$\mathcal {PT}$-symmetric optical superlattices

Longhi, Stefano

doi:10.1088/1751-8113/47/16/165302

Cited by 16 publications

(11 citation statements)

References 76 publications

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“…Numerical results show that a number of edge states can arise, either at the left or right boundaries, in a lattice with open boundary conditions and in the metallic phase, where w assumes the trivial value w = 0 (see Fig.S1 in [68]). The number of edge states sensitively depends on h. Since edge states correspond rather generally to eigenstates with complex energies, the PT symmetric phase is fragile in a system with open boundaries, as already noticed in previous works [51][52][53]. Finally, we note that, while the AAH and Nelson-Hatano Hamiltonians are related one another by a similarity transformation, the non-Hermitian skin effect observed in the latter model, i.e.…”

supporting

confidence: 69%

“…A few recent studies have considered some non-Hermitian extensions of the AAH model [51][52][53][54][55][56], mainly with a commensurate potential and with open boundary conditions. Such numerical studies investigated how gain and loss distributions affect edge states and parity-time (PT ) symmetry breaking [51][52][53]55], the Hofstadter butterfly spectrum [52], and the localization properties of eigenstates [54,56]. However, so far there is not any evidence of topological phases and topological phase transitions in non-Hermitian QCs.…”

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confidence: 99%

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Topological Phase Transition in non-Hermitian Quasicrystals

2019

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The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian models, such as failure of the conventional bulk-boundary correspondence and non-Hermitian skin effect. Advances in the understanding of the topological properties of non-Hermitian lattices with translational invariance have been reported in several recent studies, however little is known about non-Hermitian quasicrystals. Here we disclose topological phases in a quasicrystal with parity-time (PT ) symmetry, described by a non-Hermitian extension of the Aubry-André-Harper model. It is shown that the metal-insulating phase transition, observed at the PT symmetry breaking point, is of topological nature and can be expressed in terms of a winding number. A photonic realization of a non-Hermitian quasicrystal is also suggested.Introduction. The discovery of topological phases of matter has introduced a major twist in condensed matter physics [1, 2] with great impact in other areas of physics, such as photonics, atom optics, acoustics and mechanics [3][4][5][6][7][8]. Topological band theory classifies Hermitian topological systems depending on their dimensionality and symmetries [9, 10]. The bulk topological invariants are uniquely reflected in robust edge states localized at open boundaries. The ability to engineer non-Hermitian Hamiltonians, demonstrated in a series of recent experiments [11][12][13][14][15][16][17], and the related observation of unconventional topological boundary modes sparked a great interest to extend topological band theory to open systems . Striking features are the failure of the conventional bulk-boundary correspondence [27,31,35,[37][38][39], eigenstate condensation [30,31], non-Hermitian skin effect [33,37,38], and the sensitivity of the bulk spectra on boundary conditions [19,36,[39][40][41]. Most of previous studies have concerned with crystals, however little is know about topological properties of non-Hermitian quasicrystals. Quasicrystals (QCs) constitute an intermediate phase between fully periodic lattices and fully disordered media, showing a longrange order but no periodicity [42,43]. A paradigmatic model of a one-dimensional (1D) QC is provided by the Aubry-André-Harper (AAH) Hamiltonian [43][44][45], which is known to show a metal-insulator phase transition [44][45][46]. In the Hermitian case, the AAH Hamiltonian is topologically nontrivial because it can be mapped into a two-dimensional quantum Hall system on a square lattice [47][48][49][50]. A few recent studies have considered some non-Hermitian extensions of the AAH model [51][52][53][54][55][56], mainly with a commensurate potential and with open boundary conditions. Such numerical studies investigated how gain and loss distributions affect edge states and parity-time (PT ) symmetry breaking [51][52][53]55], the Hofstadter butterfly spectrum [52], and the localization properties of eig...

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confidence: 69%

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confidence: 99%

Topological Phase Transition in non-Hermitian Quasicrystals

2019

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“…Among references, effects of non-Hermiticity on AL have been studied in different contexts [63][64][65][66][67][68][69][70][71][72], but the discussion on the interplay of NHSEs and the AL with accompanying topological transitions is still lacking. Thus, natural questions arise: What is the fate of the NHSE and its topology in the presence of quasiperiodic potentials, whether there is a transition inherited from the well-known AL of the Hermitian AA model, and if yes, what is it like?…”

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confidence: 99%

Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices

et al. 2019

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Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a non-reciprocal quasiperiodic lattice, dubbed nonreciprocal Aubry-André model, and a rescaled transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a bulk-bulk correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.

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“…Both the coupled optical waveguides and microcavities were described by a tight-binding model. The tight-binding model demonstrated analytical and numerical tractability for study of the PT symmetry [31][32][33][34][35][36]. The PT -symmetric phase diagram, as well as the wave packet dynamics in PTsymmetric systems with open boundary conditions, have been investigated [37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Parity-time symmetry under magnetic flux

Jin

Song

2016

Phys. Rev. A

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We study a parity-time (PT ) symmetric ring lattice, with one pair of balanced gain and loss located at opposite positions. The system remains PT -symmetric when threaded by a magnetic flux; however, the PT symmetry is sensitive to the magnetic flux, in the presence of a large balanced gain and loss, or in a large system. We find a threshold gain/loss, above which, any nontrivial magnetic flux breaks the PT symmetry. We obtain the maximally tolerable magnetic flux for the exact PT -symmetric phase, which is approximately linearly dependent on a weak gain/loss.

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$\mathcal {PT}$-symmetric optical superlattices

Cited by 16 publications

References 76 publications

Topological Phase Transition in non-Hermitian Quasicrystals

Topological Phase Transition in non-Hermitian Quasicrystals

Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices

Parity-time symmetry under magnetic flux

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