RESEARCH  
Quantum Simulation with Trapped Ions:My current research seeks to develop a wellcontrolled, scalable quantum simulator to understand the behavior of complex, twodimensional (2D) quantum spin systems. Such a tunable and reconfigurable apparatus will have the capability to address important open questions in quantum manybody physics that are intractable to numerical calculation and inaccessible to any current experimental system. The approach will encode effective quantum spins within the wellisolated internal states of trapped ions, will build upon the many recent advances in onedimensional trappedion quantum simulators, and will be directly scalable to more than 100 individuallycontrollable spins. Feynman was the first to point out that a new paradigm of computing was needed to gain complete insight into complex quantum systems. He argued that mapping the quantummechanical problem of interest onto a physical, wellcontrolled quantum system would eliminate the need for exponential resources, allowing such problems to be solved. These ideas were experimentally realized only a few years ago, with 23 trapped atomic ions used to perform a quantum simulation of a simple Ising spin system. Since then, trapped ions have been a leading platform for more advanced quantum simulation experiments, since their wellisolated environment enables highfidelity state preparation and detection, long quantum coherence times, and extraordinarily precise quantum measurements. In all cases, however, experiments have been restricted to onedimensional ion chains emulating onedimensional spin models.
By constructing a higherdimensional ion trap quantum simulator, one can begin to address many of the open questions in quantum manybody physics associated with geometric frustration, exotic phases of matter (such as spin glasses/liquids and manybody localized states), and the relationship between entanglement, frustration, and highTc superconductivity. For instance, changing the 2D lattice geometry (an offlimits concept in 1D) can give rise to contrasting, complex, and often poorly understood phases. It is well known that antiferromagnetic Ising spins on square lattices lead to simple Neelordered ground states, and that triangular and Kagome lattices exhibit geometric frustration, highly degenerate ground states, and massive entanglement entropy. Far less is known about the behavior of XY or Heisenberg spins on frustrated lattices, and whether their ground states display longrange Neel order, shortrange correlations, broken symmetries, or some combination of the above. Less still is known about longrange interacting spin models, for which the ground state of even a simple square lattice remains an open question. Understanding the full phase diagrams and ground state behavior for these various quantum spin systems is of strong and widespread interest, but has so far proven elusive to due the complexity of numerical calculations and the dearth of clean and controllable experimental test systems. Given these motivations, I am constructing a 2D trappedion quantum simulator that retains the traditional iontrap strengths of full control at the singleparticle level, siteresolved measurements and readout, and long coherence times. This wellcontrolled quantum system will serve as an experimental testbed for exploring many of the aforementioned questions at the center of quantum condensed matter physics. The examples given here are undoubtedly a small sampling of what is possible with such an apparatus; its reprogrammability and tunability make it adaptable for investigating nearly all types of ground state or dynamical properties of interacting quantum spin models. Postdoctoral Work:My postdoctoral research was in Chris Monroe's trapped ion quantum information group at the Joint Quantum Institute. Using a linear chain of 1020 ^{171}Yb^{+} ions confined in an RF Paul trap, we performed quantum simulations of the manybody physics found in interacting spin systems. A longterm goal of the project is to scale up the number of controlled spins to 30+, where calculating system properties or dynamical evolution becomes intractable using a classical computer. Longrange spinspin interactions between the ions are generated using phononmediated, spindependent laser forces. Statedependent fluorescence imaging of the ions onto a camera allows for readout of the individual spin states and access to all possible correlation functions. By varying laser frequencies or trap voltages, one can tune the range of spinspin interaction and the amount of frustration in the manybody spin system  something traditionally difficult (or impossible) to accomplish in a real material.
Using the trapped ion system, we have performed adiabatic quantum simulations to experimentally find the ground states of a longrange Ising model with a transverse magnetic field. The spins are prepared along the transverse magnetic field, which is initially large compared to the Ising couplings and slowly reduced during the simulation. We have designed and implemented protocols to optimize the speed of these quantum simulations while remaining locally adiabatic. We have additionally proposed a technique to determine the ground state of this Hamiltonian experimentally when the ramp is nonadiabatic, and have demonstrated its success in a system of 14 interacting spins. With our quantum simulator, we have also studied the ground state magnetic phases of a classical Ising model at zero temperature, in which phase transitions cannot be driven classically due to the absence of thermal fluctuations. Instead, we introduce controlled quantum fluctuations to drive the phase transitions, map their positions in the phase diagram, and create the multiple, classically inaccessible ground states at different longitudinal field strengths. More recently, we have started to probe the dynamics of our manybody system. We have developed a spectroscopic method to resolve the excited state energy levels of our Hamiltonian and to coherently engineer highly entangled states. The method allows us to directly determine the strengths of all spinspin couplings and verify that the experimentally implemented Hamiltonian closesly matches the Hamiltonian we wish to study. We expect such verification to be crucial as the system grows beyond 30+ spins, where classical computers will be unable to confirm the results of quantum simulators. In addition, we have performed experiments to study the growth and propagation of correlations in a quantum system evolving in a farfrom equilibrium state. These measurements probe the velocity with which quantum information can be transfered throughout a manybody system, which sets the minimum timescales for entanglement growth or thermalization between disparate parts of the chain. The longrange interactions are observed to give faster propagation velocities than in the shortrange case studied by Lieb and Robinson, indicating that the wealth of important theoretical proofs about thermalization, entanglement growth, and classical simulability can no longer be applied to the ion system.

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