KRb Molecule Research Articles

Reaction interferometry with ultracold molecules.

We propose to coherently control the ultracold 2KRb → K2 + Rb2 reaction product state distribution via quantum interference. By leveraging that the nuclear spin degrees of freedom in the reaction maintain coherence, which was demonstrated in Liu, Zhu et al., arXiv, 2023, arXiv:2310.07620, https://doi.org/10.48550/arXiv.2310.07620, we explore the concept of a "reaction interferometer". Such an interferometer involves splitting one KRb molecular cloud into two, imprinting a well-defined relative phase between them, recombining the clouds for reactions, and measuring the product state distribution. We show that the interference patterns provide a mechanism to coherently control the product states, and specific product channels also serve as an entanglement witness of the atoms in the reactant KRb molecule.

The First Principle Analysis of Spin-Orbit Interaction between Excited Electronic States of the KRb Molecule

The First Principle Analysis of Spin-Orbit Interaction between Excited Electronic States of the KRb Molecule

Potential energy curves, transition and permanent dipole moments of KRb

We present extensive calculations of 48 adiabatic potential energy curves of the KRb molecule. Efforts have been focused on preparing the appropriate basis sets. Compared to previous approaches, the set of new potential energy curves is extended to higher excitations, including the single-excited K(4s2S)+Rb(5d2D) and double-excited K(4p2P)+Rb(5p2P) atomic limits. Larger distances between nuclei are also taken into account. New features of potential energy curves have been found. The present spectroscopic parameters are compared with the available experimental data and other theoretical results, among which parameters of 15 high-laying excited electronic states are provided for the first time. We also present the values of the transition and permanent dipole moment functions and discuss their features. The aims of the study are to provide high-quality data for the KRb molecule, which may be useful in the physics of low temperatures and alternatively the analysis and assignment of molecular spectra.

FCI calculations of the adiabatic electronic structure of KRb highlighting the K−Rb+ ionic limit effect

A non-relativistic description of the electronic structure for the heteronuclear molecule KRb was developed through the Full Configuration Interaction (FCI) and pseudo-potential method. Below the ionic limit K−Rb+, the ground and all excited singlet and triplet states of different symmetries Σ+, Π and Δ (in the Hund's case (a): 2s + 1Λ±) were intensively investigated. Several adiabatic results including potential energy curves (PECs), permanent and transition electric dipole moments (PEDM, TEDM) were analyzed in short and long-range of internuclear distances. Tables of these properties as functions of separation are presented. The spectroscopic constants with the vibrational levels were derived using the “Numerov” algorithm. These molecular parameters were compared with those published in the literature, feature a good agreement. In the adiabatic representation, strong couplings between successive 1Σ+ states were reached by series of avoided crossing, yielding to the appearance of the ionic character and the good illustration of charge transfer. This description of the KRb molecule was helpful in the design of the prospect photo-association experiments and the obtaining of the quantum-degenerate gas of the polar molecule.

An accurate semiempirical potential energy curve for the a3Σ+-state of KRb.

A semiempirical potential energy curve for the a3Σ+-state of the KRb molecule with only five parameters is reported. The potential is continuous over the entire range of internuclear distances and has the correct long-range attractive dispersion potential from established theory. The potential provides an equally good fit of the laser induced fluorescence Fourier transform spectroscopic data of Pashov et al. [Phys. Rev. A 76, 022511 (2007)] as their multi-parameter potential. The new potential is supported by the good agreement of the well parameters De, Re and the harmonic vibrational constant ωe with combining-rule estimates. The scattering lengths for all six isotopologues are also in excellent agreement with experiment with a 0.2% adjustment within theoretical uncertainty of the leading dispersion coefficient C6. An analysis of the harmonic vibrational constant ωe and the constant ωexe of the potential of Pashov et al. reveals a significant difference to the present potential which turned out to be due to an oscillatory deviation in their potential in the vicinity of the potential minimum. The new potential is, thus, the best available because its simplicity is ideal for further applications.

A protocol to realize triatomic ultralong range Rydberg molecules in an ultracold KRb gas

We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N = 0 and N = 2 rotational levels, is engineered which exploits the unique Rydberg electron–molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck–Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.

A Reduced Method of Coupled Vibrational Channels: Analysis of Regular Perturbations in the $${{c}^{3}}{\mathbf{\Sigma }}_{{\mathbf{\Omega }}}^{ + }$$ -State of a KRb Molecule

To reduce the dimension of a vibrational problem to be solved by the coupled channel method in the case of interacting electronic states of diatomic molecules, we propose to use the contact van Vleck transformations, which make it possible to take into account the nonadiabatic intramolecular interactions with distant states by modifying the initial potential energy matrix. The efficiency of the reduced coupled vibrational channel method (RCVCM) has been demonstrated by an example of analyzing the regular spin–orbital, electron–rotational, and spin–rotational perturbations discovered in the fine structure of vibrational–rotational levels of the $${{c}^{3}}{\Sigma\text{}}_{{\Omega\text{}}}^{ + }$$ -state of a KRb molecule by methods of high-precision laser-emission spectroscopy. The adiabatic potentials and nonadiabatic electron matrix elements, as functions of the internuclear distance necessary for application of the RCVCM, were obtained in the framework of the nonempirical high-level calculation. It has been demonstrated that the RCVCM has broad extrapolation possibilities and makes it possible to describe the position of the regularly perturbed energy levels of Ω-components of the triplet $${{c}^{3}}{\Sigma\text{}}_{{\Omega\text{}}}^{ + }$$ ‑state at the spectroscopic accuracy level.

Nonadiabatic effects in (1~2)1Π–X1Σ+ rovibronic transitions of KRb molecules

Numerical simulation of the effect of intramolecular electrostatic interactions on redistribution of relative intensities in the vibrational structure of (1 ~ 2)1Π–X1Σ+ rotationally resolved transitions of the KRb molecule is performed within the precision nonadiabatic model of coupled vibrational channels. It is established that mutual perturbation of electronically excited states modifies in a nontrivial way a nodal structure of nonadiabatic wavefunction of the (1 ~ 2)1Π complex, which is possible to use for rising efficiency of twostep laser synthesis and stabilization of ultracold ensembles of KRb molecules in the ground electronic state.

Ab initio multi-reference perturbation theory calculations of the ground and low-lying electronic states of the KRb molecule

The potential energy curves of the low-lying electronic states correlating up to the limit K(4p)+Rb(5s) of KRb molecule have been calculated using the multi-reference perturbation theory method at the CASSCF/XMCQDPT2 level of theory without and with spin–orbit coupling. The calculated parameters of the ground X1Σ+ state are in the best agreement among all previously performed ab initio calculations for the KRb molecule. The calculated vibrational intervals of the ground electronic term of the 39K85Rb molecule describe the experiment with the accuracy within ±1cm−1. The calculated intensities of the 21Σ+ (v′=3, J′=26)→X1Σ+ (v″=0…24, J″=25, 27) transitions satisfactory reflect the experimentally observed intensities distribution.

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.

Theoretical study of highly-excited states of KRb molecule

AbstractSemi-empirical adiabatic potential energy curves of highly excited states of the KRb molecule are calculated as a function of the internuclear distance R over a wide range from 3 to 150 a 0. The diatomic molecule is treated as an effective two-electron system by using the large core pseudopotentials and core polarization potentials. All calculations are performed by using the nonrelativistic CASSCF/MRCI method with accurate basis set functions. The spectroscopic constants of the calculated electronic states agree well with experimental data, including the recent ones from Lee et al., and with available theoretical results.

Analytical potential energy functions and spectroscopic properties for the ground and low-lying excited states of KRb

The potential energy curves (PECs) of the ground state X1Σ+ and two low-lying excited states 13Σ+ and 13П of KRb molecule have been calculated using the multireference configuration interaction method and the effective core potential basis set. The PECs are fitted into analytical potential energy functions (APEFs) using the Morse long-range potential. The spectroscopic parameters for the states are determined using the analytical derivatives of APEFs. The vibrational energy levels have been calculated by solving the radial Schrödinger equation of nuclear motion based on the APEFs, and compared with the theoretical and experimental works available at present.

Spectroscopic analysis of the coupled 11Π, 23Σ+ (Ω = 0−, 1), and b3Π (Ω = 0±, 1, 2) states of the KRb molecule using both ultracold molecules and molecular beam experiments

We report the spectroscopic characterization of excited electronic states of KRb by combining spectra from molecular beam (MB) experiments with those from ultracold molecules (UM) formed by photoassociation (PA) of ultracold atoms. Spectra involving the 1(1)Π, 2(3)Σ(+), and b(3)Π states in a strongly perturbed region have been identified. This approach provides a powerful method to identify the vibrational levels of the excited electronic states perturbed globally by neighboring electronic states. This is because the two sets of spectra from the UM and the MB experiments probe the same energy region from very different initial electronic states. The UM experiments utilize high v'' levels of the a(3)Σ(+) state with large internuclear separations, while the MB experiments utilize low v'' levels of the ground X(1)Σ(+) state with near-equilibrium internuclear separations. Only the Ω = 1 levels of the 2(3)Σ(+) and b(3)Π states are observed in the MB spectra, while the Ω = 0(-), 1 levels of the 2(3)Σ(+) state and the Ω = 0(±), 1, 2 levels of the b(3)Π state are observed in the UM spectra.

Internal state cooling with a femtosecond optical frequency comb

AbstractA single femtosecond optical frequency comb is implemented to induce two‐photon transitions between molecular vibrational levels to form ultracold molecules. The phase across an individual pulse in the pulse train is sinusoidally modulated with a carefully chosen modulation amplitude and frequency. Piecewise population transfer is fulfilled to the final state by each pulse in the applied pulse train providing a controlled population accumulation in the final, ultracold state. The dynamics of rovibrational cooling is discussed on an example of the KRb molecule. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Ultracold molecules from ultracold atoms: a case study with the KRb molecule

Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40K87Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum.

Efficient coherent population transfer between theaΣ3and theXΣ1states ofK39Rb85

We present calculations for a coherent population transfer [stimulated Raman adiabatic passage (STIRAP)] between the two lowest electronic ground states of the KRb molecule. In contrast to previous work on STIRAP in molecular systems, position dependent transition dipole moments are included in the calculation to take the mixed singlet-triplet nature of the intermediate state into account. Additionally, we incorporate the kinetic energy term and position dependent electronic states of the molecule. Transfer efficiencies of up to 58% can be achieved for moderate laser pulses in the picosecond range. Calculations with constant transition dipole moments show a much higher transfer of 94% and thus overestimate the efficiency significantly.

Blue satellite bands of KRb molecule: Intermediate long-range states

Three distinct satellite bands at 730–736 nm and a single shoulder at 755.5 nm that we assigned to KRb heteronuclear molecule are found in absorption measurements of hot K + Rb vapor. The interpretation of these bands is discussed in terms of recent ab initio calculations of the relevant potential curves. Semiclassical spectral simulations were performed with ab initio potentials and approximate transition dipole moment functions showing a good agreement with observations. The probabilities of cold molecule photoassociative formation into the external well of the double minimum (5)0+ state and decay to the ground state are discussed, and relative yields of molecular formation were estimated by using quantum mechanical calculations.

Critical Evaluation of the Prediction of the Dissociation Energy and the Energy Spectrum of the Ground State of KRb by the Reduced Potential Curve Method

The estimates of the value of the dissociation energy and the energy spectrum of the KRb molecule made previously (O. Bludský, M. Jur̆ek, V. S̆pirko, B. A. Brandt, and F. Jenc̆, 1995, J. Mol. Spectrosc.169, 555–582) are compared with the new experimental data (C. Amiot and J. Vergès, 2000, J. Chem. Phys.112, 7068–7074) and the efficacy of the reduced potential curve (RPC) method is demonstrated.

Theoretical Study of the Electronic Structure of the KRb Molecule

Upon request of experimentalists now engaged in high-resolution spectroscopic investigations of the molecule KRb, we have determined the potential energy of electronic states 2S+1Λ(+) correlating up to the limit K(5p) + Rb(5s) and of electronic states Ω(+/−) correlating up to the limit K(4s) + Rb(4d2D3/2) in a large range of internuclear distance R. For the five states so far observed, the agreement between calculated and experimental molecular constants is good with ΔRe < 0.08 Å, Δωe < 6 cm−1, and ΔTe < 140 cm−1. Extensive numerical data for energies versus R have been listed in a data base available at http://www.idealibrary.com.

The KRb (2)3Σ+ Electronic State

High-resolution spectra of the (3)1Π → (2)3Σ+ system of the KRb molecule, obtained after excitation with fixed frequencies Ar+ laser lines, were recorded on a Connes-type Fourier transform interferometer. Molecular constants of the first 14 vibrational levels of the (2)3Σ+ state are determined. The RKR potential energy curve is derived. The main spectroscopic constants for this triplet electronic state of the 39K 85Rb isotopic species are Te = 13 507.146(2) cm−1, ωe = 48.6385(6) cm−1, Be = 0.0254152(5) cm−1, γ = 0.00164(4) cm−1, ϵ = −0.469(2) cm−1, Re = 4.98345 Å, De = 3447 cm−1.