The ground X Σ1g+ electronic state of the cesium dimer: Application of a direct potential fitting procedure

Highly efficient creation and detection of deeply bound molecules via invariant-based inverse engineering with feasible modified drivings

Stimulated Raman Adiabatic Passage (STIRAP) and its variants, such as M-type chainwise-STIRAP, allow for efficiently transferring the populations in a multilevel system and have widely been used to prepare molecules in their rovibrational ground state. However, their transfer efficiencies are generally imperfect. The main obstacle is the presence of losses and the requirement to make the dynamics adiabatic. To this end, in the present paper, a new theoretical method is proposed for the efficient and robust creation and detection of deeply bound molecules in three-level Λ-type and five-level M-type systems via "Invariant-based shortcut-to-adiabaticity." In the regime of large detunings, we first reduce the dynamics of three- and five-level molecular systems to those of effective two- and three-level counterparts. By doing so, the major molecular losses from the excited states can be well suppressed. Consequently, the effective two-level counterpart can be directly compatible with two different "Invariant-based Inverse Engineering" protocols; the results show that both protocols give a comparable performance and have a good experimental feasibility. For the effective three-level counterpart, by considering a relation among the four incident pulses, we show that this model can be further generalized to an effective Λ-type one with the simplest resonant coupling. This generalized model permits us to borrow the "Invariant-based Inverse Engineering" protocol from a standard three-level Λ-type system to a five-level M-type system. Numerical calculations show that the weakly bound molecules can be efficiently transferred to their deeply bound states without strong laser pulses, and the stability against parameter variations is well preserved. Finally, the detection of ultracold deeply bound molecules is discussed.

The Rb2 31Π g state: Observation and analysis

This paper reports observations and analysis of the Rb₂ 3¹Π _g state. A total of 323 rovibrational term values spanning the range of the rotational quantum number J = 7 through 77 and the vibrational quantum number v = 2 through 23 (about 1/3 of the potential well depth) were measured using the optical-optical double resonance technique. The term values are simulated within a model of a piece-wise multi-parameter potential energy function based on the generalized splines. This function not only enables a reproduction of the experimental data with a reasonable quality but also approximates the available ab initio function in its whole range with a uniform accuracy.

Ab initio interatomic potentials and transport properties of alkali metal (M = Rb and Cs)-rare gas (Rg = He, Ne, Ar, Kr, and Xe) media

We performed a first principle systematic calculation on the adiabatic potential energy curves (PECs) of alkali metal (M = Rb and Cs) - rare gas (Rg = He, Ne, Ar, Kr, and Xe) van der Waals molecules over a wide range of interatomic distance R. All electron basis sets of triple and quadruple zeta valence quality were used for the He, Ne, Ar and Kr atoms. Scalar relativistic effects were taken into account for the heavy Rb, Cs and Xe atoms by means of Dirac-Fock effective core potentials. The correlated ground state energies have been obtained within the framework of the spin unrestricted open-shell coupled cluster method, with perturbative treatment of triple excitations. The electronic energies were corrected for the basis set superposition error (BSSE) using the counterpoise method. Energies were extrapolated to the complete basis set (CBS) limit using a two-point scheme. The energy convergence towards the CBS limit was monitored by the saturation of the dummy atom basis set that included bond functions centered at the midpoint of the interatomic distance. The ab initio point-wise PEC was followed to small R to the point where the energy was 0.5 Hartree above the dissociation limit. A Morse long-range (MLR, UM Rg(R)) potential possessing the correct asymptotic behavior at R → ∞ was fitted to the single point energies. The resulting set of fully analytical MLR potentials was then used to evaluate classical collision integrals over a wide range of collision energies. By this means, diffusion coefficients (DM Rg(T)) were predicted as functions of the translation temperature T ≤ 3000 K. The reliability of the present ab initio UM Rg(R) and DM Rg(T) functions was accessed through a comparison with previous theoretical and experimental results.

Re-examination of the Cs2 ground singlet X1Σg+ and triplet a3Σu+ states

This paper clarifies the disagreement in the depth of the potential energy curve of the cesium dimer singlet ground state which has lasted for nearly a decade. We point out that the origin of this disagreement must be a technical misprint in the values of the three binding energies reported by Danzl et al. [Science 321, 1062 (2008)], while the X¹Σ_g⁺ state potential reported by Coxon and Hajigeorgiou [J. Chem. Phys. 132, 094105 (2010)], based on experimental data by Amiot and Dulieu [J. Chem. Phys. 117, 5155 (2002)], is quite correct. We have recalculated the potential energy function of the triplet ground state a³Σ_u⁺ by using the available experimental data spanning both the attractive and the repulsive branches so that the potential energy function complies asymptotically with the singlet ground state X¹Σ_g⁺ potential energy function by Coxon and Hajigeorgiou. This is important for the simulation of the near dissociation properties such as Feshbach resonances, which are typically observed in modern experiments with ultracold atoms and molecules.

An accurate potential model for the a3Σu+ state of the alkali dimers Na2, K2, Rb2, and Cs2

A modified semi-empirical Tang-Toennies potential model is used to describe the a³Σ_u⁺ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth D_e, well location R_e, and the harmonic vibrational frequency ω_e of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na₂, K₂, Rb₂, and Cs₂, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li₂ and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li₂ less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

Hidden physics in molecular rovibrational spectrum

An algebraic method for rotational energies (AMr) is proposed to unearth the rotational spectrum {ɛJ} and the rovibrational interaction energies ευJint that are hidden in the rovibrational energies EυJ. The applications to the excited electronic state a3Σu+ of 7Li2 and the ground state X1Σ+ of NaF molecules show that: (1) the rotational energies ɛJ of the lighter 7Li2 molecule have better accuracies than the widely used rigid rotor rotational energies εJrr particularly for the lowest two rotational states, while the rigid rotor model produces satisfied rotational energies for the heavier NaF molecule and (2) the attractive rovibrational interaction energies ευJint stabilize a molecular rovibrational system.

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.