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Title: Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice

Abstract

We show that a periodic two-dimensional (2D) photonic lattice with Kerr nonlinearity exhibits a Berezinskii-Kosterlitz-Thouless (BKT) crossover associated with a vortex-unbinding transition. We find that averaging over random initial conditions is equivalent to Boltzmann thermal averaging with the discrete nonlinear Schro{center_dot}{center_dot}dinger Hamiltonian. By controlling the initial randomness we can continuously vary the effective temperature. Since this Hamiltonian is in the 2D XY universality class, a BKT transition ensues. We verify this prediction using experimentally accessible observables and find good agreement between theory and simulations. This opens the possibility of experimental access to interesting phase transitions known in condensed matter using nonlinear optics.

Authors:
; ;  [1]
  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)
Publication Date:
OSTI Identifier:
21537048
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.83.013806; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE; BOLTZMANN EQUATION; CRYSTAL LATTICES; HAMILTONIANS; NONLINEAR OPTICS; PHASE TRANSFORMATIONS; PHOTONS; RANDOMNESS; SIMULATION; TWO-DIMENSIONAL CALCULATIONS; VORTICES; BOSONS; CRYSTAL STRUCTURE; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; EQUATIONS; INTEGRO-DIFFERENTIAL EQUATIONS; KINETIC EQUATIONS; MASSLESS PARTICLES; MATHEMATICAL OPERATORS; OPTICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS

Citation Formats

Small, Eran, Pugatch, Rami, and Silberberg, Yaron. Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.013806.
Small, Eran, Pugatch, Rami, & Silberberg, Yaron. Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice. United States. https://doi.org/10.1103/PHYSREVA.83.013806
Small, Eran, Pugatch, Rami, and Silberberg, Yaron. 2011. "Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice". United States. https://doi.org/10.1103/PHYSREVA.83.013806.
@article{osti_21537048,
title = {Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice},
author = {Small, Eran and Pugatch, Rami and Silberberg, Yaron},
abstractNote = {We show that a periodic two-dimensional (2D) photonic lattice with Kerr nonlinearity exhibits a Berezinskii-Kosterlitz-Thouless (BKT) crossover associated with a vortex-unbinding transition. We find that averaging over random initial conditions is equivalent to Boltzmann thermal averaging with the discrete nonlinear Schro{center_dot}{center_dot}dinger Hamiltonian. By controlling the initial randomness we can continuously vary the effective temperature. Since this Hamiltonian is in the 2D XY universality class, a BKT transition ensues. We verify this prediction using experimentally accessible observables and find good agreement between theory and simulations. This opens the possibility of experimental access to interesting phase transitions known in condensed matter using nonlinear optics.},
doi = {10.1103/PHYSREVA.83.013806},
url = {https://www.osti.gov/biblio/21537048}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 83,
place = {United States},
year = {Sat Jan 15 00:00:00 EST 2011},
month = {Sat Jan 15 00:00:00 EST 2011}
}