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arXiv:0704.3056 · Physical Review Letters

Effective Spin Systems in Coupled Microcavities

Michael J. Hartmann, Fernando G. S. L. Brandão, Martin Bodo Plenio

Published Oct 15, 2007• 166 citations
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Abstract

We show that atoms trapped in microcavities that interact via the exchange of virtual photons can model an anisotropic Heisenberg spin-1/2 lattice in an external magnetic field. All parameters of the effective Hamiltonian can individually be tuned via external lasers. Since the occupations of excited atomic levels and photonic states are strongly suppressed, the effective model is robust against decoherence mechanisms, has a long lifetime, and its implementation is feasible with current experimental technology. The model provides a feasible way to create cluster states in these devices.

DOI
10.1103/physrevlett.99.160501

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We show that atoms trapped in microcavities that interact via the exchange of virtual photons can model an anisotropic Heisenberg spin-1/2 lattice in an external magnetic field. All parameters of the effective Hamiltonian can individually be tuned via external lasers. Since the occupations of excited atomic levels and photonic states are strongly suppressed, the effective model is robust against decoherence mechanisms, has a long lifetime, and its implementation is feasible with current experimental technology. The model provides a feasible way to create cluster states in these devices.
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We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in 2d2d2d steps where ddd is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states.
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We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently nonlinear, and occurs via multiphoton processes like Raman scattering and two-photon absorption and emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model.