Browsing by Author "Saxena, Avadh"

Now showing 1 - 3 of 3
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    Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks
    (Springer Nature, 2018-08-13) Harter, Andrew K.; Saxena, Avadh; Joglekar, Yogesh N.; Physics, School of Science
    Quantum walks often provide telling insights about the structure of the system on which they are performed. In PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today’s experimental systems.
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    Parity-time symmetric systems with memory
    (American Physical Society, 2021-02-11) Cochran, Zachary A.; Saxena, Avadh; Joglekar, Yogesh N.; Physics, School of Science
    Classical open systems with balanced gain and loss, i.e., parity-time (PT ) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of PT symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a PT symmetric (balanced gain and loss) system with memory and investigate its dynamics analytically and numerically. Our model consists of two coupled LC oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by PT symmetric or PT symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including a PT symmetry broken phase at vanishingly small dissipation strength. Our results indicate that PT symmetric systems with memory show a rich landscape.
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    Stability of 𝒫𝒯 and anti-𝒫𝒯-symmetric Hamiltonians with multiple harmonics
    (APS, 2024) Cen, Julia; Joglekar, Yogesh N.; Saxena, Avadh; Physics, School of Science
    Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time periodicity offers avenues to engineer the landscape of Floquet quasienergies across the complex plane. We investigate two-level non-Hermitian 𝒫𝒯 and anti-𝒫𝒯-symmetric Hamiltonians with coefficients that have multiple harmonics using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasienergies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany these cyclic changes with the biorthogonality approach. Our results demonstrate that these time-periodic Hamiltonians generate a rich landscape of stable (real) and unstable (complex) regions.