Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.

%8 12/17/2019 %G eng %U https://arxiv.org/abs/1912.07845 %0 Journal Article %J New Journal of Physics %D 2013 %T Prethermalization and dynamical transition in an isolated trapped ion spin chain %A Zhe-Xuan Gong %A L. -M. Duan %X We propose an experimental scheme to observe prethermalization and dynamical transition in one-dimensional XY spin chain with long range interaction and inhomogeneous lattice spacing, which can be readily implemented with the recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at intermediate time scale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is explained by spotting a non-trivial structure in lower half of the energy spectrum. The dynamical behavior of the system is shown to cross difference phases when the interaction range is continuously tuned, indicating the existence of dynamical phase transition. %B New Journal of Physics %V 15 %P 113051 %8 2013/11/26 %G eng %U http://arxiv.org/abs/1305.0985v1 %N 11 %! New J. Phys. %R 10.1088/1367-2630/15/11/113051 %0 Journal Article %J Physical Review A %D 2013 %T Quantum Logic between Remote Quantum Registers %A Norman Y. Yao %A Zhe-Xuan Gong %A Chris R. Laumann %A Steven D. Bennett %A L. -M. Duan %A Mikhail D. Lukin %A Liang Jiang %A Alexey V. Gorshkov %X We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. %B Physical Review A %V 87 %8 2013/2/6 %G eng %U http://arxiv.org/abs/1206.0014v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.87.022306 %0 Journal Article %D 2012 %T Reply to Comment on "Space-Time Crystals of Trapped Ions %A Tongcang Li %A Zhe-Xuan Gong %A Zhang-qi Yin %A H. T. Quan %A Xiaobo Yin %A Peng Zhang %A L. -M. Duan %A Xiang Zhang %X This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)). %8 2012/10/15 %G eng %U http://arxiv.org/abs/1212.6959v2 %R http://dx.doi.org/10.1103/PhysRevLett.109.163001 %0 Journal Article %D 2011 %T Comment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" %A Zhe-Xuan Gong %A L. -M. Duan %X Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment. %8 2011/09/22 %G eng %U http://arxiv.org/abs/1109.4696v1 %0 Journal Article %J New Journal of Physics %D 2011 %T Dynamics of Overhauser Field under nuclear spin diffusion in a quantum dot %A Zhe-Xuan Gong %A Zhang-qi Yin %A L. -M. Duan %X The coherence of electron spin can be significantly enhanced by locking the Overhauser field from nuclear spins using the nuclear spin preparation. We propose a theoretical model to calculate the long time dynamics of the Overhauser field under intrinsic nuclear spin diffusion in a quantum dot. We obtain a simplified diffusion equation that can be numerically solved and show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flop affect the nuclear spin diffusion. The results explain several recent experimental observations, where the decay time of Overhauser field is measured under different configurations, including variation of the external magnetic field, the electron spin configuration in a double dot, and the initial nuclear spin polarization rate. %B New Journal of Physics %V 13 %P 033036 %8 2011/03/25 %G eng %U http://arxiv.org/abs/0912.4322v1 %N 3 %! New J. Phys. %R 10.1088/1367-2630/13/3/033036 %0 Journal Article %J Physical Review Letters %D 2011 %T Robust Quantum State Transfer in Random Unpolarized Spin Chains %A Norman Y. Yao %A Liang Jiang %A Alexey V. Gorshkov %A Zhe-Xuan Gong %A Alex Zhai %A L. -M. Duan %A Mikhail D. Lukin %X We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. %B Physical Review Letters %V 106 %8 2011/1/27 %G eng %U http://arxiv.org/abs/1011.2762v2 %N 4 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.106.040505 %0 Journal Article %J Physical Review Letters %D 2010 %T Temperature driven structural phase transition for trapped ions and its experimental detection %A Zhe-Xuan Gong %A G. -D. Lin %A L. -M. Duan %X A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. %B Physical Review Letters %V 105 %8 2010/12/29 %G eng %U http://arxiv.org/abs/1009.0089v1 %N 26 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.265703