Modeling displaced squeezed number states in waveguide arrays

Villegas-Martínez, B. M.; Moya‐Cessa, H.; Soto‐Eguibar, Francisco

doi:10.1016/j.physa.2022.128265

Cited by 2 publications

(1 citation statement)

References 52 publications

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“…In such optical devices the discrete diffraction can be controlled by manipulating the properties of the array [2][3][4]. Also, waveguide arrays have served to study and simulate a big number of both classical and quantum phenomena like quantum walks [5], coherent and squeezed states [6][7][8][9], Talbot effect [10,11], among others [12][13][14], in both the relativistic and non-relativistic [?, 15,16] regimes. Furthermore, they have direct applications in the management of optical information.…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays

GARAY¹,

Moya‐Cessa²

2023

Preprint

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A non-unitary transformation leading to a Hatano-Nelson problem is performed on an array of equally- spaced optical waveguides. Such transformation produces a non-reciprocal system of waveguides, as the corresponding Hamiltonian becomes non-Hermitian. This may be achieved by judiciously choosing an attenuation (amplification) of the injected (or exciting) field. The non-Hermitian transport induced by such transformation is studied for several cases and closed analytical solutions are obtained. The corresponding non-Hermitian Hamiltonian may represent an open system that interacts with the environment, either loosing to or being provided with energy from the exterior.

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Section: Introductionmentioning

confidence: 99%

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays

GARAY¹,

Moya‐Cessa²

2023

Preprint

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Non-Hermitian dynamics from Hermitian systems: Do-it-yourself

Villegas-Martínez,

Soto-Eguibar,

Moya-Cessa

et al. 2024

Mod. Phys. Lett. B

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We show that several Hamiltonians that are [Formula: see text] symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. Therefore, a recipe to produce tractable non-Hermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

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Modeling displaced squeezed number states in waveguide arrays

Cited by 2 publications

References 52 publications

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays

Non-Hermitian dynamics from Hermitian systems: Do-it-yourself

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