LiRb Molecules Research Articles

Theoretical study of the Coriolis effect in LiNa, LiK, and LiRb molecules.

The non-adiabatic electronic matrix elements, LΠΣ(R), that arise from the spin-conserving electron-rotational interactions between all mΣ+ and mΠ states, where multiplicity m = 1, 3, converging to the lowest three dissociation limits of Li-containing alkali diatomics, LiM (M = Na, K, Rb), were calculated ab initio up to large internuclear distances, R. The required electronic wavefunctions were obtained within the framework of the multi-reference configuration interaction treatment of the two-valence-electron problem constructed using small-core scalar-relativistic effective core potentials and l-independent core-polarization potentials. A least squares analysis of the ab initio functions at large internuclear distances in conjunction with long-range perturbation theory (LRPT) revealed three different asymptotic behaviors of the LΠΣ(R → +∞)-functions: const. + β[n]/Rn, characterized by n = -1, 3 and 6. The asymptotic coefficients β[n], extracted from the point-wise ab initio data, were found to be in agreement with their LRPT counterparts, which were evaluated analytically using the relevant atomic parameters. The mass dependence of the LΠΣ matrix elements was investigated analytically and numerically. To confirm the reliability of the LΠΣ(R)-functions and interatomic potentials at small and intermediate distances, the empirical q-factors available for the D1Π-states of all LiM molecules studied were compared with their theoretical counterparts derived from the present ab initio data.

Ab initio study of R-dependent behavior of the hyperfine structure parameters for the [formula omitted] states of LiRb and LiCs

Diagonal a3Σ1+-a3Σ1+ and off–diagonal X1Σ0++-a3Σ0-+ magnetic hyperfine structure (HFS) matrix elements were calculated ab initio for the LiRb and LiCs molecules in a wide range of internuclear distances using the multi–reference Fock space coupled clusters method with generalized relativistic effective core potentials to describe the four–component valence wavefunctions near the nuclei. At large distances, both HFS functions vary little, though they may fluctuate by as much as 12 to 24% in the intermediate range. The plateau exhibited by the a3Σ1+-a3Σ1+ HFS function at 4–5 Å, could be attributed to pronounced spin–orbit coupling of the intersecting a3Σ+ and b3Π states.

C6 coefficients for interacting Rydberg atoms and alkali-metal dimers

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2L_j$; $L\leq 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^1\Sigma^+$; $v=0$, $J=0$). We compute the associated $C_6$ dispersion coefficients of atom-molecule pairs involving $^{133}$Cs and $^{85}$Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O(n^7)$ over the range of principal quantum numbers $40\leq n\leq 150$. For all atom-molecule pairs considered, Rydberg states $n^2S_j$ and $n^2P_j$ result in attractive $1/R^6$ potentials. In contrast, $n^2D_j$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as $n^{-5}$ for $n>40$. For intermediate values of $n\lesssim40$, both repulsive and attractive interaction energies in the order of $ 10-100 \,\mu$K can be achieved with specific atomic and molecular species. The accuracy of the reported $C_6$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\Delta C_6/C_6$ estimated to be no greater than 1\% on average.

Two-photon photoassociation spectroscopy of an ultracold heteronuclear molecule

We report on two-photon photoassociation (PA) spectroscopy of ultracold heteronuclear LiRb molecules. This is used to determine the binding energies of the loosely bound levels of the electronic ground singlet and the lowest triplet states of LiRb. We observe strong two-photon PA lines with power broadened line widths greater than 20 GHz at relatively low laser intensity of 30 W/cm$^{2}$. The implication of this observation on direct atom to molecule conversion using stimulated Raman adiabatic passage (STIRAP) is discussed and the prospect for electronic ground state molecule production is theoretically analyzed.

Production of ultracold ground-state LiRb molecules by photoassociation through a resonantly coupled state

We report on a resonantly coupled 2(1) - 4 (1) photoassociation resonance in LiRb. This pair of states displays interesting decay physics that hint at interference-like effects caused by two different decay paths. We observe decay to predominantly $X \ ^1\Sigma^+ \ v=43$, with significant numbers of molecules produced in $X \ ^1\Sigma^+ \ v=2$ - 12. This photoassociation resonance also produces $\sim$300 $X \ ^1\Sigma^+ \ v=0 \ J=0$ molecules/second. Finally, we identify a stimulated Raman adiabatic passage transfer pathway from $v=43$ to $v=0$ that has the potential to produce up to $2 \times 10^5$ LiRb molecules/second in the $X \ ^1\Sigma^+ \ v=0 \ J=0$ state.

The d 3Π state of LiRb.

We report our spectroscopic studies of the d 3Π state of ultra-cold 7Li85Rb using resonantly enhanced multi-photon ionization and depletion spectroscopy with bound-to-bound transitions originating from the metastable a 3Σ+ state. We evaluate the potential of this state for use as the intermediate state in a stimulated-Raman-adiabatic-passage transfer scheme from triplet Feshbach LiRb molecules to the X 1Σ+ ground state and find that the lowest several vibrational levels possess the requisite overlap with initial and final states, as well as convenient energies. Using depletion measurements, we measured the well depth and spin-orbit splitting. We suggest possible pathways for short-range photoassociation using deeply bound vibrational levels of this electronic state.

Ab initio studies on the spin-forbidden cooling transitions of the LiRb molecule

The spin-forbidden cooling of the LiRb molecule is investigated based on ab initio quantum chemistry calculations. The multireference configuration interaction method is used to generate the potential energy curves (PECs) of the ground state X(1)Σ(+) and the low-lying excited states a(3)Σ(+), B(1)Π, and b(3)Π. The spin-orbit coupling effects for the PECs and the transition dipole moments (TDMs) between the X(1)Σ(+), b(3)Π and a(3)Σ(+) states are also calculated. The analytical functions for the PECs are deduced. The rovibrational energy levels, the spectroscopic parameters and the Franck-Condon factors (FCF) are determined by solving the Schrödinger equation of nuclear movement with the obtained analytical functions. The b(3)Π0 ↔ X(1)Σ(+) and b(3)Π1 ↔ X(1)Σ(+) transitions have highly diagonal distributed FCFs and non-zero TDMs, demonstrating that the LiRb molecule could be a very promising candidate for laser cooling. Therefore, a three-cycle laser cooling scheme for the molecule has been proposed based on these two spin-forbidden transitions. Using the radiative lifetime and linewidth calculated from the obtained TDM functions, we present further analysis of the cooling of LiRb and the corresponding KRb molecule. The transition b(3)Π0 ↔ X(1)Σ(+) is found to be a practical transition to cool the LiRb molecule, and a sub-microkelvin cool temperature could be reached for the KRb molecule using a similar laser cooling scheme.

Analytic functions for potential energy curves, dipole moments, and transition dipole moments of LiRb molecule

The analytic potential energy functions (APEFs) of the X1Σ+, 21Σ+, a3Σ+, and 23Σ+ states of the LiRb molecule are obtained using Morse long-range potential energy function with damping function and nonlinear least-squares method. These calculations were based on the potential energy curves (PECs) calculated using the multi-reference configuration interaction (MRCI) method. The reliability of the APEFs is confirmed using the curves of their first and second derivatives. By using the obtained APEFs, the rotational and vibrational energy levels of the states are determined by solving the Schrödinger equation of nuclear movement. The spectroscopic parameters, which are deduced using Dunham expansion, and the obtained rotational and vibrational levels are compared with the reported theoretical and experimental values. The correlation effect of the electrons of the inner shell remarkably improves the results compared with the experimental spectroscopic parameters. For the first time, the APEFs for the dipole moments and transition dipole moments of the states have been determined based on the curves obtained from the MRCI calculations.

Formation of ultracold (7)Li(85)Rb molecules in the lowest triplet electronic state by photoassociation and their detection by ionization spectroscopy.

We report the formation of ultracold (7)Li(85)Rb molecules in the a(3)Σ(+) electronic state by photoassociation (PA) and their detection via resonantly enhanced multiphoton ionization (REMPI). With our dual-species Li and Rb magneto-optical trap apparatus, we detect PA resonances with binding energies up to ∼62 cm(-1) below the (7)Li 2s (2)S1/2 + (85)Rb 5p (2)P1/2 asymptote. In addition, we use REMPI spectroscopy to probe the a(3)Σ(+) state and excited electronic 3(3)Π and 4(3)Σ(+) states and identify a(3)Σ(+) (v″ = 7-13), 3(3)Π (vΠ' = 0-10), and 4(3)Σ(+) (vΣ' = 0-5) vibrational levels. Our line assignments agree well with ab initio calculations. These preliminary spectroscopic studies on previously unobserved electronic states are crucial to discovering transition pathways for transferring ultracold LiRb molecules created via PA to deeply bound rovibrational levels of the electronic ground state.

Formation of deeply bound ultracold LiRb molecules via photoassociation near the Li 2S1/2+Rb 5P3/2 asymptote

We present spectra of ultracold $^{7}\mathrm{Li}^{85}\mathrm{Rb}$ molecules in their electronic ground state formed by spontaneous decay of weakly bound photoassociated molecules. Beginning with atoms in a dual-species magneto-optical trap, weakly bound molecules are formed in the 4(1) electronic state, which corresponds to the ${B}^{1}\ensuremath{\Pi}$ state at short range. These molecules spontaneously decay to the electronic ground state and we use resonantly enhanced multiphoton ionization to determine the vibrational population distribution in the electronic ground states after spontaneous emission. Many of the observed lines from the spectra are consistent with transitions from the ${X}^{1}{\ensuremath{\Sigma}}^{+}$ ground electronic state to either the ${B}^{1}\ensuremath{\Pi}$ or the ${D}^{1}\ensuremath{\Pi}$ electronic state that has been previously observed, with levels possibly as low as ${X}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}}=2)$ being populated. We do not observe decay to weakly bound vibrational levels of the ${X}^{1}{\ensuremath{\Sigma}}^{+}$ or ${a}^{3}{\ensuremath{\Sigma}}^{+}$ electronic state in the spectra. We also deduce a lower bound of $3900 \mathrm{cm}{}^{\ensuremath{-}1}$ for the dissociation energy of the $\mathrm{LiRb}{}^{+}$ molecular ion.

Complete Quantum State Selectivity in Cold Molecular Beams Using Deflection-Resistant Dark States in a STIRAP Configuration.

One of the main goals of chemical dynamics is the creation of molecular beams composed of a single (vibrational, rotational, and magnetic) quantum state of choice. In this Letter, we propose a method to achieve complete quantum state selectivity by producing resistance to electromagnetically induced deflection (EID) and that the state to be selected can be "dialed in" at will. We illustrate the method by showing in detail how to purify thermal beams of the LiRb and IF molecules to yield molecular beams composed of a variety of prechosen single internal quantum states and/or superpositions of such states. We expect that this method will be implemented in all subsequent explorations of the fundamentals of chemical reactions and their control and the use of cold molecules as a vehicle for studying some of the most profound issues of quantum dynamics.

Formation of ultracold LiRb molecules by photoassociation near the Li(2s 2S1/2) + Rb(5p 2P1/2) asymptote

We report the production of ultracold 7Li85Rb molecules by photoassociation (PA) below the Li (2s 2S1/2) + Rb(5p 2P1/2) asymptote. We perform PA spectroscopy in a dual-species 7Li-85Rb magneto-optical trap (MOT) and detect the PA resonances using trap loss spectroscopy. We observe several strong PA resonances corresponding to the last few bound states, assign the lines and derive the long-range C6 dispersion coefficients for the Li (2s 2S1/2) + Rb(5p 2P1/2) asymptote. We also report an excited-state molecule formation rate of and a PA rate coefficient of , which are both among the highest observed for heteronuclear bi-alkali molecules. These suggest that PA is a promising route for the creation of ultracold ground-state LiRb molecules.

Structural and Spectroscopic Study of the LiRb Molecule beyond the Born–Oppenheimer Approximation

Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb(+) and Li(+) cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R(e), D(e), T(e), ω(e), ω(e)x(e), and B(e)) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)Σ(+), 8-10(3)Σ(+), 6(1,3)Π, and 3(1,3)Δ excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li(-)Rb(+) and Li(+)Rb(-) arrangements. The diabatic potential energy for the (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.

Laser spectroscopy of the X1Σ+ and B1Π states of the LiRb molecule

We have studied the X1Σ+ and B1Π states of 7Li85Rb using Laser Induced Fluorescence (LIF) Spectroscopy and Fluorescence Excitation Spectroscopy (FES). We extract molecular constants for levels v″=0–2 of the X1Σ+ state and levels v′=0–20 of the B1Π state. For the B1Π state, we have observed rotational perturbations in the e-parity component of the v′=2 level, and determined the dissociation energy. We discuss implications of our measurements in finding efficient photoassociation pathways for production of ultracold ground state LiRb molecules, and their detection via state selective ionization.

The X 1Σ+ state of LiRb studied by Fourier-transform spectroscopy

We report on the first experimental observation of the ground electronic state of the LiRb molecule at high resolution. A large body of experimental data was collected which led to an accurate potential energy curve for this state. Transitions to the lowest triplet state were also observed, but these data are rather fragmentary and allow only a first attempt for the description of this state. Both potentials were used for evaluating published Feshbach resonances of this molecule. We compare the results of this study with those of the related LiK and LiCs molecules.

Theoretical study of the electronic structure of the LiRb and NaRb molecules

The potential energy has been calculated over a wide range of internuclear distances for the 28 lowest molecular states of LiRb and NaRb molecules, using an ab initio method based on non-empirical pseudopotentials, parametrized l-dependent polarization potentials and full valence configuration interaction calculations. Molecular spectroscopic constants have been derived for the bound states with a regular shape. A good description of the experimentally known ground state for NaRb is obtained. Tables providing extensive data of energy values versus internuclear distances are available at the following address http://lasim.univ-lyon1.fr/allouche/lirbnarb.htm.