Spontaneous PT-symmetry Breaking Research Articles

Probing PT-Symmetry Breaking of Non-Hermitian Topological Photonic States via Strong Photon-Magnon Coupling.

Light-matter interaction is crucial to both understanding fundamental phenomena and developing versatile applications. Strong coupling, robustness, and controllability are the three most important aspects in realizing light-matter interactions. Topological and non-Hermitian photonics have provided frameworks for robustness and control flexibility, respectively. How to engineer the properties of the edge state such as photonic density of state by using non-Hermiticity while ensuring topological protection has not been fully studied. Here we construct a parity-time-symmetric dimerized photonic lattice and probe the spontaneous PT-symmetry breaking of the edge states by utilizing the strong coupling between the photonic mode and a spin ensemble. Our Letter presents an accurate and almost noninvasive approach for investigating non-Hermitian topological states, while also offering methodologies for the implementation and manipulation of topological light-matter interactions.

From digital to quantum epidemiology: The Quantum Data Lake concept for big data related to viral infectious diseases

The development of quantum epidemiology represents the next anticipated phase in epidemiology transformation, driven by the emergence of new quantum technologies. Epidemiology is currently transitioning into the digital era and undergoing a paradigm shift from a data-driven to a value-driven strategy. Epidemiology data are characterized by uncertainty, multidimensionality, and disconnection, thereby correlating with the preferential quantum approach for data exposition, value creation, and modeling. Examples of such complex epidemiology data include the data on DNA viruses with associated symptoms and diseases. The Quantum Data Lake concept is proposed and consists of several layers and quantum tools, including Robson semantic triples, Quantum Universal Exchange Language, Hyperbolic Dirac Net, “quantum ribosome” structure, quantum random access memory, teleportation, Quantum Query Language, non-Hermitian gates, and tensor networks (e.g., matrix product state, projected entangled pair state, and multiscale entanglement renormalization ansatz [MERA]), alongside PT-symmetry properties. PT-symmetry can serve as an intuitive modeling tool, and PT-symmetry breaking can detect the hidden shift in the information that is permanently updated in the Data Lake. The computational output is presented as PT-symmetry gain/loss equilibrium breaking in the form of a complex number, i.e., two possible variants of epidemic modeling. For MERA, non-Hermiticity with spontaneous PT-symmetry breaking can theoretically appear as a violation of the entanglement monotonicity and local entanglement gain, leading to a non-reversible character of the coarse-graining transformation. The duality of PT-symmetry equilibrium breaking can be compared to, for example, the estimation of the best and worst scenarios simultaneously, or the gain of entanglement can display a significant correlation between some studied parameters embedded into the data. The fundamental difference between digital and quantum epidemiology is the implementation of quantum logic and reliance on a quantum theory.

Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model

We investigate the dynamics of the out-of-time-order correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies PT-symmetry. The spontaneous PT-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of the nonlocal operator in OTOCs and the time reversal induced by non-Hermitian-driven potential.

Impact of [formula omitted]-symmetric imaginary potentials on edge states of one-dimensional rhombus lattice

We theoretically investigate the band structure of the one-dimensional rhombus lattice by considering the existence of PT-symmetric imaginary potentials. Results show that the effects of such potentials are tightly determined by their presence manners. When they are applied to the end sites of the lattice, topological edge states can be efficiently modulated. Meanwhile, more edge states caused by PT-symmetry imaginary potential appear in the system, and the system undergoes the spontaneous PT-symmetry breaking transition. When local magnetic flux is incorporated, edge states can be further adjusted. However once PT-symmetric imaginary potentials are added to each unit cell of the lattice, they are less effective in manipulating the edge states despite the modification in the band structure. Based on these results, we better comprehend the adjustability of the edge states of the rhombus lattice by applying the PT-symmetric imaginary potentials.

Quasi-parity-time symmetric dynamics in periodically driven two-level non-Hermitian system

<sec>In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare.</sec><sec></sec><sec>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.</sec>

Quasi-Parity-Time symmetric dynamics in a periodcially driven two-level non-Hermitian system

In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare.<br>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.

Spontaneous and explicit parity-time-symmetry breaking in drift-wave instabilities.

A method of parity-time- (PT) symmetry analysis is introduced to study the high-dimensional, complicated parameter space of drift-wave instabilities. We show that spontaneous PT-symmetry breaking leads to the ion temperature gradient instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.

Spontaneous PT-symmetry breaking in lasing dynamics

Parity-time (PT) symmetric lasers exploit the modulation of optical gain and loss and have led to important fundamental demonstrations in non-Hermitian physics. The current theoretical analysis of PT-symmetric laser physics is performed on the basis of the adiabatic elimination of the medium polarization. This approximation doesn’t hold true for a more general optical system with strong photon-particle interactions, where the Rabi oscillation of active particles plays a non-negligible role in the lasing action. Here, we propose a model that takes into account the internal dynamics of active particles and numerically investigate the PT symmetry of macroscopic- and microscopic-sized laser systems that operate in the strong-coupling regime. The distinct phase diagrams are drawn according to the features of intracavity photon numbers and emission spectra. Our work extends the PT-symmetric optics from the weak- to the strong-coupling limit, potentially paving the way towards nonclassical PT-symmetric light sources for integrated photonic networks and ultrasensitive sensors.

Parity-Time symmetric system based on the thermoacoustic effect.

This paper deals with the experimental study of an acoustic Parity-Time (PT) symmetric system based on the thermoacoustic amplification process. Such a system is presented and consists of two acoustic units connected through side branches to a waveguide. One unit contains a thermoacoustic core that provides an acoustic gain which balances the thermal and viscous losses taking place in the second unit. Two control parameters are set to adjust the impedance of the two units and thereby achieve the PT-symmetry condition. The results show that a good balance between gain and loss is achieved within a frequency range from 45 Hz to 60 Hz. The spontaneous PT-symmetry breaking and the existence of exceptional points, which are characteristic of the behavior of PT-symmetric systems, are explored in this frequency range. Moreover, the distance between the two units is shown to be a control parameter to slightly shift the frequency at which the exceptional points occur.

Non-Hermitian dynamic strings and anomalous topological degeneracy on a non-Hermitian toric-code model with parity-time symmetry

In this paper, with the help of Hermitian/non-Hermitian dynamic strings, the theory of non-Hermitian topological order is developed based on a non-Hermitian Wen-plaquette model. The effective models for bosonic topological excitations (e-particle and m-particle) are Hermitian tight-binding lattice model; the effective model for fermionic topological excitation (f-particle) becomes a non-Hermitian tight-binding lattice model. In addition, the effective pseudo-spin model for topologically degenerate ground states is derived by calculating the expectation values of Hermitian/non-Hermitian topological closed dynamic strings. For the topologically degenerate ground states of non-Hermitian Wen-plaquette model on an even-by-odd, odd-by-even and odd-by-odd lattice, anomalous topological degeneracy occurs, i.e., the number of the topologically protected ground states may be reduced from 2 to 1. Now, the effective pseudo-spin model turns into the typical PT-symmetric non-Hermitian Hamiltonian with spontaneous PT-symmetry breaking. At exceptional points, the topologically degenerate ground states merge with each other and the topological degeneracy turns into non-Hermitian degeneracy. In the end, the application of the non-Hermitian Z2 topological order and its possible physics realization are discussed.

Mode Control of Quasi-PT Symmetry in Laterally Multi-Mode Double Ridge Semiconductor Laser * *Supported by the National Key R&D Program of China (Grant Nos. 2016YFB0401804 and 2016YFA0301102), and the National Natural Science Foundation of China (Grant Nos. 91850206, 61535013, and 11981260014).

In traditional semiconductor lasers, it is usual to obtain single lateral mode operation by narrowing the ridge of waveguide, which is sensitive to fabrication inaccuracies. To overcome this shortcoming, a quasi-PT (parity-time) symmetric double ridge semiconductor laser is proposed to reach single lateral mode operation for an intrinsic multi-mode stripe laser. The coupled mode theory is used to analyze the non-Hermitian modulation of the gain (or loss) of the PT symmetric double ridge laser to obtain the coupling coefficient between the two ridge waveguides. Finally, the mode field distributions of the quasi-PT symmetric double ridge laser are simulated before and after the spontaneous PT symmetry breaking, which keep the laser operating in single lateral mode.

Resonances and PT symmetry in quantum curves

In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex spectra and resonances, and in some cases, to PT-symmetric spectral problems. The correspondence leads to precise predictions about the spectral properties of these non-Hermitian operators. In this paper we develop techniques to compute the complex spectra of these quantum curves, providing in this way precision tests of these predictions. In addition, we analyze quantum Seiberg-Witten curves with PT symmetry, which provide interesting and exactly solvable examples of spontaneous PT-symmetry breaking.

Controlling photonic spin Hall effect via exceptional points

The photonic spin Hall effect (SHE), featured by a spin-dependent transverse shift of an impinging optical beam driven by its polarization handedness, has many applications including precise metrology and spin-based nanophotonic devices. It is highly desirable to control and enhance the photonic SHE. However, such a goal remains elusive, due to the weak spin-orbit interaction of light, especially for systems with optical loss. Here we reveal a flexible way to modulate the photonic SHE via exceptional points, by exploiting the transverse shift in a parity-time (PT) symmetric system with balanced gain and loss. The underlying physics is associated with the near-zero value and abrupt phase jump of the reflection coefficients at exceptional points. We find that the transverse shift is zero at exceptional points, but it is largely enhanced in their vicinity. In addition, the transverse shift switches its sign across the exceptional point, resulting from spontaneous PT-symmetry breaking. Due to the sensitivity of transverse shift at exceptional points, our work also indicates that the photonic SHE can enable a precise way to probe the location of exceptional point in photonic systems.

Novel acoustic flat focusing based on the asymmetric response in parity-time-symmetric phononic crystals

We present a two-dimensional (2D) parity-time-symmetric (PT-symmetry) phononic crystals (PCs) with balanced gain and loss medium. Using the super cell method of rectangular lattice, we exhibit the thresholdless spontaneous PT-symmetry breaking in the band structure. The numerical results show that the asymmetric scattering properties obviously occur in a non-Hermitian system. At two specific incident frequencies, unidirectional reflectionless and perfect transmission behaviors exist individually in opposite directions, which are accompanied by a phase transition of π. Based on the generalized Snell’s law, combining such a PT-symmetric medium, we design a novel metamaterial crystal for PT-symmetric acoustic flat focusing. Its focus frequency can also be modulated by the gain/loss parameter. The novel flat focusing based on the PT-symmetry that we propose opens a new door for high-dimensional applications of non-Hermitian metamaterials in acoustic wave manipulation.

Kelvin-Helmholtz instability is the result of parity-time symmetry breaking

Parity-Time (PT)-symmetry is being actively investigated as a fundamental property of observables in quantum physics. We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability is the result of spontaneous PT-symmetry breaking. It is expected that all classical conservative systems governed by Newton's law admit PT-symmetry, and the spontaneous breaking thereof is a generic mechanism for classical instabilities. Discovering the PT-symmetry of systems in fluid dynamics and plasma physics and identifying the PT-symmetry breaking responsible for instabilities enable new techniques to classical physics and enrich the physics of PT-symmetry.

Parity–time symmetric photonics

Abstract The establishment of non-Hermitian quantum mechanics (such as parity–time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to complex quantum potentials, photonics provides an ideal platform for the visualization of many conceptually striking predictions from non-Hermitian quantum theory. A rapidly developing field has emerged, namely, PT-symmetric photonics, demonstrating intriguing optical phenomena including eigenstate coalescence and spontaneous PT-symmetry breaking. The advance of quantum physics, as the feedback, provides photonics with brand-new paradigms to explore the entire complex permittivity plane for novel optical functionalities. Here, we review recent exciting breakthroughs in PT-symmetric photonics while systematically presenting their underlying principles guided by non-Hermitian symmetries. The potential device applications for optical communication and computing, biochemical sensing and healthcare are also discussed.

Complex Classical Mechanics of a QES Potential**Support from Department of Science and Technology (DST), Govt. of India under SERC Project Sanction Grant No. SR/S2/HEP-0009/2012

We study a combined parity (P) and time reversal (T) invariant non-Hermitian quasi-exactly solvable (QES) potential, which exhibits PT phase transition, in the complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle escapes to an open orbits even with real energy if it is placed beyond a certain distance from the center of the well. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. Our study reveals that spontaneous PT symmetry breaking does not affect the qualitative features of the particle trajectories in the analogous complex classical model.

Parity-time-symmetry breaking in double-slab surface-plasmon-polariton waveguides.

We theoretically demonstrate spontaneous PT-symmetry breaking behavior of surface-plasmon polaritons (SPP) in coupled double-slab (DS) waveguides. By virtue of a flat-top field at critical wavelength, the imaginary index of a DS-SPP mode can be controlled via changing the core thickness, while the real index is kept constant. Therefore, a waveguide coupler that consists of a pair of DS-SPP waveguides with different core thicknesses can represent a passive PT-symmetric system, which always maintains symmetry under a real potential. This set-up also represents a good opportunity to investigate the underlying physics of PT-symmetry breaking in non-Hermitian Hamiltonian systems.

Quantum noise and mode nonorthogonality in non-HermitianPT-symmetric optical resonators

PT-symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We calculate the frequency-resolved output radiation intensity of such systems and relate it to a suitable measure of excess noise and mode nonorthogonality. The lineshape differs depending on whether the emission lines are isolated (as for weakly amplifying, almost hermitian systems) or overlapping (as for the almost degenerate resonances in the vicinity of exceptional points associated to spontaneous PT-symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi one-dimensional resonator set-up. In our derivations we also allow for the more general case of a resonator in which the amplifying and absorbing regions are not related by symmetry.

Universal routes to spontaneousPT-symmetry breaking in non-Hermitian quantum systems

PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous PT-symmetry breaking can occur via two distinct mechanisms, whose predominance is associated to different universality classes. Present optical experiments fall into the orthogonal class, where symmetry-induced level crossings render the characteristic absorption rate independent of the coupling strength between the symmetry-related parts of the system.