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

Michael L. Wall, Arghavan Safavi-Naini, and Ana Maria Rey
Phys. Rev. A 95, 013602 – Published 3 January 2017

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 a single sideband of boson excitation (i.e., a single-beam Mølmer-Sørensen 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 a truncated Magnus series and numerical simulations. In addition to XY spin-spin interactions that can be nonperturbatively 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.

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  • Received 31 October 2016

DOI:https://doi.org/10.1103/PhysRevA.95.013602

©2017 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Michael L. Wall*, Arghavan Safavi-Naini, and Ana Maria Rey

  • JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA

  • *Present address: The Johns Hopkins Applied Physics Laboratory, Laurel, Maryland 20723, USA; mwall.physics@gmail.com

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Issue

Vol. 95, Iss. 1 — January 2017

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