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In this work we present the eigenspectra of a novel species of Wannier excitons when exposed to crossed electric and magnetic fields. In particular, we compute the eigenenergies of giant-dipole excitons in $\textrm{Cu}_2\textrm{O}$ in crossed fields. In our theoretical approach, we calculate the excitonic spectra within both an approximate as well as a numerically exact approach for arbitrary field configurations. We verify that stable bound excitonic giant-dipole states are only possible in the strong magnetic field limit, as this is the only regime providing sufficiently deep potential wells for their existence. Comparing both analytic as well as numerical calculations, we obtain excitonic giant-dipole spectra with level spacings in the range of $0.6\ldots100\, \mu \textrm{eV}$.

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to $s$-wave scattering, the next higher order of $p$-wave scattering in the Fermi-pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born--Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces., Comment: 8 pages, 7 figures

In this work we perform a Green's function analysis of giant-dipole systems. First we derive the Green's functions of different magnetically field-dressed systems, in particular of electronically highly excited atomic species in crossed electric and magnetic fields, so-called giant-dipole states. We determine the dynamical polarizability of atomic giant-dipole states as well as the adiabatic potential energy surfaces of giant-dipole molecules in the framework of the Green's function approach. Furthermore, we perform an comparative analysis of the latter to and exact diagonalization scheme and show the general divergence behavior of the widely applied Fermi-pseudopotential approach. Finally, we derive the giant-dipole's regularized Green's function representation., Comment: 11 pages, 4 figures, few changes compared to first version, published in "Special issue on correlations in light-matter interactions" of J. Phys. B: At. Mol. Opt. Phys

In this work we predict the existence of a novel species of Wannier excitons when exposed to crossed electric and magnetic fields. In particular, we present a theory of giant-dipole excitons in $\textrm{Cu}_2\rm O$ in crossed fields. Within our theoretical approach we perform a pseudoseparation of the center-of-mass motion for the field-dressed excitonic species, thereby obtaining an effective single-particle Hamiltonian for the relative motion. For arbitrary gauge fields we exactly separate the gauge-dependent kinetic energy terms from the effective single-particle interaction potential. Depending on the applied field strengths and the specific field orientation, the potential for the relative motion of electron and hole exhibits an outer well at spatial separations up to several micrometers and depths up to $380\, \mu \rm eV$, leading to possible permanent excitonic electric dipole moments of around three million Debye., Comment: 11 pages, 6 figures, 1 table, only minor changes compared to the first version, accepted for publication in Phys. Rev. B (in print)

We investigate polyatomic ultralong-range Rydberg molecules consisting of three ground state atoms bound to a Rydberg atom via $s$- and $p$-wave interactions. By employing the finite basis set representation of the unperturbed Rydberg electron Green's function we reduce the computational effort to solve the electronic problem substantially. This method is subsequently applied to determine the potential energy surfaces of triatomic systems in electronic $s$- and $p$-Rydberg states. Their molecular geometry and resulting vibrational structure are analyzed within an adiabatic approach that separates the vibrational bending and stretching dynamics. This procedure yields information on the radial and angular arrangement of the nuclei and indicates in particular that kinetic couplings between bending and stretching modes induce a linear structure in triatomic $l=0$ ultralong-range Rydberg molecules., Comment: 32 pages, 12 figures

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an $s$-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically motivated., Comment: 9 pages, 1 figure

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 acquires 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 of the specific degree of electronic excitation. This allows 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 $2-250$ MHz. Both properties are analyzed with of varying field strengths., Comment: 15 pages, 13 figures, 2 tables

We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using the Born-Oppenheimer approximation including s- and p-wave scattering, reproduces the measured binding energies. The calculated molecular wavefunctions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or anti-alignment with respect to the magnetic field axis., Comment: 10 pages and 8 figures including supplementary

We investigate the impact of an electric field on the structure of ultralong-range polar diatomic Rydberg molecules. Both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows to shift the corresponding potential wells in such a manner that the importance of the p-wave interaction can be controlled and the individual wells are energetically lowered at different rates. As a consequence the equilibrium configuration and corresponding energetically lowest well move to larger internuclear distances for increasing field strength. For strong fields the admixture of non-polar molecular Rydberg states leads to the possibility of exciting the large angular momentum polar states via two-photon processes from the ground state of the atom. The resulting properties of the electric dipole moment and the vibrational spectra are analyzed with varying field strength., Comment: 9 pages, 7 figures, accepted for publication in Physical Review A

We show the existence of ultra-long-range giant dipole molecules formed by a neutral alkali ground state atom that is bound to the decentered electronic wave function of a giant dipole atom. The adiabatic potential surfaces emerging from the interaction of the ground state atom with the giant dipole electron posses a rich topology depending on the degree of electronic excitation. Binding energies and the vibrational motion in the energetically lowest surfaces are analyzed by means of perturbation theory and exact diagonalization techniques. The resulting molecules are truly giant with internuclear distances up to several $\mu m$. Finally, we demonstrate the existence of intersection manifolds of excited electronic states that potentially lead to a vibrational decay of the ground state atom dynamics., Comment: 6 pages, 4 figures