We Are Never Ever Getting (back to) Ideal Symmetry: Structure and Luminescence in a Ten-Coordinated Europium(III) Sulfate Crystal

Our theoretical treatment of electronic structure in coordination complexes often rests on assumptions of symmetry. Experiments rarely provide fully symmetric systems to study. In solution, fluctuation in solvation, variations in conformation, and even changes in constitution occur and complicates the picture. In crystals, lattice distortion, energy transfer, and phonon quenching is in play, but we are able to have distinct symmetries. Yet the question remains: How is the real symmetry in a crystal compared to ideal symmetries? Moreover, at what level of detail do we need to study a system to determine, if the electronic structure behaves as if it has ideal symmetry? Here, we have revisited the Continues Shape Measurement (CShM) approach developed by Ruiz-Martínez and Alvarez to evaluate the structure of ten-coordinated europium(III) ions in a K5Na[Eu2(SO4)6] structure. By comparing the result of the symmetry deviation analysis to luminescence data, we are able to show the effect of small deviations from ideal symmetry. We suggest using a symmetry deviation value, σideal, determined by using our updated approach to Continues Shape Measurements, where we also align the structure via our AlignIt code. AlignIt includes normalization and relative orientation in the symmetry comparison, and by combining the calculated values with the experimentally determined energy level splitting, we were able create the first point on a scale that can show how close to ideal an experimental structure actually is.

Fourth order exceptional points with spinning resonators

Investigation of exceptional points mostly focuses on the second order case and employs the gain-involved parity-time (PT) symmetric systems. Here, we propose an approach to implementing fourth order exceptional points (FOEPs) using directly coupled optical resonators with rotation. On resonance, the system manifests FOEP through tuning the spinning velocity to targeted values. Eigenfrequency bifurcation and enhanced sensitivity for nanoparticle have been presented. Also, near FOEP, nonreciprocal light propagation exhibits great boost and dramatic change, which may be applied to high-efficiency isolators and circulators.

Exceptional points in oligomer chains

Symmetry underpins our understanding of physical law. Open systems, those in contact with their environment, can provide a platform to explore parity-time symmetry. While classical parity-time symmetric systems have received a lot of attention, especially because of the associated advances in the generation and control of light, there is much more to be discovered about their quantum counterparts. Here we provide a quantum theory which describes the non-Hermitian physics of chains of coupled modes, which has applications across optics and photonics. We elucidate the origin of the exceptional points which govern the parity-time symmetry, survey their signatures in quantum transport, study their influence for correlations, and account for long-range interactions. We also find how the locations of the exceptional points evolve as a function of the chain length and chain parity, capturing how an arbitrary oligomer chain transitions from its unbroken to broken symmetric phase. Our general results provide perspectives for the experimental detection of parity-time symmetric phases in one-dimensional arrays of quantum objects, with consequences for light transport and its degree of coherence.

SELCIE: a tool for investigating the chameleon field of arbitrary sources

The chameleon model is a modified gravity theory that introduces an additional scalar field that couples to matter through a conformal coupling. This `chameleon field' possesses a screening mechanism through a nonlinear self-interaction term which allows the field to affect cosmological observables in diffuse environments whilst still being consistent with current local experimental constraints. Due to the self-interaction term the equations of motion of the field are nonlinear and therefore difficult to solve analytically. The analytic solutions that do exist in the literature are either approximate solutions and or only apply to highly symmetric systems. In this work we introduce the software package SELCIE (https://github.com/C-Briddon/SELCIE.git). This package equips the user with tools to construct an arbitrary system of mass distributions and then to calculate the corresponding solution to the chameleon field equation. It accomplishes this by using the finite element method and either the Picard or Newton nonlinear solving methods. We compared the results produced by SELCIE with analytic results from the literature including discrete and continuous density distributions. We found strong (sub-percentage) agreement between the solutions calculated by SELCIE and the analytic solutions.

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

Quantum simulation of PT-arbitrary-phase-symmetric systems

Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT-symmetric systems and its featured properties start to be investigated. In this work, we develop the PT- and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT-φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT-symmetry, unifying the PT and anti-PT symmetries and having properties intermediate between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH-system of two-dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.

Quantum Steering in Two- and Three-Mode ??-Symmetric Systems

We consider two PT-symmetric models, consisting of two or three single-mode cavities. In both models, the cavities are coupled to each other by linear interactions, forming a linear chain. Additionally, the first and last of such cavities interact with an environment. Since the models are PT-symmetric, they are described by non-Hermitian Hamiltonians that, for a specific range of system parameters, possess real eigenvalues. We show that in the models considered in the article, the steering generation process strongly depends on the coupling strengths and rates of the gains/losses in energy. Moreover, we find the values of parameters describing the system for which the steering appears.

Experimental demonstration of coherence flow in PT- and anti-PT-symmetric systems

Non-Hermitian parity-time ($${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T ) and anti-parity-time ($${{{{{{{\mathcal{APT}}}}}}}}$$ APT )-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems were previously studied, coherence flow has been rarely investigated. Here, we experimentally demonstrate single-qubit coherence flow in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems using an optical setup. In the symmetry unbroken regime, we observe different periodic oscillations of coherence. Particularly, we observe two complete coherence backflows in one period in the $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T -symmetric system, while only one backflow in the $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric system. Moreover, in the symmetry broken regime, we observe the phenomenon of stable value of coherence flow. We derive the analytic proofs of these phenomena and show that most experimental data agree with theoretical results within one standard deviation. This work opens avenues for future study on the dynamics of coherence in $${{{{{{{\mathcal{P}}}}}}}}{{{{{{{\mathcal{T}}}}}}}}$$ P T - and $${{{{{{{\mathcal{APT}}}}}}}}$$ APT -symmetric systems.