Ultracold rare-earth magnetic atoms with an electric dipole moment

We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm$^{-1}$ with electronic angular momentum $J=10$, and at 17514.50 cm$^{-1}$ with $J=9$, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, we predict a magnetic dipole moment up to 13 Bohr magnetons, and an electric dipole moment up to 0.22 Debye, which is similar to the values obtained for alkali-metal diatomics. When a magnetic field is present, we show that the electric dipole moment is strongly dependent on the angle between the fields. The lifetime of the field-mixed levels is found in the millisecond range, thus allowing for suitable experimental detection and manipulation.