Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement

TL;DR

This paper reveals a connection between boson-mediated XY and Ising spin models, showing how off-resonant driving can realize XY interactions and analyzing the resulting spin-boson entanglement and effective fields.

Contribution

It demonstrates that XY models can be realized via off-resonant bosonic excitation, linking them to Ising models with transverse fields, and analyzes the emergent dynamics and entanglement.

Findings

Effective XY Hamiltonian matches Ising scheme in rotating frames

Transverse field depends on boson thermal energy

Spin-boson entanglement persists over time

Abstract

The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an XY model by off-resonant driving of single sideband of boson excitation (i.e.~a single-beam M{\o}lmer-S{\o}rensen scheme) and a boson-mediated Ising simulator in the presence of a transverse field. In particular, we show that these two schemes have the same effective Hamiltonian in suitably defined rotating frames, and analyze the emergent effective XY spin model through truncated Magnus series and numerical simulations. In addition to XY spin-spin interactions that can be non-perturbatively renormalized from the naive Ising spin-spin coupling constants, we find an effective transverse field that is dependent on the thermal energy of the bosons, as well as other spin-boson couplings that cause spin-boson entanglement not to vanish at any time. In the case of a boson-mediated Ising simulator with transverse field, we discuss the crossover from transverse-field Ising-like to XY-like spin behavior as a function of field strength.