Generalized Berry phase for a bosonic Bogoliubov system with exceptional points

Ohashi, Terumichi; Kobayashi, Shingo; Kawaguchi, Yuki

doi:10.1103/physreva.101.013625

Cited by 24 publications

(9 citation statements)

References 158 publications

(220 reference statements)

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“…The concept of rotation-time symmetry was previously introduced only in fermionic systems 43 – 45 . However, bosonic systems are currently a topic of intense research 24 , 39 , 46 – 52 due to being a promising platform for gain and loss engineering in physical experiments 3 . We demonstrate that invariance allows a given system to have a real energy spectrum, which becomes singular, as a result of a symmetry phase transition.…”

Section: Introductionmentioning

confidence: 99%

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

Lange

Chimczak

Kowalewska-Kudłaszyk

et al. 2020

Sci Rep

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We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ($${{\mathscr{PT}}}$$ PT ) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time ($${\mathscr{RT}}$$ RT ) symmetry. We observe that $${\mathscr{RT}}$$ RT -symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing $${\mathscr{RT}}$$ RT -symmetric Hamiltonians. We believe that our results on the $${\mathscr{RT}}$$ RT -symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the $${{\mathscr{PT}}}$$ PT -symmetric systems.

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Section: Introductionmentioning

confidence: 99%

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

Lange

Chimczak

Kowalewska-Kudłaszyk

et al. 2020

Sci Rep

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“…The presence of positive imaginary parts in the spectrum indicates parametric amplification and the subsequent dynamical instability [815,816]. Such a non-Hermitian aspect of Bogoliubov excitations has recently been revisited in the context of band topology [817]. Lattice models that demonstrate the same essential physics, such as the bosonic Kitaev chain [818], have been proposed to be realizable in optomechanical arrays and superconducting circuits subject to parametric drivings [819].…”

Section: Quadratic Problemsmentioning

confidence: 99%

Non-Hermitian Physics

Ashida,

Gong,

Ueda

2020

Preprint

129

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A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

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“…Other symmetries, such as chiral-time (CT ) and charge-parity (CP) symmetries, have been investigated [24,41,48,83,84]. The topological aspects of non-Hermitian systems, including edge modes [84,85], topological invariant [63,[86][87][88][89][90][91][92], band theory [92][93][94][95], topological pumping [56,59,[96][97][98], classification [99][100][101][102][103][104][105], high-order non-Hermitian topological systems [106][107][108][109][110][111], * jinliang@nankai.edu.cn semimetals [112][113][114][115][116][117], and symmetry-protected topological phases and localized states have been investigated [90,[118][119][120]…”

Section: Introductionmentioning

confidence: 99%

Inversion symmetric non-Hermitian Chern insulator

Jin

Song

2019

Phys. Rev. B

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We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial phase. The band touching points are isolated and protected by the symmetry. The band touching affects the existence of helical edge states. Moreover, topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction. The detaching points between the edge states and the bulk states are predicted by the winding number associated with the vector field of average values of Pauli matrices. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.

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Generalized Berry phase for a bosonic Bogoliubov system with exceptional points

Cited by 24 publications

References 158 publications

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

Non-Hermitian Physics

Inversion symmetric non-Hermitian Chern insulator

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