Correspondence between Non-Hermitian Topology and Directional Amplification in the Presence of Disorder

Wanjura, Clara C.; Brunelli, Matteo; Nunnenkamp, Andreas

doi:10.1103/physrevlett.127.213601

Cited by 43 publications

(18 citation statements)

References 48 publications

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“…As stated in Ref. [75], even on the single-particle level there are many natural generalizations to, e.g., other NH band topology [31,34,35,40,127] and exceptional structures [37-39, 128, 129], and to systems with disorder [130], which are ubiquitous in real experiments. One may also consider how the bath-mediated interaction between the emitters, which is already nontrivial for atomic arrays in the vacuum [10,[131][132][133], could be enriched by introducing "unnatural" non-Hermiticity.…”

Section: Discussionmentioning

confidence: 99%

Bound states and photon emission in non-Hermitian nanophotonics

Gong¹,

Bello²,

Malz³

et al. 2022

Preprint

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We establish a general framework for studying the bound states and the photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In the singleexcitation sector, the system can be described exactly by a non-Hermitian formalism. We have pointed out in the accompanying letter [Gong et al., arXiv:2205.05479] that a single emitter coupled to a one-dimensional non-Hermitian lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we provide further detail on these observations. We also present several additional examples on the cases with multiple quantum emitters or in higher dimensions. Our work unveils the tip of the iceberg of the rich non-Hermitian phenomena in dissipative nanophotonic systems.

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Section: Discussionmentioning

confidence: 99%

Bound states and photon emission in non-Hermitian nanophotonics

Gong¹,

Bello²,

Malz³

et al. 2022

Preprint

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show abstract

“…These are illustrated in Fig. 1 in terms of the simplest non-trivial model covered by our framework, namely an unconditional implementation of the NH Hatano-Nelson model in an array of coupled cavities [28,58]. As shown in Sec.…”

Section: Summary Of the Main Resultsmentioning

confidence: 99%

“…, N . As long as the inner bound imposed on the PBC spectrum by this maximally disordered configuration does not cross the origin, robustness is guaranteed [58]. On the other hand, when Eq.…”

Section: Robustness Against Disordermentioning

confidence: 99%

Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification

Brunelli¹,

Wanjura²,

Nunnenkamp³

2022

Preprint

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Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and extreme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary correspondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and without symmetries. We obtain the desired NH Hamiltonian from the (mean-field) unconditional evolution of driven-dissipative cavity arrays, in which NH terms-in the form of non-reciprocal hopping amplitudes, gain and loss-are explicitly modelled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the definition of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamiltonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value ν of the topological invariant defined in the bulk corresponds to |ν| singular vectors exponentially localized at the system edge under open boundary conditions, in which the sign of ν determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.

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“…A fully consistent quantum mechanical description in terms of Lindbland master equations [45] appropriate for Markovian dissipative systems [46][47][48][49][50][51] has earlier been studied and fruitfully employed in the context of preparing or stabilizing Hermitian topological phases [52][53][54][55][56]. Recent pioneering work has highlighted that also in such fully quantum mechanically consistent description the sensitivity to boundary conditions remains [57][58][59][60][61][62][63][64], but it is fair to say that a comprehensive understanding is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Liouvillian Skin Effect in an Exactly Solvable Model

Yang,

Jiang,

Bergholtz

2022

Preprint

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The interplay between dissipation, topology and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open and periodic boundary conditions. We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution of the density matrix giving rise to a Liouvillian Skin Effect. This leads to several intriguing phenomena including boundary sensitive damping behavior, steady state currents in finite periodic systems, and diverging relaxation times in the limit of large systems. We illuminate how the role of topology in these systems differ in the effective non-Hermitian Hamiltonian limit and the full master equation framework.

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Correspondence between Non-Hermitian Topology and Directional Amplification in the Presence of Disorder

Cited by 43 publications

References 48 publications

Bound states and photon emission in non-Hermitian nanophotonics

Bound states and photon emission in non-Hermitian nanophotonics

Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification

Liouvillian Skin Effect in an Exactly Solvable Model

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