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arXiv:1907.03853 · Physical Review A

Purely long-range polar molecules composed of identical lanthanide atoms

Hui Li, Goulven Quéméner, Jean-François Wyart, Olivier Dulieu, Maxence Lepers

Published Oct 29, 2019• 4 citations
arXivHTMLPDF

Abstract

Doubly polar molecules, possessing an electric dipole moment and a magnetic dipole moment, can strongly couple to both an external electric field and a magnetic field, providing unique opportunities to exert full control of the system quantum state at ultracold temperatures. We propose a method for creating a purely long-range doubly polar homonuclear molecule from a pair of strongly magnetic lanthanide atoms, one atom being in its ground level and the other in a superposition of quasidegenerate opposite-parity excited levels [Phys. Rev. Lett. 121, 063201 (2018)]. The electric dipole moment is induced by coupling the excited levels with an external electric field. We derive the general expression of the long-range, Stark, and Zeeman interaction energies in the properly symmetrized and fully-coupled basis describing the diatomic complex. Taking the example of holmium, our calculations predict a few shallow long-range wells in the potential energy curves that support vibrational levels accessible by direct photoassociation from pairs of ground-level atoms.

DOI
10.1103/physreva.100.042711

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Doubly polar molecules, possessing an electric dipole moment and a magnetic dipole moment, can strongly couple to both an external electric field and a magnetic field, providing unique opportunities to exert full control of the system quantum state at ultracold temperatures. We propose a method for creating a purely long-range doubly polar homonuclear molecule from a pair of strongly magnetic lanthanide atoms, one atom being in its ground level and the other in a superposition of quasidegenerate opposite-parity excited levels [Phys. Rev. Lett. 121, 063201 (2018)]. The electric dipole moment is induced by coupling the excited levels with an external electric field. We derive the general expression of the long-range, Stark, and Zeeman interaction energies in the properly symmetrized and fully-coupled basis describing the diatomic complex. Taking the example of holmium, our calculations predict a few shallow long-range wells in the potential energy curves that support vibrational levels accessible by direct photoassociation from pairs of ground-level atoms.
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.
We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm^{-1} with electronic angular momentum J=10, and at 17514.50 cm^{-1} with J=9, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, i.e., an electric field of 5 kV/cm, we predict a large magnetic dipole moment up to 13 Bohr magnetons, and sizeable electric dipole moment up to 0.22 D. When a magnetic field is present, we show that the induced electric dipole moment is strongly dependent on the angle between the fields. The lifetime of the field-mixed levels is found in the millisecond range, thus allowing for suitable experimental detection and manipulation.
Abstract Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er 2 Feshbach molecules which were produced recently. Since inside each molecule individual atoms conserve their identity, the intermolecular potential energy can be expanded as the sum of pairwise atomic potential energies. In the case of Er 2 Feshbach molecules, we show that the interaction between atomic magnetic dipoles gives rise to the usual term of the multipolar expansion, where R is the intermolecular distance, but also to additional terms scaling as and so on. Those terms are due to the interaction between effective molecular multipole moments, and are strongly anisotropic with respect to the orientation of the molecules. Similarly, the atomic pairwise van der Waals interaction results in ... terms in the intermolecular potential energy. By calculating the reduced electric-quadrupole moment of erbium ground level a.u., we also demonstrate that the electric–quadrupole interaction energy is negligible with respect to the magnetic dipole and van der Waals interaction energies. The general formalism presented in this article can be applied to calculate the long-range potential energy between arbitrary charge distributions composed of almost free subsystems.
Cold and ultracold Rydberg atoms are in considerable vogue for their ability to creating strong interactions, stemming from their exaggerated and readily tunable properties. Ultralong-range Rydberg molecules have been predicted to form from the interaction of ultracold Rydberg atoms with ground-state atoms and polar molecules. In this work, we discuss and demonstrate how such molecules, which are homonuclear, form substantially large permanent electric dipole moments. A corollary benefit of such strong hybridisation is the realisation of high angular momentum degenerate Rydberg molecules (so-called trilobite molecules) with standard photoassociation techniques.
The properties of the electronic ground state of the polar and paramagnetic europium--S-state-atomS\text{-state-atom}S-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium--alkali-metal-atom, EuX(X=Li,Na,K,Rb,Cs)\mathrm{Eu}X(X=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs})EuX(X=Li,Na,K,Rb,Cs), europium--alkaline-earth-metal-atom, EuY(Y=Be,Mg,Ca,Sr,Ba)\mathrm{Eu}Y(Y=\mathrm{Be},\mathrm{Mg},\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})EuY(Y=Be,Mg,Ca,Sr,Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances C6{C}_{6}C6​ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.
We experimentally show that an electric dipole moment of more than 1 Debye can be induced in the dysprosium (Dy) atom, in a long-lived state that is about 17 513 cm − 1 above the ground state. This metastable state is part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, we determine the approximately 1.12 cm − 1 doublet spacing for the five stable bosonic isotopes of Dy with kilohertz-level accuracy. From the shift of the microwave transition frequency in low electric fields (below 150 V/cm) and from optical spectra in high electric fields (up to 150 kV/cm), a reduced transition dipole moment of 7.65 ± 0.05 Debye between the doublet states is extracted. In high electric fields the doublet interacts with a third state at 17 727 cm − 1 that connects to the ground state via an electric-dipole transition. The three-state Stark interaction enables preparation of Dy atoms in the metastable state via single-photon excitation from the ground state. Our work experimentally validates predicted characteristics of the opposite-parity doublet and provides an effective route to the first doubly polar quantum gas of atoms.