Cavity-quantum-electrodynamical toolbox for quantum magnetism

TL;DR

This paper proposes a versatile quantum simulation platform using cavity QED with ultracold atoms to realize and control various long-range quantum spin Hamiltonians, enabling exploration of complex magnetic orders.

Contribution

It introduces a generic scheme for implementing diverse long-range spin interactions in a cavity QED system, including Heisenberg and Dzyaloshinskii-Moriya types, with tunable parameters.

Findings

Achiral domain-wall antiferromagnetic order observed

Chiral spin-spiral order demonstrated

Phase transition controlled by mirror reflectivity

Abstract

The recent experimental observation of spinor self-ordering of ultracold atoms in optical resonators has set the stage for the exploration of emergent magnetic orders in quantum-gas--cavity systems. Based on this platform, we introduce a generic scheme for the implementation of long-range quantum spin Hamiltonians composed of various types of couplings, including Heisenberg and Dzyaloshinskii-Moriya interactions. Our model is comprised of an effective two-component Bose-Einstein condensate, driven by two classical pump lasers and coupled to a single dynamic mode of a linear cavity in a double $\Lambda$ scheme. Cavity photons mediate the long-range spin-spin interactions with spatially modulated coupling coefficients, where the latter ones can be tuned by modifying spatial profiles of the pump lasers. As experimentally relevant examples, we demonstrate that by properly choosing the spatial profiles of the pump lasers achiral domain-wall antiferromagnetic and chiral spin-spiral orders emerge beyond critical laser strengths. The transition between these two phases can be observed in a single experimental setup by tuning the reflectivity of a mirror. We also discuss extensions of our scheme for the implementation of other classes of spin Hamiltonians.