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arXiv:1212.5328 · Physical Review A

Quantum simulation of Heisenberg spin chains with next-nearest-neighbor interactions in coupled cavities

Zhixin Chen, Zheng-Wei Zhou, Xingxiang Zhou, Xiang-Fa Zhou, Guang‐Can Guo

Published Feb 5, 2010• 44 citations
arXivHTMLPDF

Abstract

We propose a scheme to simulate one-dimensional $\mathit{XXZ}$-type Heisenberg spin models with competing interactions between nearest neighbors (NNs) and next NNs in photon-coupled microcavities. Our scheme exploits the rich resources and flexible controls available in such a system to realize arbitrarily adjustable ratios between the effective NN and next-NN coupling strengths. Such a powerful capability allows us to simulate frustration phenomena and disorder behaviors in one-dimensional systems arising from next-NN interactions, a large class of problems of great importance in condensed-matter physics. Our scheme is robust due to the lack of atomic excitations, which suppresses spontaneous emission and cavity decay strongly.

DOI
10.1103/physreva.81.022303

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We propose a scheme to simulate one-dimensional XXZ\mathit{XXZ}XXZ-type Heisenberg spin models with competing interactions between nearest neighbors (NNs) and next NNs in photon-coupled microcavities. Our scheme exploits the rich resources and flexible controls available in such a system to realize arbitrarily adjustable ratios between the effective NN and next-NN coupling strengths. Such a powerful capability allows us to simulate frustration phenomena and disorder behaviors in one-dimensional systems arising from next-NN interactions, a large class of problems of great importance in condensed-matter physics. Our scheme is robust due to the lack of atomic excitations, which suppresses spontaneous emission and cavity decay strongly.
We propose a scheme to realize the Heisenberg spin chain in a one-dimensional array of cavities connected by optical fibers. The proposed scheme is based on the off-resonant Raman transitions between two ground states of atoms, and is induced by the cavity modes and external fields. Under the interactions between the nearest neighbors (NNs) and the next NNs, the result shows that the atoms, via the exchange of virtual photons, can be effectively equal to a spin-1/2 Heisenberg model under certain conditions. The parameters of the effective Hamiltonian can be controlled by tuning the laser fields.
We present design techniques for special optical lattices that allow quantum simulation of spin frustration in two-dimensional systems. By carefully overlaying optical lattices with different periods and orientations we are able to adjust the ratio between the nearest-neighbor and next-nearest-neighbor interaction strengths in a square spin lattice and realize frustration effects. We show that only laser beams of a single frequency are required and the parameter space reachable in our design is broad enough to study the important phases in the J1{J}_{1}J1​-J2{J}_{2}J2​ frustrated Heisenberg model and checkerboard antiferromagnet model. By using the polarization spectroscopy for detection, distinct quantum phases and quantum phase transition points can be characterized straightforwardly. Our design thus offers a suitable setup for simulation of frustrated spin systems.
Simulating photonic lattices remains to be an interesting and important goal for quantum technologies. Here, we propose several simulation schemes of one- and quasi-one-dimensional photonic lattices based on arrays of diverse three-level giant-atom dimers. The resulting models, including diamond, Su-Schrieffer-Heeger, and ladder lattices, exhibit protected nearest-neighbor and greatly inhibited next-nearest-neighbor interactions, which are challenging with most state-of-the-art experimental platforms. Our proposals based on circuit quantum electrodynamics are tunable, scalable, and reconfigurable, thus providing opportunities for simulating more advanced photonic lattices and exploring unprecedented phenomena with no counterparts in conventional condensed matter physics.
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In an array of coupled cavities where the cavities are doped with an atomic V -system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing phenomena in condensed matter physics, such as the spin-(1/2) Ising, XX , Heisenberg, and XXZ models. The ability to construct networks of arbitrary geometry also allows for the simulation of topological effects. By tuning the number of excitations present, the dimension of the spin to be simulated can be controlled, and mixtures of different spin types produced. The facility of single-site addressing, the use of only the natural hopping photon dynamics without external fields, and the recent experimental advances towards strong coupling, makes the prospect of using these arrays as efficient quantum simulators promising.
The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.