• Open Access

Breaking of PT Symmetry in Bounded and Unbounded Scattering Systems

Philipp Ambichl, Konstantinos G. Makris, Li Ge, Yidong Chong, A. Douglas Stone, and Stefan Rotter
Phys. Rev. X 3, 041030 – Published 18 December 2013

Abstract

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the nonunitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry-breaking points of such an unbounded scattering system to those of the underlying bounded systems. In particular, we show how the PT thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.

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  • Received 16 July 2013

DOI:https://doi.org/10.1103/PhysRevX.3.041030

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Philipp Ambichl1,*, Konstantinos G. Makris1,2, Li Ge3, Yidong Chong4, A. Douglas Stone5, and Stefan Rotter1,†

  • 1Institute for Theoretical Physics, Vienna University of Technology, A–1040 Vienna, Austria, EU
  • 2Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 3Department of Engineering Science and Physics, College of Staten Island, CUNY, New York 10314, USA
  • 4Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371, Singapore
  • 5Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA

  • *philipp.ambichl@tuwien.ac.at
  • stefan.rotter@tuwien.ac.at

Popular Summary

Imagine coupling a gain material that amplifies light with a lossy material that absorbs light. If the gain and loss are carefully balanced to have the same strength, you expect to end up with a system that has no net amplification or absorption. Surprisingly, such gain-loss couplers have been shown to spontaneously break this balance in favor of either amplification or absorption at a specific value of the gain-loss strength. This fundamental “symmetry-breaking” phenomenon has recently received a surge in interest. In the present work, we show that the corresponding symmetry-breaking point is actually extremely robust, being insensitive to the details of the optical boundary conditions of the gain-loss coupler as long as those conditions meet the constraint of spatial symmetry.

The optical boundary conditions for a gain-loss coupler can be modified by a set of mirrors placed around the coupler. The naive expectation is that the mirrors, by inducing strong light confinement between themselves and causing resonance effects, could influence the specific value of the symmetry-breaking point. We have shown, however, the very opposite of this expectation: The symmetry-breaking point remains unperturbed by any arrangements of the mirrors, as long as the mirrors are placed symmetrically. This fundamental surprise has its origin in the fact that the mechanism behind the symmetry breaking is not a resonance phenomenon.

Our prediction holds for arbitrarily complex arrangements of balanced gain-loss materials and should be directly testable in the experimental setups that have recently been put forward by several groups.

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Vol. 3, Iss. 4 — October - December 2013

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