Atomic and molecular samples reduced to temperatures below one microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating the interactions between their constituent particles. As a result of this resolution, atoms can be made to scatter resonantly on demand, through the precise control of a magnetic field. For simple atoms, such as alkalis, scattering resonances are extremely well characterized. However, ultracold physics is now poised to enter a new regime, where much more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense set of resonances in ultracold collision cross-sections will probably exhibit essentially random fluctuations, much as the observed energy spectra of nuclear scattering do. According to the Bohigas-Giannoni-Schmit conjecture, such fluctuations would imply chaotic dynamics of the underlying classical motion driving the collision. This would necessitate new ways of looking at the fundamental interactions in ultracold atomic and molecular systems, as well as perhaps new chaos-driven states of ultracold matter. Here we describe the experimental demonstration that random spectra are indeed found at ultralow temperatures. In the experiment, an ultracold gas of erbium atoms is shown to exhibit many Fano-Feshbach resonances, of the order of three per gauss for bosons. Analysis of their statistics verifies that their distribution of nearest-neighbour spacings is what one would expect from random matrix theory. The density and statistics of these resonances are explained by fully quantum mechanical scattering calculations that locate their origin in the anisotropy of the atoms' potential energy surface. Our results therefore reveal chaotic behaviour in the native interaction between ultracold atoms.

We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.

We report the measurement of the anisotropic ac polarizability of ultracold polar (40)K(87)Rb molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a "magic" angle between the laser polarization and the quantization axis is found where the polarizability of the |N=0,m(N)=0> and the |N=1,m(N)=0> states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the coherence time. This paves the way for precise spectroscopic measurements and coherent manipulations of rotational states as a tool in the creation and probing of novel quantum many-body states of polar molecules.

An experiment to search for the electron electric dipole moment (eEDM) on the metastable H 3 1 state of ThO molecule was proposed and now prepared by the ACME Collaboration [http://www.electronedm.org]. To interpret the experiment in terms of eEDM and dimensionless constant k T, P characterizing the strength of the T,P-odd pseudoscalar-scalar electron-nucleus neutral current interaction, an accurate theoretical study of an effective electric field on electron, E eff , and a parameter of the T,P-odd pseudoscalar-scalar interaction, W T ,P , in ThO is required. We report our results for E eff (84 GV/cm) and W T ,P (116 kHz) together with the hyperfine structure constant, molecule frame dipole moment, and H 3 1 → X 1 + transition energy, which can serve as a measure of reliability of the obtained E eff and W T ,P values. Besides, our results include a parity assignment and evaluation of the electric-field dependence for the magnetic g factors in the -doublets of H 3 1 .

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P− and T,P−violating interactions. The parameters of P− and T,P−odd terms of the spin-rotational Hamiltonian have been calculated for the 2 Σ electronic ground state of 223 RaF molecule. They include the Wa parameter, which is critical in experimental search for nuclear anapole moment and the parameters W d and WSP required to obtain restrictions on the electric dipole moment of the electron and T,P−odd scalar−pseudoscalar interactions, respectively. The parameter X corresponding to the "volume effect" in the T,P−odd interaction of the 223 Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for 223 RaF and 223 Ra + have been computed as well, demonstrating the accuracy of the methods employed.

We explore the anisotropic nature of Feshbach resonances in the collision between ultracold magnetic submerged-shell dysprosium atoms, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where most Feshbach resonances are hyperfine induced and due to rotation-less bound states. Our first-principle coupled-channel calculation of the collisions between spin-polarized bosonic dysprosium atoms reveals a striking correlation between the anisotropy in the magnetic dipole-dipole interaction and the anisotropy in the dispersion interaction. This latter anisotropy is absent in alkali-metal and chromium collisions. We show that both types of anisotropy significantly affect the Feshbach spectrum as a function of an external magnetic field. Effects of the electrostatic quadrupolequadrupole interaction are small. Over a 20 mT magnetic field range we predict about a ten Feshbach resonances and show that the resonance locations depend on the dysprosium isotope.A strongly interacting quantum gas of magnetic atoms, placed in an optical lattice, provides the opportunity to examine strongly correlated matter, creating a plat-form to explore exotic many-body phases known in solids, quantum ferrofluids, quantum liquid crystals, and supersolids [1,2]. Recent experimental advances [3][4][5][6][7][8][9][10] in trapping and cooling magnetic atoms pave the way towards these goals.In general, interactions between magnetic atoms are orientationally dependent or anisotropic. At room temperature anisotropic interactions are much smaller than kinetic energies and other major interactions between atoms, therefore can be ignored. The situation is different for an ultracold gas of atoms with a large magnetic moment. For example, the anisotropy due to magnetic dipole-dipole interactions between ultracold chromium atoms leads to an anisotropic deformation of a Bose Einstein condensate (BEC) [11]. Moreover, anisotropy plays a dominant role in collisional relaxation of ultracold atoms with large magnetic moments [5][6][7][12][13][14][15].

In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two dimensional geometry can be reduced by using the anisotropy of the dipole-dipole interaction and that this reduction follows a universal dipolar behavior.

Ultracold 174Yb+ ions and 40Ca atoms are confined in a hybrid trap. The charge exchange chemical reaction rate constant between these two species is measured and found to be 4 orders of magnitude larger than recent measurements in other heteronuclear systems. The structure of the CaYb+ molecule is determined and used in a calculation that explains the fast chemical reaction as a consequence of strong radiative charge transfer. A possible explanation is offered for the apparent contradiction between typical theoretical predictions and measurements of the radiative association process in this and other recent experiments.