Frustration and glassiness in spin models with cavity-mediated interactions

TL;DR

This paper demonstrates that cavity-mediated interactions among three-level atoms can induce disordered, frustrated spin systems and spin glass phases, with unique quantum dynamics akin to a disordered Bose-Hubbard model, suggesting new experimental avenues.

Contribution

It introduces a novel mechanism for realizing disordered and frustrated spin systems using cavity-mediated interactions in atomic ensembles.

Findings

Cavity-mediated interactions are long-ranged and sign-changing, similar to RKKY interactions.

Disordered and frustrated spin systems, including spin glasses, can be realized with many cavity modes.

Quantum dynamics resemble a disordered Bose-Hubbard model exhibiting a random-singlet glass phase.

Abstract

We show that the effective spin-spin interaction between three-level atoms confined in a multimode optical cavity is long-ranged and sign-changing, like the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in positional randomness can realize spin systems having disordered and frustrated interactions. We argue that, whenever the atoms couple to sufficiently many cavity modes, the cavity-mediated interactions give rise to a spin glass. In addition, we show that the quantum dynamics of cavity-confined spin systems is that of a Bose-Hubbard model with strongly disordered hopping but no on-site disorder; this model exhibits a random-singlet glass phase, absent in conventional optical-lattice realizations. We briefly discuss experimental signatures of the realizable phases.