Quantum non-Hermitian topological sensors

Koch, Florian; Budich, Jan Carl

doi:10.1103/physrevresearch.4.013113

Cited by 61 publications

(24 citation statements)

References 39 publications

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“…Optical systems, such as coupled waveguide arrays [35,83,84] and topolectric circuits [85,86] are also excellent candidate platforms. Our work naturally opens the door to the study of other sources of gain, such as parametric processes [87,88], with applications to the design of novel lattice amplifiers and sensors [51][52][53].…”

Section: Discussionmentioning

confidence: 96%

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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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Section: Discussionmentioning

confidence: 96%

“…with symmetries, multiple bands or higher dimensions, and to provide an ideal starting point for investigating NH topology in open quantum systems [47][48][49][50]. Finally, our framework is directly relevant for sensing applications in NH lattices [51][52][53] and for designing novel directional amplifiers [54][55][56][57].…”

Section: Introductionmentioning

confidence: 99%

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

Brunelli¹,

Wanjura²,

Nunnenkamp³

2022

Preprint

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“…Dynamical probes of the quantum Fisher information [44] and the application as NH topological sensors [43] provides intriguing questions for future investigation. Meanwhile, the current model reveals the Liouvillian skin effect in the relaxation process while poses the question on the search for steady states that inherit the exceptional topology of the non-Hermitian damping matrix.…”

Section: Boundary Sensitivitymentioning

confidence: 99%

“…Experiments displaying the novel NH bulk-boundary correspondence have so far been limited to classical systems including mechanical [39,40], electrical [41] and photonic [42] platforms. Moreover, the remarkable sensitivity to boundary conditions has recently been suggested to be harnessed in applications as NH topological sensors [37], and a quantum input-output theory of such systems has been developed [43,44]. 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].…”

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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“…However, whether real spectra exist in general non-Hermitian systems with no symmetry constraints remains elusive.Recently, nonreciprocal systems have inspired considerable research interest [36][37][38]. The energy spectra of such systems are very sensitive to the change of boundary conditions [39], which can be utilized to design new types of quantum sensors [40,41]. For systems with nonreciprocal hopping and under open boundary conditions (OBCs), the non-Hermitian skin effect (NHSE) will emerge with all the bulk states localized at the boundaries.…”

mentioning

confidence: 99%

Real Spectra and Phase Transition of Skin Effect in Nonreciprocal Systems

Zeng,

Lü

2022

Preprint

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We study the one-dimensional nonreciprocal lattices with real nearest neighboring hopping and find that the energy spectra under open boundary conditions can be entirely real or imaginary without imposing any symmetries. We further investigate the spectral properties and the non-Hermitian skin effect in the one-dimensional mosaic lattices with real nonreciprocal hopping introduced at equally spaced sites. The eigenenergies of such lattices undergo a real-complex-imaginary or realcomplex transition as the nonreciprocity varies. Moreover, the skin effect exhibits phase transitions depending on the period of the mosaic nonreciprocity. The bulk states are abruptly shifted from one end of the lattice to the opposite one by crossing the critical points, accompanied by the closing and reopening of point gaps in the spectra under periodic boundary conditions. The phase diagrams of the transition are presented and the critical boundaries are analytically determined. Our work unveils the intriguing properties of the energy spectrum and skin effect in non-Hermitian systems.The study on non-Hermitian systems has attracted much attention during the past few years [1-5]. Non-Hermiticity may appear due to the interactions between the systems and the external environment, which are commonly represented by physical gain and loss in the model Hamiltonian and can exist in both classical [6][7][8][9][10][11][12][13][14][15][16] and quantum systems [17][18][19][20][21][22][23][24][25][26]. The energy spectra of non-Hermitian systems are normally complex but can be entirely real when or pseudo-Hermiticity [30][31][32][33][34][35] is respected. The existence of real spectra ensures the stabilities of non-Hermitian systems, which facilitates their applications in various fields. However, whether real spectra exist in general non-Hermitian systems with no symmetry constraints remains elusive.Recently, nonreciprocal systems have inspired considerable research interest [36][37][38]. The energy spectra of such systems are very sensitive to the change of boundary conditions [39], which can be utilized to design new types of quantum sensors [40,41]. For systems with nonreciprocal hopping and under open boundary conditions (OBCs), the non-Hermitian skin effect (NHSE) will emerge with all the bulk states localized at the boundaries. The NHSE impacts a multitude of physical phenomena significantly [42][43][44][45][46][47][48][49][50][51][52][53][54], such as the bulk-boundary correspondence of topological phases [43,44,[55][56][57][58][59][60][61] and Anderson localization phenomenon [62][63][64][65][66][67][68]. Though the NHSE is found to be connected to the point gap in the spectra under periodic boundary conditions (PBCs) [69][70][71], how the behavior of NHSE is influenced by the variation of nonreciprocity is less studied.

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Quantum non-Hermitian topological sensors

Cited by 61 publications

References 39 publications

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

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

Liouvillian Skin Effect in an Exactly Solvable Model

Real Spectra and Phase Transition of Skin Effect in Nonreciprocal Systems

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