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In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.

Parity–time synthetic photonic lattices

Journal of Statistical Mechanics: theory and experiment

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

Heat machines on the atomic scale are surprisingly similar to their macroscopic classical counterparts. Theorists show that all different engine types become thermodynamically equivalent in the quantum regime.

Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures

The ability of the internal states of a working fluid to be in a coherent superposition is one of the basic properties of a quantum heat engine. It was recently predicted that in the regime of small engine action, this ability can enable a quantum heat engine to produce more power than any equivalent classical heat engine. It was also predicted that in the same regime, the presence of such internal coherence causes different types of quantum heat engines to become thermodynamically equivalent. Here, we use an ensemble of nitrogen vacancy centers in diamond for implementing two types of quantum heat engines, and experimentally observe both effects.

Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines.

Quantum heat engines (QHE) are thermal machines where the working substance is quantum. In the extreme case the working medium can be a single particle or a few level quantum system. The study of QHE has shown a remarkable similarity with the standard thermodynamical models, thus raising the issue what is quantum in quantum thermodynamics. Our main result is thermodynamical equivalence of all engine type in the quantum regime of small action. They have the same power, the same heat, the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature, i.e thermodynamic measurements can confirm the presence of quantum coherence in the device. The coherent work extraction mechanism enables power outputs that greatly exceed the power of stochastic (dephased) engines.

Quantum Equivalence and Quantum Signatures in Heat Engines

In open quantum systems where the effective Hamiltonian is not Hermitian, it is known that the adiabatic (or instantaneous) basis can be multivalued: by adiabatically transporting an eigenstate along a closed loop in the parameter space of the Hamiltonian, it is possible to end up in an eigenstate different from the initial eigenstate. This ‘adiabatic flip’ effect is an outcome of the appearance of a degeneracy known as an ‘exceptional point’ inside the loop. We show that contrary to what is expected of the transport properties of the eigenstate basis, the interplay between gain/loss and non-adiabatic couplings imposes fundamental limitations on the observability of this adiabatic flip effect.

https://iopscience.iop.org/article/10.1088/1751-8113/44/43/435302/pdf

On the observability and asymmetry of adiabatic state flips generated by exceptional points

For non-Hermitian Hamiltonians with an isolated degeneracy (‘exceptional point’), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.

/pdf/slow-non-hermitian-cycling-exact-solutions-and-the-stokes-41a1fq5ahj.pdf

Raam Uzdin

Papers

Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures

Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines.

Quantum Equivalence and Quantum Signatures in Heat Engines

On the observability and asymmetry of adiabatic state flips generated by exceptional points

Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon