Zero field splittings in molecules originate from the intrinsic spin and orbital angular momentum of unpaired electrons. Here, we close a knowledge gap on a diatomic molecule built from spin-8 ground-state dysprosium atoms, where zero-field splittings correspond to the energies of states with different alignments of the two spins. We predict a paramagnetic molecular ground state with parallel Dy spins aligned along the internuclear axis. A diamagnetic state with anti-parallel spins is the first excited state with a small energy cost of hc × 2 cm−1 predominantly due to the magnetic dipole-dipole interaction. We also determine the rotations and vibrations of the diatom and show that centrifugal forces double the splittings between these para- and dia-magnetic states. The vibrational spacings and zero-field splittings have similar magnitude. Finally, the Dy2 ground state has a magnetic moment that is twice that of the atom and, thus, arrays of ultracold Dy2 can be used to simulate strongly interacting magnets. Zero-field splittings in molecules arise from the spin and orbital angular momentum of unpaired electrons, yet their behaviour in diatomic molecules with spin-8 dysprosium atoms remains underexplored. Here, the authors predict a paramagnetic ground state with parallel Dy spins and reveal implications for simulating strongly interacting magnets using ultracold Dy2 arrays.
The nature of the interaction between ultracold atoms with a large orbital and spin angular momentum has attracted considerable attention. It was suggested that such interactions can lead to the realization of exotic states of highly correlated matter. Here, we report on a theoretical study of the competing anisotropic dispersion, magnetic dipole-dipole, and electric quadrupole-quadrupole forces between two dysprosium atoms. Each dysprosium atom has an orbital angular momentum of L = 6 and a magnetic moment of μ = 10 μ(B). We show that the dispersion coefficients of the ground state adiabatic potentials lie between 1865 a.u. and 1890 a.u., creating a non-negligible anisotropy with a spread of 25 a.u. and that the electric quadrupole-quadrupole interaction is weak compared to the other interactions. We also find that for interatomic separations R < 50a(0) both the anisotropic dispersion and magnetic dipole-dipole potential are larger than the atomic Zeeman splittings for external magnetic fields of order 10 G to 100 G. At these separations the atomic angular momentum can be reoriented. We finish by describing two scattering models for these inelastic m-changing collisions. A universal scattering theory is used to model loss due to the anisotropy in the dispersion and a Born approximation is used to model losses from the magnetic dipole-dipole interaction for the (164)Dy isotope. These models find loss rates that are of the same order of magnitude as the experimental value.
We establish a correspondence between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole matrix elements of a magnetic dipole associated with an elemental spin
F. It is shown that this correspondence makes it possible to perform quantum simulation of the single-particle spectrum and the dipole-dipole interactions of magnetic dipoles in a static external magnetic field
B with symmetric top molecules subject to a static external electric field
EDC. We further show that no such correspondence exists for
1Σ molecules in static fields, such as the alkali metal dimers. The effective spin angular momentum of the simulated magnetic dipole corresponds to the rotational angular momentum of the symmetric top molecule, and so quantum simulation of arbitrarily large integer spins is possible. Further, taking the molecule CH
3F as an example, we show that the characteristic dipole-dipole interaction energies of the simulated magnetic dipole are a factor of 620, 600, and 310 larger than for the highly magnetic atoms Chromium, Erbium, and Dysprosium, respectively. We present several applications of our correspondence for many-body physics, including long-range and anisotropic spin models with arbitrary integer spin
S using symmetric top molecules in optical lattices, quantum simulation of molecular magnets, and spontaneous demagnetization of Bose-Einstein condensates due to dipole-dipole interactions. Our results are expected to be relevant as cold symmetric top molecules reach quantum degeneracy through Stark deceleration and opto-electrical cooling.
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.
We unravel some peculiar properties of ultra-long-range Rydberg molecules formed by an
s-state
87Rb Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the
s-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open interesting possibilities for accessing the physics of relativistic electron-atom scattering experimentally.
Abstract We excite diatomic oxygen and nitrogen to high rotational states with an optical centrifuge and study their dynamics in an external magnetic field. Ion imaging is employed to directly visualize, and follow in time, the rotation plane of the molecular superrotors. The two different mechanisms of interaction between the magnetic field and the molecular angular momentum in paramagnetic oxygen and non-magnetic nitrogen lead to qualitatively different behaviour. In nitrogen, we observe the precession of the molecular angular momentum around the field vector. In oxygen, strong spin–rotation coupling results in faster and richer dynamics, encompassing the splitting of the rotation plane into three separate components. As the centrifuged molecules evolve with no significant dispersion of the molecular wave function, the observed magnetic interaction presents an efficient mechanism for controlling the plane of molecular rotation.
The properties of the electronic ground state of the polar and paramagnetic europium--
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), europium--alkaline-earth-metal-atom,
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 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.