Monopole-antimonopole instability in non-Hermitian coupled waveguides

Hayward, Rosie; Biancalana, Fabio

doi:10.1103/physreva.101.043846

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Underlying these effects are fundamental differences between Hermitian and non-Hermitian Hamiltonians; this includes that eigenstates can coalesce and become defective at exceptional points, that the left and right eigenfunctions will typically be different from each other, and that the eigenenergies can become complex [13,26]. One important consequence of these differences is that the Berry phase will, in general, become complex-instead of real-valued, implying that the amplitude as well as the phase of a state will vary under adiabatic dynam-ical evolution [4][5][6][7][28][29][30][31].…”

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confidence: 99%

“…3) are all purely imaginary, and they diverge as we approach the PT -symmetry breaking transition, where adiabaticity breaks down. (Analytical expressions of the Berry connections and associated Berry curvatures are derived in the Supplemental Material, and can be interpreted in terms of a complex hyperbolic pseudo-magnetic monopole in parameter space [11,31].) This in turn means that the only non-vanishing part of the non-Hermitian Berry phase (Eq.…”

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confidence: 99%

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Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

Singhal¹,

Martello²,

Agrawal³

et al. 2022

Preprint

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The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site PT -symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for non-cyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov-Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken PT symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards the further studies of non-Hermitian and topological physics in synthetic metamaterials.

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confidence: 99%

Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

Singhal¹,

Martello²,

Agrawal³

et al. 2022

Preprint

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“…In recent years, the concept of parity-time (PT ) symmetry has attracted extensive research interest in different systems [43][44][45][46][47][48][49][50][51][52][53]. Interestingly, Hamiltonians that are symmetric under the combined operation of parity and time reversal transformation (PT symmetric operators) can have a real spectrum even though the operators are non-Hermitian [54][55][56].…”

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confidence: 99%

Exceptional points and dynamics of a non-Hermitian two-level system without PT symmetry

Wang¹,

Wang²,

Shen³

et al. 2020

EPL

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In this work, taking the most general non-Hermitian Hamiltonian without paritytime (PT ) symmetry and with non-Hermitian off-diagonal elements into account, we study the exceptional points of the model system. We find that there exists an exceptional ellipse in theory, compared with the exceptional ring studied in non-Hermitian PT symmetry Hamiltonian, in which the parameters in the model Hamiltonian take particular values. We also report on the dynamics of the model Hamiltonian and PT symmetry Hamiltonian. We find that they display different dynamical behaviors under different parameters. Moreover, there exists an unstable behavior of the system. The unstable behavior has a surprising property by which the gain always dominates at long times no matter how small the gain is. This phenomenon enables the compensation for losses in dissipative systems and opens a wide range of applications in quantum optics, plasmonics, and optoelectronics, where the loss is inevitable but can be compensated by the gain.

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Measuring the adiabatic non-Hermitian Berry phase in feedback-coupled oscillators

Singhal,

Martello,

Agrawal

et al. 2023

Phys. Rev. Research

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Monopole-antimonopole instability in non-Hermitian coupled waveguides

Cited by 3 publications

References 25 publications

Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

Exceptional points and dynamics of a non-Hermitian two-level system without PT symmetry

Measuring the adiabatic non-Hermitian Berry phase in feedback-coupled oscillators

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