Alkaline-earth-metal atoms in their lowest $(\mathrm{nsnp})$ ${}^{3}{P}_{2}$ state are exceptionally long lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth-metal atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. This paper develops a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. This analysis illuminates the nature of the coupling between the various degrees of freedom. The consequences are illustrated by application to a system of practical interest: metastable ${}^{88}\mathrm{Sr}.$ Using atomic parameters determined in a nearly ab initio calculation, we compute adiabatic potential-energy curves. The anisotropic interatomic interaction, in combination with the applied magnetic field, is demonstrated to induce the formation of a long-range molecular potential well. This curve correlates to two fully polarized, low-field seeking atoms in a rotational s-wave state. The coupling among molecular rotational states controls the existence of the potential well, and its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable ${}^{88}\mathrm{Sr}$ displays a resonance at a field of 339 G.
Alkaline-earth-metal atoms in their lowest (nsnp)3P2 state are exceptionally long lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth-metal atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. This paper develops a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. This analysis illuminates the nature of the coupling between the various degrees of freedom. The consequences are illustrated by application to a system of practical interest: metastable 88Sr. Using atomic parameters determined in a nearly ab initio calculation, we compute adiabatic potential-energy curves. The anisotropic interatomic interaction, in combination with the applied magnetic field, is demonstrated to induce the formation of a long-range molecular potential well. This curve correlates to two fully polarized, low-field seeking atoms in a rotational s-wave state. The coupling among molecular rotational states controls the existence of the potential well, and its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable 88Sr displays a resonance at a field of 339 G.
Ultracold collisions of spin-polarized 24Mg, 40Ca, and 88Sr in the metastable 3P2 excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.
Metastability and long-range interactions of Mg, Ca, and Sr in the lowest-energy metastable 3P2 state are investigated. The calculated lifetimes are 38 min for Mg∗, 118 min for Ca∗, and 17 min for Sr∗, supporting feasibility of cooling and trapping experiments. The quadrupole-quadrupole long-range interactions of two metastable atoms are evaluated for various molecular symmetries. Hund's case (c) 4g potential possesses a large 100--1000 K potential barrier. Therefore magnetic trap losses can possibly be reduced using cold metastable atoms in a stretched M=2 state. Calculations were performed in the framework of ab initio relativistic configuration interaction method coupled with the random-phase approximation.
Ultracold collisions between metastable bosonic 88Sr [(5s5p)3P2] and fermionic 87Sr [(5s5p)3P2(i=9/2)] atoms are investigated based on an approach of tensorial analysis. The scattering physics of two atoms in fully polarized s-wave entrance channels is studied in detail. In the Born-Oppenheimer approximation, the strong anisotropic interatomic interaction is demonstrated to induce formations of long-range molecular potential wells. However, besides significantly modifying the elastic scattering, the anisotropic interatomic interaction leads to the strong multichannel coupling between different partial waves, which triggers a high rate of inelastic losses. By applying an external static magnetic field B0=B0ez, the inelastic scattering can be suppressed while the elastic scattering is significantly enhanced. Additionally, the energy-dependent complex s-wave scattering lengths at a given relative collision energy strongly depend on the strength of magnetic field. We, moreover, self-consistently investigate ultracold collisions of two atoms at low temperatures in an optical lattice site. In the $\ensuremath{\delta}$-function pseudopotential approximation, we derive the effective s-wave scattering lengths, energy eigenvalues, elastic and inelastic scattering rates, and their dependence on the external magnetic field. We find that (i) the effective scattering lengths of ultracold atoms in entrance channels of interest display resonance behavior at certain values of magnetic field and (ii) the extra Zeeman interaction not only leads to the suppression of inelastic scattering but also enlarges the elastic scattering rates.
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.
Anisotropy induced Feshbach resonances in mixture of 6Li(2S)+171Yb(3P2)
We theoretically explore the scattering properties in collisions between in the ground state and fermionic in the metastable state. Unlike the role of the electronic spin degree of freedom in collisions of two alkali-metal atoms, the orbital degrees of freedom from the p electron of the metastable atoms, which induce not only mixings between different partial waves but also couplings between channels in different fine-structure manifolds, introduce the anisotropic interactions for producing broad-enough Feshbach resonances. Our closed-coupling calculation shows that this mechanism is similar to that in highly magnetic atoms, but the resonances also suffer from a large inelastic rate at the magnitude of to lower-lying fine-structure states or Zeeman sublevels, which will be an obstacle for associating ultracold polar molecules with both electron spin and electric dipole momentum. However, such a rich mixture of inelastic processes, and the experimental advantage of immunity from intraspecies inelastic collisions for metastable fermionic allow for precise investigations on the interspecies scattering properties for systems with excited-state atoms included.
Recently, alkaline-earth (-like) atoms and alkaline earth metals (AEL) gained experimental and theoretical interest principally related to the possibility offered in metrological field by the excitation of visible and UV clock transitions. AEL atoms, in their neutral \nform and in the ground state, have a null total electronic momentum, resulting nearly insensitive to external magnetic fields. While the absence of magnetic coupling does not allow the simply interactions tuning by exploiting Feshbach resonances as it occurs \nin alkaline atoms, these atoms are characterized by highly symmetric ground states allowing the simulation of SU(N) systems. This characteristic, that can be attributed in AEL atoms to the decoupling between electronic and nuclear atomic momenta, can be \nexploited to perform quantum simulation of a wealth of novel systems and constitutes a fundamental property of isotopes that have a nonzero nuclear spin, as it occurs for all the fermionic species and in particular for 173Yb and 87Sr. This feature also ensures the \nabsence of spin-changing collisions in ground state sublevels, implying that nuclear-spin mixtures are observationally stable. This attribute is fundamental for the study of transitions between different nuclear-spin states, for example by exploiting the two-photon \nRaman coupling. The degeneracy related to the SU(N) symmetry can be controllably removed by applying a two-photon Raman coupling, allowing for the simulation of systems with broken symmetries. \nBesides the possibility to induce couplings within the nuclear-spin degree of freedom, AEL atoms also offer the possibility to access a second, electronic degree of freedom; the possibility to address visible doubly-forbidden transitions between long-lived electronic \nclock states comprises a fantastic tool that allowed the building of optical lattice clocks improving metrological measurements and offering a richer platform for simulating complex systems. \nThe main difference between the two internal degrees of freedom offered by AEL atoms is that the possibility to address ultranarrow optical clock transitions exists also for AEL bosonic isotopes in which the nuclear-spin degree of freedom is not present because the \ntotal atomic momentum is absent. \nThe possibilities related to the excitation of long-lived metastable triplet levels, that, referring only to the lowest lying atomic levels are 3P(0;2) (in Russell-Saunders approximation they result doubly forbidden with respect to the electric dipole operator), are \nmultiple. If bosonic atoms are considered, the metrological applications based on the clock transition at the state of the art have performances comparable to optical lattice clocks realized with fermionic isotopes. Bosonic isotopes, requiring external fields in order \nto excite transitions from the ground state to long-lived states, have been proposed as good candidates in order to build a reliable and fast system in which controllable qu-bits could be realized. Most of these applications, and in particular the possibility to create \nquantum computers with neutral atoms, crucially rely on the control of the scattering properties of atoms in different electronic states. \nRegarding fermionic isotopes, the clock transitions recently allowed for the demonstration of spin-orbit coupling and quantum simulation via the synthetic dimension approach. As recently discovered, the clock transitions from the ground to the 3P(0;2) states give rise to rich interactions possibilities between atoms in the fundamental and in the metastable states. The spin-exchange interaction that has been observed between ground and metastable states, supports also a new kind of Feshbach resonance, called Orbital Feshbach Resonance (OrbFR). As occurs in magnetic Feshbach resonances for alkali atoms, also the OrbFR, that occurs in AEL atoms, supports the existence of extremely shallow homonuclear molecules. After considering the (s-wave) scattering parameters of all the AEL atoms that have been characterized experimentally, 173Yb is the only isotope in which the production and manipulation of Orbital Feshbach molecules (produced e.g. with photoassociation) is experimentally viable. Molecules generated by employing this atom, may lead to the investigation of fermionic superfluidity in still-unexplored regimes. In this thesis we report the characterization of interactions in bosonic 174Yb isotope by probing the clock transition between the singlet 1S0 ground state and the triplet 3P0 \nmetastable excited state. Interactions and inelastic losses between ground-state and excited metastable-state atoms have been experimentally determined with high accuracy, resulting consistent with an indipendent evaluation realized in the same period by Yb \nBEC group at LKB. \nThe obtained values for the interactions among ground and metastable atoms for the specified isotope constitute a first step in order to design an experimental system in which quantum information can be realized by means of exploiting the clock transition of bosonic Yb atoms. \nThis work, by exploiting the internal degrees of freedom of 173Yb atoms, reports a study on Orbital Feshbach molecules, showing experimentally the possibility to employ the nuclear degree of freedom in 173Yb atoms to manipulate and precisely detect homo-nuclear photoassociated molecules. \nThis first result regarding this new kind of shallow-bound molecules allowed the characterization of interactions between ground-state and metastable-state of 173Yb atoms. \nThis first intensive study of orbital Feshbach molecules is a fundamental step for future studies on the possibilities offered by these homo-nuclear molecules. \nFinally, we exploited the ground state SU(N) symmetry and its controlled breaking via Raman coupling (in 173Yb N = 1...6) to simulate the physical processes that are supposed to be driven by the hybridation of d-orbitals of iron atoms in iron based-superconductors, \nin which orbital-selective Mott insulating phases have been experimentally observed and are suspected to be the fundamental ingredient to achieve high-temperature superconductivity in these compounds.