Anisotropy induced Feshbach resonances in a quantum dipolar gas of magnetic atoms Alexander Petrov, 1 Eite Tiesinga, 2 and Svetlana Kotochigova 1, ∗ 1 Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 and National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA † 2 Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA We explore the anisotropic nature of Feshbach resonances in the collision between ultracold mag- netic 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 reso- nances are hyperfine induced and due to rotation-less bound states. Our novel first-principle coupled- channel calculation of the collisions between open-4f-shell spin-polarized bosonic dysprosium reveals a striking correlation between the anisotropy due to magnetic dipole-dipole and electrostatic in- teractions and the Feshbach spectrum as a function of an external magnetic field. Over a 20 mT magnetic field range we predict about a dozen Feshbach resonances and show that the resonance locations are exquisitely sensitive to the dysprosium isotope. PACS numbers: 03.65.Nk, 31.10.+z, 34.50.-s 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 super- solids [1, 2]. Recent experimental advances [3–10] in trap- ping and cooling magnetic atoms pave the way towards these goals. In general, interactions between magnetic atoms are orientationally dependent or anisotropic. At room tem- perature anisotropic interactions are much smaller than kinetic energies and other major interactions between atoms, therefore can be ignored. The situation is differ- ent for an ultracold gas of atoms with a large magnetic moment. It was, for example, demonstrated that the anisotropy due to magnetic dipole-dipole interactions be- tween 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 mo- ments [5–7, 12–15]. In this Letter we pursue ideas for using anisotropic magnetic and dispersion interactions to control collisions of ultracold magnetic atoms by using Feshbach reso- nances [16]. Resonances, shown schematically in Fig. 1, appear when the energy of “embedded” bound states cross the energy of the entrance channel or initial scat- tering state. The embedded state is a level of a potential dissociating to a closed channel whose asymptotic energy is larger than that of the entrance channel. Coupling with the entrance channel leads to a resonance. Feshbach resonances make it possible to convert a weakly interacting gas of atoms into one that is strongly interacting and along the way promise to make avail- able many of the collective many-body states mentioned above. Alternatively, interactions can be turned off all together to create an ideal Fermi or Bose gas, for which thermodynamic properties are known analytically. Fes- hbach resonances can also be used to create BECs of weakly-bound molecules [17], which can be optically sta- bilized to deeply-bound molecules [18]. For fermionic atoms the BCS-BEC phase transition [19] and univer- sal many-body behavior of strongly interacting magnetic atoms can be studied via Feshbach resonances. Finally, three-body Efimov physics [20] can be explored. 100 200 300 R (units of a 0 ) -5 0 5 10 15 20 25 V/k (mK) B -16 -15 -14 -13 -12 -11 m J l=0 4 6 8 10 2 FIG. 1: (Color online) Potential energy curves for a 164 Dy+ 164 Dy collision in an external magnetic field B as a function of internuclear separation. The (red) dashed line with zero energy indicates the energy of the entrance chan- nel. Two Feshbach resonances are schematically shown by (red) horizontal lines, which end at the classical outer turn- ing point of a closed channel. Their energy increases, in- dicated by arrows, with magnetic field and a resonance oc- curs when this energy equals the entrance-channel energy. There are 91 diagonal potential matrix elements for chan- nels |(j1j2)jmj , ℓm ℓ 〉 with mj + m ℓ = −16 and even ℓ ≤ 10. We use B = 50 G. The curves are colored by their mj value, while for mj = −16 curves their ℓ value is indicated. Here 1 G=0.1 mT, a0 =0.0529177 nm is the Bohr radius, and k =1.38065 · 10 -23 J/K is the Boltzmann constant. arXiv:1203.4172v1 [physics.atom-ph] 19 Mar 2012