Theoretical Study of the Electronic States of the Rb(2) Molecule

Full-Dimensional Global Potential Energy Surface for the KRb + KRb → K2Rb2* → K2 + Rb2 Reaction with Accurate Long-Range Interactions and Quantum Statistical Calculation of the Product State Distribution under Ultracold Conditions

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K₂Rb₂* → K₂ + Rb₂ reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K₂ and Rb₂ product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K₂Rb₂* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

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.

Desorption Dynamics of Rb2 Molecules Off the Surface of Helium Nanodroplets

The desorption dynamics of rubidium dimers (Rb₂) off the surface of helium nanodroplets induced by laser excitation is studied by employing both nanosecond and femtosecond ion imaging spectroscopy. Similarly to alkali metal atoms, we find that the Rb₂ desorption process resembles the dissociation of a diatomic molecule. However, both angular and energy distributions of detected Rb₂⁺ ions appear to be most crucially determined by the Rb₂ intramolecular degrees of freedom rather than by those of the Rb₂He_N complex. The pump-probe dynamics of Rb₂⁺ is found to be slower than that of Rb⁺, pointing at a weaker effective guest-host repulsion for excited molecules than for single atoms.

Coherent Amplification of Ultrafast Molecular Dynamics in an Optical Oscillator

Optical oscillators present a powerful optimization mechanism. The inherent competition for the gain resources between possible modes of oscillation entails the prevalence of the most efficient single mode. We harness this "ultrafast" coherent feedback to optimize an optical field in time, and show that, when an optical oscillator based on a molecular gain medium is synchronously pumped by ultrashort pulses, a temporally coherent multimode field can develop that optimally dumps a general, dynamically evolving vibrational wave packet, into a single vibrational target state. Measuring the emitted field opens a new window to visualization and control of fast molecular dynamics. The realization of such a coherent oscillator with hot alkali dimers appears within experimental reach.

Observations and analysis with the spline-based Rydberg-Klein-Rees approach for the 3(1)Σg(+) state of Rb2

Ro-vibrational term values of the 3(1)Σg (+) state of (85,85)Rb2 and (85,87)Rb2 and resolved fluorescence spectra to the A(1)Σu (+) state are recorded following optical-optical double resonance excitation. The experimental data are heavily perturbed, and as a result, the standard analysis based on Dunham series representation of the energy levels fails. The analysis is done via modeling the adiabatic potential function with the Rydberg-Klein-Rees potential constructed from the generalized smoothing spline interpolation of the vibrational energies Gv and rotational constants Bv.

Relativistic state-specific multireference perturbation theory incorporating improved virtual orbitals: Application to the ground state single-bond dissociation

Using four-component (4c) relativistic spinors, we present a computationally economical relativistic ab initio method for molecular systems employing our recently proposed second-order state-specific multireference perturbation theory (SSMRPT) incorporating the improved virtual orbital-complete active space configuration interaction (IVO-CASCI) reference wavefunction. The resulting method, 4c-IVO-SSMRPT [calculate one state at a time] is tested in pilot calculations on the homonuclear dimers including Li(2), Na(2), K(2), Rb(2), F(2), Cl(2), and Br(2) through the computations of the ground state potential energy curves (PECs). As SSMRPT curbs intruder effects, 4c-IVO-SSMRPT is numerically stable. To our knowledge, the SSMRPT in the 4c relativistic framework has not been explored in the past. Selective spectroscopic constants that are closely related to the correct shape and accuracy of the energy surfaces have been extracted from the computed PECs. For the halogen molecules, a relativistic destabilization of the bond has been found. Relativistic and electron correlation effects need to be incorporated to get reliable estimates. Our results are in good accordance with reference theoretical and experimental data which manifests the computational accuracy and efficiency of the new 4c-IVO-SSMRPT method. The method opens for an improved description of MR systems containing heavy elements. The inexpensiveness of IVO-CASCI makes 4c-IVO-SSMRPT method promising for studies on large systems of heavy elements.

High-lying electronic states of the rubidium dimer-Ab initio predictions and experimental observation of the 5(1)Σu(+) and 5(1)Πu states of Rb2 by polarization labelling spectroscopy

Two-colour polarization labelling experiments have been used to explore the excitation spectrum of the rubidium dimer in the region 25,500-27,000 cm(-1), probing two mutually interacting states, identified from ab initio calculations as the 5(1)Σu(+) and 5(1)Πu states whose atomic dissociation products are Rb(5s) + Rb(5d). Treating the rather irregular progressions observed in the excitation spectra as transitions to single states with (numerous) local perturbations, we propose spectroscopic parameters and potential energy curves to describe the investigated levels. Observations cover more than 20 vibrational levels in the inner minima of both the 5(1)Πu and 5(1)Σu(+) states. Analysis was guided by ab initio calculations performed to describe the (1,3)Λg,u electronic states of Rb2 up to the Rb(5s) + Rb(5f) atomic asymptote. The theoretical potential energy curves are given in ASCII format in an electronic supplement to this paper.

Relations between harmonic frequencies of diatomic molecules

The relations between the harmonic frequencies of different molecules are revealed with the aid of the spring constants of atoms in molecules. Using the atomic spring constants in the related molecules, the force constants for a new molecule can be estimated. The simplest scheme to obtain the force constant of a given molecule is similar to a simple chemical reaction formula, such as A(2) + B(2) → AB, and the corresponding relation between the molecular force constants is k(AB)(-1) = (2k(A(2)))(-1) + (2k(B(2)))(-1). For a given molecule, one can design numerous schemes to obtain its force constant from the atomic spring constants in other molecules. A high degree of periodical regularity appears in the application of different kinds of schemes to the ground states. The reliable schemes for the ground electronic states can be adopted for the excited states. Over two hundred molecules with experimental data available for comparison have been tested. The discrepancies between the calculated and the experimental harmonic frequencies can reach 1% and better; the results show that the present approach is simple in theory and handy to use. The harmonic frequencies for dozens of hetero-nuclear molecules of the transition-metal elements are also predicted.

Formation of ultracold Rb2 molecules in the v'' = 0 level of the a(3)Σ+(u) state via blue-detuned photoassociation to the 1(3)Π(g) state

We report on the observation of blue-detuned photoassociation in Rb(2), in which vibrational levels are energetically above the corresponding excited atomic asymptote. (85)Rb atoms in a MOT were photoassociated at short internuclear distance to levels of the 1(3)Π(g) state at a rate of approximately 5 × 10(4) molecules s(-1). We have observed most of the predicted vibrational levels for all four spin-orbit components; 0(+)(g), 0(-)(g), 1(g), and 2(g), including levels of the 0(+)(g) outer well. These molecules decay to the metastable a(3)Σ(+)(u) state, some preferentially to the v'' = 0 level, as we have observed for photoassociation to the v' = 8 level of the 1(g) component.

Unravelling complex spectra of a simple molecule: REMPI study of the 420 nm band system of KRb

Complex spectra of the KRb 420 nm system are analyzed by mass-resolved resonance enhanced two-photon ionization in a cold molecular beam. Vibronic structures of three singlet-singlet (4(1)Π, 7(1)Σ(+), and 5(1)Π←X(1)Σ(+)) transitions were identified for the first time. By comparing with highly accurate ab initio calculations, we assigned the singlet excited electronic states, and determined their electronic term values and vibrational constants. Weak singlet-triplet transitions were observed and identified as the 5(3)Π(0(+))←X(1)Σ(+) transitions by the homogeneous perturbation selection rule.

A pump-probe study of the photoassociation of cold rubidium molecules

The dynamics of the excited state during the photoassociation of cold molecules from cold rubidium atoms is studied in a series of pump-probe experiments. Dipole transitions similar to those of the atoms are observed in the molecular signal. While such behaviour is characteristic of the long-range molecules, the photoassociation of bound molecules is confirmed in additional experiments. The pump-probe signal observed on a 250 ps time scale did not, however, reveal wavepacket oscillations predicted by theory. This result is discussed using numerical simulations of photoassociation and a modification to the current experiments that could lead to the detection of wavepacket dynamics is suggested.

Ultracold triplet molecules in the rovibrational ground state

We report here on the production of an ultracold gas of tightly bound Rb2 triplet molecules in the rovibrational ground state, close to quantum degeneracy. This is achieved by optically transferring weakly bound Rb2 molecules to the absolute lowest level of the ground triplet potential with a transfer efficiency of about 90%. The transfer takes place in a 3D optical lattice which traps a sizeable fraction of the tightly bound molecules with a lifetime exceeding 200 ms.

Spin-forbidden transitions in the vicinity of the 2 (1)pi(u) <-- X (1)sigma(g)+ band system of Rb2

We have investigated the Rb2 475 nm system by resonance enhanced two-photon ionization spectroscopy in a pulsed molecular beam. Strong extra bands accompanying the 2 (1)Pi(u) v' = 5 - 8 <-- X (1)Sigma(g)(+) v'' = 0 bands were newly observed. Rotational analysis of the main and extra bands reveals that the 2 (1)Pi(u) v' = 5 - 8 levels are significantly perturbed, mainly by the 3 (3)Sigma(u)(+)(1 u) state and also by the 2 (3)Pi(u)(1 u) state. For the major perturber, 3 (3)Sigma(u)(+)(1 u), the intensity borrowing has been found to be facilitated by the 2 (1)Pi(u)-3 (3)Sigma(u)(+)(1 u) potential energy curve crossing near 21,100 cm(-1). For the vibronic-band intensities of the 2 (3)Pi(u)(1 u) v' <-- X (1)Sigma(g)(+) v'' = 0 transitions observed in this spectral region, intensity borrowing was most effective when the 2 (3)Pi(u)(1 u) levels were close to the 3 (3)Sigma(u)(+)(1 u) levels. A deperturbation fit for the perturbing bands has provided the 2 (1)Pi(u)-3 (3)Sigma(u)(+)(1 u) coupling constants.

Accurate time propagation for the Schrodinger equation with an explicitly time-dependent Hamiltonian

Several different numerical propagation techniques for explicitly time-dependent Hamiltonians are discussed and compared, with the focus on models of pump-probe experiments. The quality of the rotating wave approximation is analyzed analytically, and we point out under which circumstances the modeling becomes inaccurate. For calculations with the fully time-dependent Hamiltonian, we show that for multistate systems, with either time or space dependence in the interstate coupling, the fourth order truncated Magnus expansion can be reformulated so that no commutators appear. Our results show that the split-operator method should only be used when low accuracy is acceptable. For accurate and efficient time stepping, the Magnus-Lanczos approach appears to be the best choice.

On the doublet states of the potassium trimer

The potassium trimer is investigated in its lowest electronic doublet states, employing several high-level ab initio methods (coupled cluster with single, double, and noniterative triple excitations, multiconfiguration self-consistent field, and multireference Rayleigh-Schrodinger perturbation theory of second order). One-dimensional cuts through the lowest 12 electronic states at C(2v) symmetry give insight in the complex electronic structure of the trimer, showing several (pseudo-)Jahn-Teller distortions that involve two or three excited states. Contour plots of the involved molecular orbitals are shown to prove the validity of the shell model frequently used for a qualitative description of metallic clusters.

Heteronuclear and homonuclear high-spin alkali trimers on helium nanodroplets

The electronic excitation spectra of all possible homo- and heteronuclear high-spin (quartet) trimers of K and Rb (KxRb(3-x), x=0...3) assembled on the surface of superfluid helium droplets, are measured in the spectral range from 10,600 to 17,400 cm(-1). A regular series of corresponding bands is observed, reflecting the similar electronic structure of all these trimers. For the assignment and separation of overlapping bands, we determine x directly, with mass-selected beam depletion, and indirectly with a V-type double-resonance scheme. The assignment is confirmed by high-level ab initio calculations of the electronic structure of the bare trimers. The level structure is rationalized in terms of harmonic-oscillator states of the three valence electrons in a quantum-dot-like confining potential. We predict that three should be a magic number for high-spin alkali clusters.

Mass-resolved resonance enhanced ionization study of complicated excited electronic states of Rb2 near 430 nm and their predissociation dynamics

We have investigated the Rb2 430 nm system by resonance enhanced two-photon ionization and photofragment yield spectroscopy. Four electronically excited states have been assigned, and their two-channel (fast and slow) predissociation has been observed. For the 3 1Piu, 3 1Sigmau+, 3 3Piu(0u+), and 3 3Piu(1u) states, electronic term values (Te) and vibrational constants (omegae and omegaexe) have been determined. For the predissociation dynamics, we have observed the fast predissociation threshold between the isotopically shifted 3 1Piu v' = 14 levels of 85Rb2 and 85Rb87Rb where the 4 2D5/2 + 5 2S1/2 atomic fine-structure limit is located. The 1 3Deltau state corresponding to the 4 2D5/2 + 5 2S1/2 atomic fine-structure limit has been assigned to the predissociating perturber responsible for the fast channel. Also, we have found that the fast channel branches out into two finer product channels due to long-range potential crossing.

Reduced-Order Modeling, Error Estimation, and the Role of the Start-Vector: The Recursive Residue Generation Method Revisited

The recursive residue generation method (RRGM) [Wyatt, R. E. Adv. Chem. Phys. 1989, 73, 231] is re-derived using the formalism of reduced-order modeling [Bai, Z. Appl. Numerical Math. 2002, 43, 9]. A stopping criteria for the RRGM recursions is proposed, on the basis of an expression for an upper bound to the absolute error [Bai, Z.; Ye, Q. Electron. Trans. Numerical Anal. 1998, 7, 1]. It is further pointed out that, in general, the start-vector has a negligible effect on the convergence of the RRGM.

Vibrationally State-Selective Spin−Orbit Transfer with Strong Nonresonant Pulses

By dynamic Stark shift using strong nonresonant pulses, we show that it is in principle possible to prepare arbitrary superposition states of mixed multiplicity. By a proper choice of parameters, the transfer of population is shown to follow the Rabi formula, where the initial and target states are now vibrational states of two light-induced molecular potentials of different multiplicity. Starting from nonstationary wave packets, the spin transfer can proceed via parallel transfer using a single pulse or by sequential transfer using a pulse sequence. A simple model is proposed to analyze the properties of both schemes and the feasibility of their experimental implementation for spin-orbit transitions in Rb2.

Calculation of highly excited vibrational states using a Richardson-Leja-Davidson scheme

An efficient computational scheme for calculating highly excited vibrational eigenstates is proposed, combining a Richardson-Leja spectral filter with a novel version of the Davidson method [J. Comput. Phys. 17, 87 (1975)]. Highly excited eigenstates of the Rb2 and H2O molecules are computed to test and verify the method. On the average less than 2.5 outer recursions per eigenstate are needed. For each outer Davidson recursion, less than 20 inner filter recursions per eigenstate are needed on the average.

Optical control of the singlet-triplet transition in Rb2

By controlling nonresonant dynamic Stark shifts it is possible to effectively decouple the intramolecular couplings of simple molecules. We have illustrated this effect in the 1 (1)Sigma(u)-->1 (3)Pi(u) transition in Rb(2). The laser scheme implies two important control knobs: the laser frequency, which must be chosen to avoid both single and multiphoton resonances and to select different electronic environments for the singlet and triplet states, and the pulse intensity, which must amplify the asymmetry in the dynamic polarizabilities that allows the decoupling, avoiding undesired strong-pulse effects. The mechanism of the scheme implies not only brute-force energy shifts but also light-induced reshaping of the potentials to avoid the undesired crossings. Quantitative aspects of the method are analyzed by using molecular models of increasing complexity for Rb(2).

Pump-dump iterative squeezing of vibrational wave packets

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.

Bound-bound state quantum wave packet dynamics in the intermediate coupling range: the A1Sigma+u (0+u) and b3IIu (0+u) system in Rb2

The real-time quantum dynamics of a wave packet confined to two coupled bound states at intermediate interaction strength is probed by experiment and calculations on the A1Sigma(+)(u) approximately b (3)II(u) system in Rb2 molecules. The general dynamics consists of rapid spreading out over the whole phase space. Particular conditions exist, however, under which the initial wave packet motion separates into two mesobatic trajectories with distinct frequencies. These diabatic or adiabatic hybrid trajectories are analogous to those responsible for longevity resonances in bound-unbound systems.