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Physical Review A

Electron-bound states in the field of dipolar molecules

Michel Bawin

Published Aug 1, 2004• 25 citations
Publisher

Abstract

We study Clary's theory for an electron in the field of a dipolar molecule. We find for a molecule of rotor constant $B$ and dipole moment $\ensuremath{\mu}$ that Clary's ``rotationally adiabatic'' molecular potential ${ϵ}_{ad}(r)$ behaves like $\ensuremath{-}64{r}^{4}∕3{\ensuremath{\mu}}^{4}$ near $r=0$ and like $\ensuremath{-}{\ensuremath{\mu}}^{2}∕6B{r}^{4}$ at infinity. We show, using general results about the spectrum of the Schr\"odinger Hamiltonian, that the salient features of the electron bound states spectrum, i.e., the existence of only a few weakly bound states, are a consequence of these asymptotic formulas. We argue that the long-range $(1∕{r}^{4})$ part of the interaction may be interpreted as resulting from the angle-averaged molecular dipole potential at some rotation temperature. Our results should be contrasted with those of Camblong et al. Phys. Rev. Lett. 87, 220402 (2001), who claim that these features arise from the renormalization of the static point dipole interaction.

DOI
10.1103/physreva.70.022505

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We study Clary's theory for an electron in the field of a dipolar molecule. We find for a molecule of rotor constant BBB and dipole moment \ensuremathμ\ensuremath{\mu}\ensuremathμ that Clary's ``rotationally adiabatic'' molecular potential ϵad(r){ϵ}_{ad}(r)ϵad​(r) behaves like \ensuremath−64r4∕3\ensuremathμ4\ensuremath{-}64{r}^{4}∕3{\ensuremath{\mu}}^{4}\ensuremath−64r4∕3\ensuremathμ4 near r=0r=0r=0 and like \ensuremath−\ensuremathμ2∕6Br4\ensuremath{-}{\ensuremath{\mu}}^{2}∕6B{r}^{4}\ensuremath−\ensuremathμ2∕6Br4 at infinity. We show, using general results about the spectrum of the Schr"odinger Hamiltonian, that the salient features of the electron bound states spectrum, i.e., the existence of only a few weakly bound states, are a consequence of these asymptotic formulas. We argue that the long-range (1∕r4)(1∕{r}^{4})(1∕r4) part of the interaction may be interpreted as resulting from the angle-averaged molecular dipole potential at some rotation temperature. Our results should be contrasted with those of Camblong et al. Phys. Rev. Lett. 87, 220402 (2001), who claim that these features arise from the renormalization of the static point dipole interaction.
By making use of the quantization rule of Raab and Friedrich [Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules.
We explore the character of a novel set of ``field-linked'' states that were predicted by Avdeenkov and Bohn [Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasibound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the two-dimensional Schr\"odinger equation to find bound states, whose energies correlate well with resonance features found in fully converged multichannel scattering calculations.
We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024
The authors outline an asymptotic calculation of adiabatic potential curves for diatomic quasimolecular systems that happens to be quite accurate in the domain of long-range forces, even for atoms with complex electronic configurations. A formula for the molecular oscillator strength expressed via the oscillator strengths of the constituent atoms and the eigenfunctions of the effective Hamiltonian is presented. Quite general theoretical results on the electrostatic interaction within these quasimolecular systems are then applied to a calculation of the dipole-dipole interaction for the quasimolecule Eu-Sr, leading to the adiabatic potentials in the region of interatomic distances larger than approximately 1.0 nm. These results are checked by comparing the quasistatic absorption coefficient for the blue quasistatic wing of the Eu resonance line broadened by the influence of Sr atoms to the experimentally derived profile [K. Niemax, Phys. Rev. Lett. 55. 56 (1985)]. Excellent agreement is obtained. A great influence of the molecular oscillator strengths on the shape of the quasistatic profile is found, so that, in general, the character of the interaction potential could not be judged from log-log plots of the absorption coefficient alone.
Ultra-cold long-range Rydberg-ground molecule consisting of a Rydberg atom and one or more ground-state atoms is formed by low-energy scattering between the Rydberg electron and ground-state atoms located inside the Rydberg electron’s wave function. The low-energy scattering interaction, initially investigated by Fermi and Omont, has been predicted to lead to molecular binding in a novel type of Rydberg molecules, including the trilobite and butterfly molecules. Their unconventional binding mechanism, which is unlike covalent, or ionic, or van der Waals bonds, results in loosely bound molecules with bond lengths on the order of thousands of Bohr radius. This kind of molecule with large size and huge permanent electric dipole moment is a good candidate for realizing the certain strongly correlated many-body gases and for quantum information processing, as well as for dipolar quantum gases and spin systems with long-range interactions. Consequently, these molecules have received considerable attention in recent years. In this paper, we review the recent theoretical and experimental investigations of ultra-cold long-range Rydberg-ground molecules, including the scattering interaction between the Rydberg electron and ground-state atom and the resulting adiabatic potential curves, experimental observations of photo-associated Rydberg-ground molecules spectra, as well as the measurements of permanent electric dipole moment. Ultra-cold long-range Rydberg-ground molecules are prepared by photoassociation in a high-density cold atom sample. Therefore, the Rydberg electron can bind several ground-state atoms to form a polyatomic Rydberg-ground molecule. The permanent molecular electric-dipole moments are revealed by spectral line broadening in the electric fields. The latest research pointed out that the permanent electric dipole moments of the Cs nDJ -type Rydberg-ground molecules are negative, which is different from the previous reports (the electric dipole moments are positive). The negative sign reflects a deficiency of Rydberg-electron density near the ground-state perturber, which is caused by electronic configuration mixing.
The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to long-range molecules with binding energies typically ranging from 10 to $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$ MHz. These energies are comparable to the relativistic and hyperfine structure of the separate atomic components. Studies of molecular formation aiming to reproduce observations with spectroscopic accuracy must therefore include the hyperfine splitting of the neutral atom and the spin-orbit splittings of both the Rydberg atom and the electron-atom interaction. Adiabatic potential energy curves and permanent electric dipole moments are presented for Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs2{\mathrm{Cs}}_{2}Cs2​. The influence of spin degrees of freedom on the potential energy curves and multipole moments probed in recent experimental work is elucidated, and the observed dipole moments of butterfly molecules are explained by the generalized 3PJ^{3}P_{J}3PJ​ pseudopotential derived here.