We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic molecule with $-C_n/r^n$ ($n>2$) asymptotic interaction can have only 1, 2, and up to a maximum of $n-2$ rotational states. A classification scheme of diatomic molecules is proposed, in which each class has a distinctive rotational structure and corresponds to different atom-atom scattering properties above the dissociation limit.
A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical, the other where the center-of-mass motion is treated classically while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion, and that it departs from the Mathieu equation solution found for a…
We present a theoretical study of the impact of an electric field combined with a magnetic field on the rotational dynamics of open shell diatomic molecules. Within the rigid rotor approximation, we solve the time-independent Schrödinger equation including the fine-structure interactions and the Λ-doubling effects. We consider three sets of molecule specific parameters and several field regimes and investigate the interplay between the different interactions identifying the dominant one. The possibility of inducing couplings between the spin and rotational degrees of freedom is demonstrated.
We present a detailed comparison of strong-field ionization of diatomic molecules and their companion atoms with nearly equal ionization potentials. We perform calculations in the length and velocity gauge formulations of the molecular strong-field approximation and with the molecular tunneling theory, and in both cases we consider effects of nuclear motion. A comparison of our results with experimental data shows that the length gauge strong-field approximation gives the most reliable predictions.
This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is…
We show that dressing of diatomic molecules by running laser waves gives rise to conical intersections (CIs). Due to presence of such CIs, the rovibronic molecular motions are strongly coupled. A pronounced impact of the CI on the spectrum of $Na_2$ molecule is demonstrated via numerical calculation for weak and moderate laser intensity, and an experiment is suggested on this basis. The position of the light induced CI and the strength of its non-adiabatic couplings can be chosen by changing the frequency and intensity of the used running laser wave. This offers new possibilities to control th…
The scaling of nuclear spin-dependent parity violating effects with increasing nuclear charge $Z$ is discussed in two series of isovalent open-shell diatomic molecules. The parameter $W_\mathrm{a}$ characterising the strength of parity violation in diatomic molecules is calculated in the framework of the zeroth-order regular approximation (ZORA) and found to be in good agreement with the $R(Z) Z^k$ scaling law derived for atoms in which $R(Z)$ represents a relativistic enhancement factor. The influence of electron correlation is studied on the molecular level, with spin-polarisation effects be…
The development of the magneto-optical trap revolutionized the fields of atomic and quantum physics by providing a simple method for the rapid production of ultracold, trapped atoms. A similar technique for producing a diverse set of dense, ultracold diatomic molecular species will likewise transform the study of strongly interacting quantum systems, precision measurement, and physical chemistry. We demonstrate one- and two-dimensional transverse laser cooling and magneto-optical trapping of the polar molecule yttrium (II) oxide (YO). Using a quasicycling optical transition we observe transver…
We show that the relative effect of variation of the fine structure constant in microwave transitions between very close and narrow rotational-hyperfine levels may be enhanced 2-3 orders of magnitude in diatomic molecules like LaS, LaO, LuS, YbF, etc. The enhancement is a result of cancellation between the hyperfine and rotational intervals.
We present calculations of the hyperfine coupling constants for all the heteronuclear alkali-metal diatomic molecules at the equilibrium geometry of the electronic ground state. These constants are important in developing methods to control ultracold polar molecules. The results are based on electronic structure calculations using density functional theory, and are in good agreement with experiment for the limited set of molecules for which experiments are so far available.
We explore the electronic structure of ultralong-range pentaatomic Rydberg molecules from a merger of a Rydberg atom and two ground state heteronuclear diatomic molecules. Our focus is on the interaction of Rb($23s$) and Rb($n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the pentaatomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and ori…
We present a simple method for determination of absolute vibrational numbering of isolated near dissociation levels in diatomic molecules, usually observed in cold physics experiments. The method is based on the isotope shift and works even when energies of only two levels from one isotopologue and one level from another isotopologue have been measured. It is demonstrated on data from recently reported precise measurements of binding energies of levels lying close to the dissociation limits in ultracold Yb2, CsYb, RbSr and RbYb molecules. Its predictions agree with these of much more elaborate…
We demonstrate a scheme for optical cycling in the polar, diatomic molecule strontium monofluoride (SrF) using the $X ^2Σ^+\toA^2Π_{1/2}$ electronic transition. SrF's highly diagonal Franck-Condon factors suppress vibrational branching. We eliminate rotational branching by employing a quasi-cycling $N=1\to N^\prime=0$ type transition in conjunction with magnetic field remixing of dark Zeeman sublevels. We observe cycling fluorescence and deflection through radiative force of an SrF molecular beam using this scheme. With straightforward improvements our scheme promises to allow more than $10^5$…
Nuclear-spin-dependent (NSD) parity violating effects are studied for a number of diatomic molecules using relativistic Hartree-Fock and density functional theory and accounting for core polarization effects. Heavy diatomic molecules are good candidates for the successful measurement of the nuclear anapole moment, which is the dominant NSD parity violation term in heavy elements. Improved results for the molecules studied in our previous publication [Borschevsky et al., Phys. Rev. A 85, 052509 (2012)] are presented along with the calculations for a number of new promising candidates for the nu…
We present a magnetically enhanced laser cooling scheme applicable to multi-level type-II transitions and further diatomic molecules with adiabatic transfer. An angled magnetic field is introduced to not only remix the dark states, but also decompose the multi-level system into several two-level sub-systems in time-ordering, hence allowing multiple photon momentum transfer. For complex multi-level diatomic molecules, although the enhancement gets weakened, our simulations still predict a $\sim 4\times$ larger value of the maximum achievable cooling force and a wider coolable velocity range com…
We present a computer program to calculate the quantised rotational and hyperfine energy levels of $^{1}Σ$ diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments.
Astrophysical molecular spectroscopy is an important means of searching for new physics through probing the variation of the proton-to-electron mass ratio, $μ$. New molecular probes could provide tighter constraints on the variation of $μ$ and better direction for theories of new physics. Here we summarise our previous paper \citep{19SyMoCu.CN} for astronomers, highlighting the importance of accurate estimates of peak molecular abundance and temperature as well as spectral resolution and sensitivity of telescopes in different regions of the electromagnetic spectrum. Whilst none of the 11 astro…
Using a three-dimensional quasiclassical technique we explore the double ionization pathways of a diatomic molecule driven by an intense infrared (800nm) ultrashort laser pulse. For intensities corresponding to the tunneling regime, we find that the three main ionization mechanisms have distinct traces when considering the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape. In addition, we find that the previously observed "finger-like" structure in the correlated momenta of the strongly driven He is also present for strongly driven diatomic mo…
We demonstrate the mixing of rotational states in the ground electronic state using microwave radiation to enhance optical cycling in the molecule yttrium (II) monoxide (YO). This mixing technique is used in conjunction with a frequency modulated and chirped continuous wave laser to slow longitudinally a cryogenic buffer gas beam of YO. We generate a measurable flux of YO below 10~m/s, directly loadable into a three-dimensional magneto-optical trap. This technique opens the door for laser cooling of molecules with more complex structure.
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical one in the limit of a large number of kicks. The opposite behavior emerges for a small number of kicks. Quantum and classical dissociation probabilities do not coincide for any parameter combinations of the force. This can be attributed to a scaling property in the classical system which is broken quantum mechanically.
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle time-independent Dirac equation. The first one is based on a min-max principle and uses a two-spinor formulation as a starting point. The second one is the Rayleigh-Ritz variational method combined with kinematically balanced basis functions. Both methods use a B-spline basis function expansion. We show that accurate results can be obtained with both methods and that n…
We present a novel slowing scheme for beams of laser-coolable diatomic molecules reminiscent of Zeeman slowing of atomic beams. The scheme results in efficient compression of the 1-dimensional velocity distribution to velocities trappable by magnetic or magneto-optical traps. 3D Monte Carlo simulations for the prototype molecule $^{88}\mathrm{Sr}^{19}\mathrm{F}$ and experiments in an atomic testbed demonstrate a performance comparable to traditional atomic Zeeman slowing and an enhancement of flux below v=35 m/s by a factor of $\approx 20$ compared to white-light slowing. This is the first exp…
The generation of high-order harmonics in diatomic molecules is investigated within the framework of the strong-field approximation. We show that the conventional saddle-point approximation is not suitable for large internuclear distances. An adapted saddle-point method that takes into account the molecular structure is presented. We analyze the predictions for the harmonic-generation spectra in both the velocity and the length gauge. At large internuclear separations, we compare the resulting cutoffs with the predictions of the simple-man's model. Good agreement is obtained only by using the …
We present ab initio calculations of the $W_A$ parameter of the P-odd spin-rotational Hamiltonian for a variety of diatomic molecules, including the group--2 and --12 halides. The results were obtained by relativistic Dirac--Hartree--Fock and density functional theory approaches, and corrected for core polarization effects. Strong enhancement of $W_A$ is found for the group--12 diatomic halides, which should be helpful in future determination of the nuclear anapole moment.
Current situation in studies of mean lifetimes of excited electronic-vibro-rotational states of hydrogen molecule (including the H2, D2, HD and T2 isotopomers) is reviewed in brief. All measured values of the lifetimes (published before November 2008) are collected and presented in tabular form. Complete bibliography of papers devoted to semi-empirical determination and non-empirical calculation of the lifetimes is presented. The experimental data obtained in various papers are compared with the results of semi-empirical determination and non-empirical calculations.
The energies at geometries close to the equilibrium for the e$^+$BeO and e$^+$LiF ground states were computed by means of diffusion Monte Carlo simulations. These results allow us to predict the equilibrium geometries and the vibrational frequencies for these exotic systems,and to discuss their stability with respect to the various dissociation channels. Since the adiabatic positron affinities were found to be smaller than the dissociation energies for both complexes, we propose these two molecules as possible candidates in the challenge to produce and detect stable positron-molecule systems.
In the present paper, we investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong field approximation (SFA) model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum, and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these in…
We present a theoretical model of high-harmonic generation from diatomic molecules. The theory includes effects of alignment as well as nuclear motion and is used to predict results for N$_2$, O$_2$, H$_2$ and D$_2$. The results show that the alignment dependence of high-harmonics is governed by the symmetry of the highest occupied molecular orbital and that the inclusion of the nuclear motion in the theoretical description generally reduces the intensity of the harmonic radiation. We compare our model with experimental results on N$_2$ and O$_2$, and obtain very good agreement.
We investigate electron correlation effects in internuclear-distance-dependent enhanced ionization of $\mathrm{H}_2$, $\mathrm{LiH}$, and $\mathrm{HF}$ molecules by intense near-infrared laser pulses using a 3D description of the systems with the time-dependent generalized-active-space configuration-interaction method. This method systematically incorporates electron-electron correlation of the quantum many-electron system under consideration. Our correlated description of diatomic molecules shows that enhanced ionization occurs at certain critical internuclear separations and electron correla…
We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of $^{40}$K$^{87}$Rb+$^{87}$Rb. We show multiple types of resonance due to long-range states with ro…
We present an analysis of the deceleration and trapping of heavy diatomic molecules in low-field seeking states by a moving electric potential. This moving potential is created by a 'ring-decelerator', which consists of a series of ring-shaped electrodes to which oscillating high voltages are applied. Particle trajectory simulations have been used to analyze the deceleration and trapping efficiency for a group of molecules that is of special interest for precision measurements of fundamental discrete symmetries. For the typical case of the SrF molecule in the (N,M) = (2, 0) state, the ring-dec…
Laser cooling and trapping are central to modern atomic physics. The workhorse technique in cold-atom physics is the magneto-optical trap (MOT), which combines laser cooling with a restoring force from radiation pressure. For a variety of atomic species, MOTs can capture and cool large numbers of particles to ultracold temperatures (<1 mK); this has enabled the study of a wide range of phenomena from optical clocks to ultracold collisions whilst also serving as the ubiquitous starting point for further cooling into the regime of quantum degeneracy. Magneto-optical trapping of molecules could p…
We describe an inexpensive instructional experiment that demonstrates the rotational energy levels of diatomic nitrogen, using the emission band spectrum of molecular nitrogen ionized by various processes in a commercial AC capillary discharge tube. The simple setup and analytical procedure is introduced as part of a sequence of educational experiments employed by a course of advanced atomic and molecular spectroscopy, where the study of rotational spectra is combined with the analysis of vibrational characteristics for a multifaceted picture of the quantum states of diatomic molecules.
We consider the influence of variation in the fine structure constant alpha on a promising experiment proposed by DeMille et al. to search for variation in the electron-to-proton mass ratio mu using diatomic molecules [DeMille et al., Phys. Rev. Lett. 100, 043202 (2008)]. The proposed experiment involves spectroscopically probing the splitting between two nearly-degenerate vibrational levels supported by different electronic potentials. Here we demonstrate that this splitting may be equally or more sensitive to variation in alpha as to variation in mu. For the anticipated experimental precisio…
Rotational levels of molecular free radicals can be tuned to degeneracy using laboratory-scale magnetic fields. Because of their intrinsically narrow width, these level crossings of opposite-parity states have been proposed for use in the study of parity-violating interactions and other applications. We experimentally study a typical manifestation of this system using $^{138}$BaF. Using a Stark-mixing method for detection, we demonstrate level-crossing signals with spectral width as small as 6 kHz. We use our data to verify the predicted lineshapes, transition dipole moments, and Stark shifts,…
We analyze the influence of different recombination scenarios, involving one or two centers, on high-order harmonic generation (HHG) in diatomic molecules, for different values of the internuclear separation. We work within the strong-field approximation, and employ modified saddle-point equations, in which the structure of the molecule is incorporated. We find that the two-center interference patterns, attributed to high-order harmonic emission at spatially separated centers, are formed by the quantum interference of the orbits starting at a center $C_{j}$ and finishing at a different center …
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter characterizing the vibrational-rotational interaction have been proposed for the potentials whose the creation and annihilation operators can be constructed. Expressions for the expansion of the wave function of the vibrational-rotational states in a set of wave functions of the rotationless vibrational states have been obtained of the second order in the p…
The direct above-threshold ionization (ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet (IR+XUV) laser fields is investigated by the frequency-domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ioni…
The generation of high harmonics (HHG) in atomic systems by the highly non-linear response to an intense laser field is a prominent pathway to the synthesis of ever shorter laser pulses at increasingly higher photon energies. Extensions of this process to molecules add to the complexity but also offers novel opportunities as multi-center effects and the coupling to nuclear degrees of freedom can influence HHG. In this work we theoretically explore the impact of coherent vibronic excitations of diatomic molecules on the HHG spectrum within the framework of time-dependent density functional theo…
The single ionization of noble gas atoms by the combined action of XUV attopulses and an infrared laser field is theoretically investigated by means of a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret the angular distributions as two-center interferences where the separation between the centers is governed by the infrared laser field. Angular distributions are compared to the available experimental data showing a good agreement. Finally, we deduce the conditio…
Following the first principles the elements of the analytic theory of potential curves for diatomic molecules (diatomics) are presented. It is based on matching the perturbation theory at small internuclear distances $R$ and multipole expansion at large distances, modified by instanton-induced trans-series for homonuclear case, with addition of the phenomenologically described equilibrium configuration, if exists. It leads to a new class of (generalized) meromorphic potentials (modified by exponential terms) with difference in degrees of polynomials in numerator and denominator equal to 4 (6) …
We calculate angle-resolved above-threshold ionization spectra for diatomic molecules in linearly polarized laser fields, employing the strong-field approximation. The interference structure resulting from the individual contributions of the different scattering scenarios is discussed in detail, with respect to the dependence on the internuclear distance and molecular orientation. We show that, in general, the contributions from the processes in which the electron is freed at one center and rescatters off the other obscure the interference maxima and minima obtained from single-center processe…
We address the influence of the orbital symmetry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to the electron emission at spatially separated centers. The interference patterns survive the in…
We present an implementation of a time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method [R. Anzaki et al., Phys. Chem. Chem. Phys. 19, 22008 (2017)] with the full configuration interaction expansion for coupled electron-nuclear dynamics in diatomic molecules subject to a strong laser field. In this method, the total wave function is expressed as a superposition of different configurations constructed from time-dependent electronic Slater determinants and time-dependent orthonormal nuclear basis functions. The primitive basis functions of nuclei and electrons are strictly in…
We analyze the imprint of nodal planes in high-order harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semi-analytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole op…
We explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on interaction of Rb($27s$) Rydberg atom with KRb($N=0$) diatomic polar molecule. There's significant electronic hybridization of Rb($n=24$, $l\ge 3$) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born-Oppenheimer potential curves, ess…
Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme was employed to form these molecules in states which correlate to $np(n+1)s$ dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair…
Recent improvements in experimental techniques for preparing ultracold molecules that contain alkali atoms (e.g., Li, Na, and K) have been reported. Based on these advances in ultracold molecules, new searches for the electric dipole moment of the electron and the scalar-pseudoscalar interaction can be proposed on such systems. We calculate the effective electric fields (Eeff) and the S-PS coefficients (Ws) of SrA and HgA (A = Li, Na, and K) molecules at the Dirac-Fock (DF) and the relativistic coupled cluster (RCC) levels. We elaborate on the following points: i) Basis set dependence of the m…
We explore the properties of 3-atom complexes of alkali-metal diatomic molecules with alkali-metal atoms, which may be formed in ultracold collisions. We estimate the densities of vibrational states at the energy of atom-diatom collisions, and find values ranging from 2.2 to 350~K$^{-1}$. However, this density does not account for electronic near-degeneracy or electron and nuclear spins. We consider the fine and hyperfine structure expected for such complexes. The Fermi contact interaction between electron and nuclear spins can cause spin exchange between atomic and molecular spins. It can dri…
Diatomic molecules (e.g., O$_2$) in intense laser field exhibit a peculiar suppressed ionization behavior compared to their companion atoms. Several physical models have been proposed to account for this suppression while no consensus has been achieved. In this letter, we aim to clarify the underlying mechanisms behind this molecular ionization suppression. Experimental data recorded at midinfrared laser wavelength and its comparison with that at near-infrared wavelength revealed a peculiar wavelength and intensity dependence of the suppressed ionization of O$_2$ with respect to its companion …
Born and Oppenheimer reported an approximate separation of molecular eigenfunctions into electronic, vibrational, and rotational parts, but at the end of their paper showed that the two angles describing rotation of the nuclei in a diatomic molecule are exactly separable. A year later in a two-part work devoted strictly to diatomic molecules, Wigner and Witmer published (1) an exact diatomic eigenfunction and (2) the rules correlating the electronic state of a diatomic molecule to the orbital and spin momenta of the separated atoms. The second part of the Wigner-Witmer paper became famous for …
Sensitivity to temporal variation of the fundamental constants may be strongly enhanced in transitions between narrow close levels of different nature. This enhancement may be realized in a large number of molecules due to cancelation between the ground state fine structure omega_f and vibrational interval omega_v (omega=omega_f - n omega_v is close to zero, delta omega/omega= K (2 delta alpha/alpha +0.5 delta mu/mu), K >>1, mu=m_p/m_e). The intervals between the levels are conveniently located in microwave frequency range and the level widths are very small. Required accuracy of the shift mea…
We study ionization dynamics of aligned diatomic molecules N$_2$ in strong elliptical laser fields experimentally and theoretically. The alignment dependence of photoelectron momentum distributions (PMDs) of N$_2$ measured in experiments is highlighted with comparing to Ar measured synchronously. Our results show that the PMDs of N$_2$ depend strongly on the alignment of the molecule, relative to the main axis of the laser ellipse. In particular, the most-probable electron-emission angle which is often used in attosecond measurement, differs remarkably when changing the molecular alignment. We…
