Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo${}_x$Y${}_{1-x}$F${}_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases.

Figure 1

(a) Dysprosium atoms are optically pumped into the $M_J=-8$ component of the ground ${}^5{I}_8$ electronic state, using ${\sigma }_{-}$-polarized 626 nm excitation to the ${(8,1)}_9^o$ state. (b) The ground $J=8$ level is split into nine $|M_J|$ components with a $\pi$-polarized light far detuned from the 626 nm transition. A multiphoton transverse field $\Omega$ connects the effective spin states, $M_J=-8$ and $M_J=+8$, without populating any intermediate levels.

Figure 2

(a) Interaction of a test spin with a single dipolar spin, indicating ferromagnetic (FM) and antiferromagnetic (AFM) regions. (b) Interaction of a test spin with two dipolar spins. Shaded regions indicate where the interaction is frustrated.

Figure 3

Phase diagram of the system as a function of spin concentration $x$, featuring paramagnetic (PM), ferromagnetic (FM), spin-glass (SG), and a possible antiglass (AG) phases; see Refs. 2 and 7.