Browsing by Author "Lee, Tony E."

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    Anomalous Edge State in a Non-Hermitian Lattice
    (APS, 2016-04) Lee, Tony E.; Department of Physics, School of Science
    We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental realization with arrays of coupled resonator optical waveguides.
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    Floquet engineering from long-range to short-range interactions
    (APS, 2016-10) Lee, Tony E.; Department of Physics, School of Science
    Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and it is applicable to all experimental systems with long-range interactions: trapped ions, polar molecules, Rydberg atoms, nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a short-range interaction without relying on Hubbard superexchange.
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    Ion crystals in anharmonic traps
    (AIP, 2017-01) Bastin, S. R.; Lee, Tony E.; Department of Physics, School of Science
    There is currently intensive research into creating a large-scale quantum computer with trapped ions. It is well known that for a linear ion crystal in a harmonic potential, the ions near the center are more closely spaced compared to the ions near the ends. This is problematic as the number of ions increases. Here, we consider a linear ion crystal in an anharmonic potential that is purely quartic in position. We find that the ions are more evenly spaced compared to the harmonic case. We develop a variational approach to calculate the properties of the ground state. We also characterize the zigzag transition in an anharmonic potential.
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    PT -symmetric Rabi model: Perturbation theory
    (APS, 2015-10) Lee, Tony E.; Joglekar, Yogesh N.; Department of Physics, School of Science
    We study a non-Hermitian version of the Rabi model, where a two-level system is periodically driven with an imaginary-valued drive strength, leading to alternating gain and loss. In the Floquet picture, the model exhibits PT symmetry, which can be broken when the drive is sufficiently strong. We derive the boundaries of the PT phase diagram for the different resonances by doing perturbation theory beyond the rotating-wave approximation. For the main resonance, we show that the non-Hermitian analog of the Bloch-Siegert shift corresponds to maximal PT breaking. For the higher-order resonances, we capture the boundaries to lowest order. We also solve the regime of high frequency by mapping to the Wannier-Stark ladder. Our model can be experimentally realized in waveguides with spatially modulated loss or in atoms with time-modulated spontaneous decay.
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    PT-breaking threshold in spatially asymmetric Aubry-André and Harper models: Hidden symmetry and topological states
    (APS, 2016-06) Harter, Andrew K.; Lee, Tony E.; Joglekar, Yogesh N.; Department of Physics, School of Science
    Aubry-André-Harper lattice models, characterized by a reflection-asymmetric sinusoidally varying nearest-neighbor tunneling profile, are well known for their topological properties. We consider the fate of such models in the presence of balanced gain and loss potentials ±iγ located at reflection-symmetric sites. We predict that these models have a finite PT-breaking threshold only for specific locations of the gain-loss potential and uncover a hidden symmetry that is instrumental to the finite threshold strength. We also show that the topological edge states remain robust in the PT-symmetry-broken phase. Our predictions substantially broaden the possible experimental realizations of a PT-symmetric system.
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    String order via Floquet interactions in atomic systems
    (APS, 2016) Lee, Tony E.; Joglekar, Yogesh N.; Richerme, Philip; Department of Physics, School of Science
    We study the transverse-field Ising model with interactions that are modulated in time. In a rotating frame, the system is described by a time-independent Hamiltonian with many-body interactions, similar to the cluster Hamiltonians of measurement-based quantum computing. In one dimension, there is a three-body interaction, which leads to string order instead of conventional magnetic order. We show that the string order is robust to power-law interactions that decay with the cube of distance. In two and three dimensions, there are five- and seven-body interactions. We discuss adiabatic preparation of the ground state as well as experimental implementation with trapped ions, Rydberg atoms, and polar molecules.