Revisiting the optical PTPT-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.Comment: 25 pages, 12 figure

PT-symmetry from Lindblad dynamics in a linearized optomechanical system

We analyze a lossy linearized optomechanical system in the red-detuned regime under the rotating wave approximation. This so-called optomechanical state transfer protocol provides effective lossy frequency converter (quantum beam-splitter-like) dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time (PT) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the PT-symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level

Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields

Exceptional points (EPs) are degeneracies of non-Hermitian systems, where both eigenvalues and eigenvectors coalesce. Classical and quantum systems exhibiting high-order EPs have recently been identified as fundamental building blocks for the development of novel, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear amplification processes that could limit their potential applications, particularly in the quantum realm. In this work, we show that high-order EPs can be designed by means of linear, time-modulated, chain of inductively coupled RLC (where R stands for resistance, L for inductance, and C for capacitance) electronic circuits. With a general theory, we show that $N$ coupled circuits with $2N$ dynamical variables and time-dependent parameters can be mapped onto an $N$-site, time-dependent, non-Hermitian Hamiltonian, and obtain constraints for $\mathcal{PT}$-symmetry in such models. With numerical calculations, we obtain the Floquet exceptional contours of order $N$ by studying the energy dynamics in the circuit. Our results pave the way toward realizing robust, arbitrary-order EPs by means of synthetic gauge fields, with important implications for sensing, energy transfer, and topology

Symmetry in optics and photonics: a group theory approach

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.Comment: 20 page, 5 figure