excite NaK molecules from a selected ro-vibrational level of the molecular ground state 1(X) 1 R + to the ''intermediate state'', which is a level of the 2(A) 1 R + electronic state or a level with mixed 1(b) 3 P X $ 2(A) 1 R + character [8,9,12,14,15]. The mixed levels 1(b) 3 …”

“…[9,14], and [52] the magnitude of the spin-orbit matrix element n is given approximately as a product of an electronic term |H el | times a vibrational overlap integral:…”

“…Heteronuclear alkali molecules have permanent dipole moments and are, therefore, of particular interest because, in principle, they can be oriented in an optical lattice [1][2][3][4][5][6][7]. In our laboratory at Lehigh University we have carried out a series of high-resolution spectroscopic studies of various excited electronic states of the heteronuclear alkali diatomic molecule NaK [8][9][10][11][12][13][14][15][16][17]. We have been particularly interested in the fine and hyperfine structure of these states and how variations in these structures with vibrational and rotational quantum numbers reflect changes in the electronic wavefunction with internuclear separation.…”

Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules

“…We emphasize that table I is by no mean an exhaustive listing of spectroscopic studies on bialkali molecules. For example recent studies have been made on LiNa [73,92,[97][98][99][100], LiK [101], LiCs [102], NaK [103], NaRb [104], NaCs [105], KCs [106][107][108][109][110][111][112], RbCs [113][114][115]. However we show in following sections that a more precise de-TABLE I. References for all the electronic PECs used in the calculations (SOCME ≡ Spin-Orbit Coupling Matrix Elements).…”