<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">PT</mml:mi></mml:mrow></mml:math>optical lattices and universality in beam dynamics

Mei, Zhigang; Christodoulides, Demetrios N.; Fleischmann, Ragnar; Kottos, Tsampikos

doi:10.1103/physreva.82.010103

Cited by 233 publications

(232 citation statements)

References 29 publications

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“…Unbroken PT -symmetry, that is, a purely real eigenvalue spectrum, can be achieved only in lattices with d a ¼ d b and an inhomogeneous inter-site coupling 25,26 .…”

Section: Resultsmentioning

confidence: 99%

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

et al. 2013

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Within all physical disciplines, it is accepted that wave transport is predetermined by the existence of disorder. In this vein, it is known that ballistic transport is possible only when a structure is ordered, and that disorder is crucial for diffusion or (Anderson-)localization to occur. As this commonly accepted picture is based on the very foundations of quantum mechanics where Hermiticity of the Hamiltonian is naturally assumed, the question arises whether these concepts of transport hold true within the more general context of nonHermitian systems. Here we demonstrate theoretically and experimentally that in ordered time-independent PT -symmetric systems, which are symmetric under space-time reflection, wave transport can undergo a sudden change from ballistic to diffusive after a specific point in time. This transition as well as the diffusive transport in general is impossible in Hermitian systems in the absence of disorder. In contrast, we find that this transition depends only on the degree of dissipation.

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“…Unbroken PT -symmetry, that is, a purely real eigenvalue spectrum, can be achieved only in lattices with d a ¼ d b and an inhomogeneous inter-site coupling 25,26 .…”

Section: Resultsmentioning

confidence: 99%

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

et al. 2013

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“…In addition, Eqs. (7,8) lead to phase relationships among the reflection and transmission coefficients:…”

Section: Generalized Unitarity Relationsmentioning

confidence: 99%

“…[4,5] and were shown to exhibit a variety of exotic photon transport phenomena, such as double refraction [5], power oscillations [5][6][7], and non-monotonic behavior of the transmission loss with increased dissipation [8]. The initial studies focused on parallel waveguide structures with alternating loss and gain, in which the transverse variation of the electrical field, in the paraxial approximation to the wave equation, maps precisely onto a 1D or discrete Schrodinger equation, similar to the earlier quantum studies [4][5][6][7][8][9]. The parallel waveguide realization of PT symmetric photonic structures has recently found a promising application to compact optical isolators and circulators [10].…”

Section: Introductionmentioning

confidence: 99%

Conservation relations and anisotropic transmission resonances in one-dimensionalPT-symmetric photonic heterostructures

2012

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We analyze the optical properties of one-dimensional (1D) PT -symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT -symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT -symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT -symmetry and of PT -symmetry breaking transitions. The uniqueness of PT -symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

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“…While, in the Schrödinger context, numerous studies have addressed the large and infinite number of nodes limit [17][18][19], this is far less so the case in the context of oscillators where this analysis is really at a nascent stage. In such lattice contexts, it would be of particular interest to consider genuine breather-type solutions in the form of exponentially localized in space and periodic in time orbits.…”

Section: Conclusion and Future Challengesmentioning

confidence: 99%

“…However, one of the major milestones (and a principal thrust of recent activity) regarding the physical and experimental realizability of the corresponding Hamiltonians stemmed from progress in optics both at the theoretical [4,5] and at the experimental [6,7] levels. In particular, the realization that, in optics, the ubiquitous loss can be counteracted by an overwhelming gain in order to create a PT -symmetric setup, e.g., in a waveguide dimer [7], paved the way for numerous developments, especially so at the level of nonlinear systems, as several researchers studied nonlinear stationary states, stability, and dynamics of few site configurations [8][9][10][11][12][13][14][15][16] as well as of infinite lattices [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

PT-symmetric dimer of coupled nonlinear oscillators

Khare

2015

Pramana - J Phys

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We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and antisymmetric breather solutions, as well as symmetry-breaking variants thereof. We propose a reduction of the system to a Schrödinger-type PT -symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.

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PToptical lattices and universality in beam dynamics

Cited by 233 publications

References 29 publications

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

Conservation relations and anisotropic transmission resonances in one-dimensionalPT-symmetric photonic heterostructures

PT-symmetric dimer of coupled nonlinear oscillators

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