Anisotropy-Induced Feshbach Resonances in a Quantum Dipolar Gas of Highly Magnetic Atoms

We explore the anisotropic nature of Feshbach resonances in the collision between ultracold highly magnetic submerged-shell dysprosium atoms in their energetically lowest magnetic sublevel, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where broadest (strongest) Feshbach resonances are hyperfine induced and due to rotationless bound states. Our first-principle coupled-channel calculation of the collisions between these spin-polarized bosonic dysprosium atoms reveals a strong interplay between the anisotropies in the dispersion and magnetic dipole-dipole interaction. The former 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 quadrupole-quadrupole interaction are small. Over a 20 mT magnetic field range, we predict about 10 Feshbach resonances and show that the resonance locations depend on the dysprosium isotope.

Figure 1

Potential energy curves for ${}^{164}\mathrm{Dy}+{}^{164}\mathrm{Dy}$ collisions in a magnetic field $B$ as a function of internuclear separation. The (red) dashed line with zero energy indicates the energy of the entrance channel. A resonance occurs when a bound state energy equals the entrance-channel energy. The graph shows the 91 diagonal potential matrix elements at $B=50\mathrm{G}$ for channels $|(j_1{j}_2)j{m}_j,\ell m_{\ell }⟩$ with $m_j+m_{\ell }=-16$ and even $\ell \le 10$. The curves are colored by their $m_j$ value. The $\ell$ value for $m_j=-16$ curves is indicated. Here $1\mathrm{G}=0.1\mathrm{mT}$, $a_0=0.0529177$ nm is the Bohr radius, and $k=1.38065\times {10}^{-23}\mathrm{J}/\mathrm{K}$ is the Boltzmann constant.

Figure 2

Scattering length of $m=-8$ ${}^{164}\mathrm{Dy}$ atoms as a function of magnetic field with and without the magnetic dipole-dipole or the anisotropic contribution of the dispersion interaction. We use a collision energy of $E/k=30\mathrm{nK}$. Channels with even partial waves $\ell$ up to 10 are included. The top panel shows the case when all interactions are included. At $B=0$ the scattering length is $89a_0$. For the three broad resonances the first partial wave for which the resonance appears is shown. The middle and bottom panels are obtained when the dispersion and magnetic dipole-dipole anisotropy is set to zero, respectively.

Figure 3

Scattering length as a function of magnetic field for the bosonic isotopes ${}^{162}\mathrm{Dy}$ (top panel) and ${}^{160}\mathrm{Dy}$ (bottom panel). The initial state and number of included $\ell$ as in Fig. 2.