Parity-time Research Articles

Effect of imaginary potential energy with parity-time symmetry on band structures and edge states of T-graphene

This paper investigates the regulatory effect of non-Hermitian mechanisms on energy spectra and edge states by applying a single- or double-layer imaginary potential with parity-time (PT) symmetry to both sides of the T-graphene ribbon. The findings indicate that the type of imaginary potential applied has a significant modulation effect on the energy band structure and localization of the system. Specifically, when an imaginary potential is applied to the outermost monolayer lattice point of the ribbon, the energy of the edge state appears in the imaginary part. For its probability density distribution, its locality changes from both-sided to one-sided locality, and becomes stronger with the increase of imaginary potential. Additionally, the PT symmetry phase transition occurs in the topologically trivial region. Notably, as the imaginary potential reaches a critical value, new imaginary-energy edge state emerges within the bulk state energy gap and also shows the phenomenon that the localization is on one side of the system. Furthermore, when double-layer imaginary potentials are applied, two different edge states will appear in the system. The first type appears in the top band and the bottom band, localized on one side of the system. The second type emerges in the middle of the second energy band and the third energy band, displaying relatively weak localization and not penetrating the energy gap. This work contributes to understanding the regulatory effect of the edge imaginary potential of PT symmetry on the physical properties of T-graphene structures.

Unidirectional and bidirectional photon transport blockade in driven atomic lattices of parity-time antisymmetry

We propose a scheme for realizing exact parity-time ( PT ) antisymmetry of complex susceptibility in a wide range of probe detuning by considering a one-dimensional lattice of cold atoms driven into the simplest three-level Λ configuration. This is attained by modulating the intensity of a standing-wave coupling field with a proper phase shift to counteract the product of a single-photon detuning and a two-photon detuning. Such a dynamically controlled PT -antisymmetric lattice supports the integration of a few nontrivial scattering behaviors including unidirectional light reflectionless, asymmetric perfect absorption, and directional signal quenching. These behaviors, depending in particular on atomic densities and lattice lengths, facilitate the on-demand realization of unidirectional or bidirectional photon transport blockade.

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

Optofluidic passive parity-time-symmetric systems.

This research introduces a novel methodology of harnessing liquids to facilitate the realization of parity-time (PT)-symmetric optical waveguides on highly integrated microscale platforms. Additionally, we propose a realistic and detailed fabrication process flow, demonstrating the practical feasibility of fabricating our optofluidic system, thereby bridging the gap between theoretical design and actual implementation. Extensive research has been conducted over the past two decades on PT-symmetric systems across various fields, given their potential to foster a new generation of compact, power-efficient sensors and signal processors with enhanced performance. Passive PT-symmetry in optics can be achieved by evanescently coupling two optical waveguides and incorporating an optically lossy material into one of the waveguides. The essential coupling distance between two optical waveguides in air is usually less than 500 nm for near-infrared wavelengths and under 100 nm for ultraviolet wavelengths. This necessitates the construction of the coupling region via expensive and time-consuming electron beam lithography, posing a significant manufacturing challenge for the mass production of PT-symmetric optical systems. We propose a solution to this fabrication challenge by introducing liquids capable of dynamic flow between optical waveguides. This technique allows the attainment of evanescent wave coupling with coupling gap dimensions compatible with standard photolithography processes. Consequently, this paves the way for the cost-effective, rapid and large-scale production of PT-symmetric optofluidic systems, applicable across a wide range of fields.

Exceptional points with waveguide-coupled nanolasers

Exceptional points (EPs) attract lots of attention due to the richness of the phenomenology associated to their presence in the complex eigenspectrum of coupled non-Hermitian systems. Here we provide both a coupled mode theory analysis and an experimental investigation of two nanolasers interacting through a channel-mediated coupling. We demonstrate the transition from Parity-Time (PT) symmetric to PT-broken regime using a thermo-optic control over the laser frequency detuning

Quantum Conductance within Luttinger Liquid from Parity Inversion and Time Rversal Symmetryic Interaction

Quantum Conductance within Luttinger Liquid from Parity Inversion and Time Rversal Symmetryic Interaction

Effects of parity, seasonal heat stress, and colostrum collection time postpartum on colostrum quality of Holstein cattle in an arid region.

The aim of this study was to determine effects of parity (primiparous vs. multiparous), seasonal heat stress at calving (summer vs. winter), and time postpartum on some parameters associated with colostrum quality in Holstein cows reared in the Sonoran Desert ecosystem. Forty-seven cows (11 primiparous and 36 multiparous) expected to calve during summer, and 46 cows during winter (14 primiparous and 32 multiparous) were randomly selected. Management and feeding before and after parturition were similar for cows in both seasons. After parturition, colostrum from all cows was evaluated for volume, weight, temperature, density, and content of fat, protein, solids non-fat (SNF), and immunoglobulins (IGG). Data were analyzed with a model that included effects of parity status, calving season, and time postpartum, as well as all interactions. Colostrum produced in summer was warmer (P < 0.01) by almost 6°C than winter colostrum, while colostrum from multiparous was warmer (P = 0.02) by 1.2°C than that produced by primiparous cows. Colostrum volume and weight were not impacted by parity, calving season or time postpartum. Density, protein, and SNF content in colostrum were higher (P < 0.01) in multiparous vs. primiparous cows, as well as at parturition (0h postpartum) than at 12h postpartum (P < 0.01). At calving (0h), spring colostrum had higher fat content (P < 0.01) and lower (P < 0.01) IGG concentration than that collected in summer, and no difference (P > 0.05) between seasons was observed for these components at 12h postpartum. Multiparous cows produced colostrum with higher (P < 0.01) IGG concentrations than primiparous cows. In conclusion, only 0-h colostrum and that from multiparous cows was categorized as "Excellent," meanwhile the colostrum produced under summer heat stress was characterized as "Good" with reduced fat content. While the lacteal secretion collected at 12 post-partum still classified as colostrum, substantially lower contents of IGG, protein, fat, and SNF decreased its classification to "Poor" from the classification of "Excellent" at 0h postpartum.

Parity‐Time Symmetry in Magnetic Materials and Devices

AbstractNon‐Hermitian Hamiltonians may still possess real eigenvalues in case of the existence of parity‐time (PT) symmetry. Exceptional points (EPs) occur at the phase transition from real to complex eigenvalues due to PT‐symmetry breaking in the parameter space. Magnonic devices use magnons to carry, transport, and process information, which have the advantages of low energy dissipation, wave‐based computing, and nonlinear data processing. The combination of PT‐symmetry and magnonics may lead to novel physics as well as unprecedented functional device applications. Recently, the research of PT‐symmetry in magnetism has developed rapidly. In this review, the theoretical predictions as well as experimental findings of PT‐symmetry in magnetism are summarized. First, a brief introduction to PT symmetry, EPs, and anti‐PT symmetry is presented. Second, the theoretical and experimental progress of magnonic PT symmetry are summarized. Third, the theoretical predictions of higher‐order EPs and anti‐PT symmetry in magnonic systems are given. Finally, the study concludes by discussing the future challenges and research prospects in magnonic PT‐symmetry, and proposals for experimental observations of magnonic higher‐order EPs and anti‐PT symmetry are suggested.

Time-reversal and parity-time symmetry breaking in non-Hermitian field theories.

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely, oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pretransitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode.

Wirelessly powered motor operation in dynamic scenarios using non-Hermitian parity-time symmetry

Motors arise as a heart of the mobility society, and wirelessly operated motors may improve our standard of living. Wireless power transfer in the kilohertz and megahertz range has been extensively explored, finding various potential applications in consumer electronics, electric vehicles, and medical implants. However, stable operation of wirelessly powered motors remains challenging due to voltage fluctuations for motors occurring in dynamic scenarios, e.g., the rotating speed of the motors is varied. Here, we theoretically and experimentally demonstrate the operation of a motor, where the power is wirelessly transferred via coils, is robust against the rotating speed by employing the analogy with non-Hermitian parity-time (PT) symmetry. In addition, our system is robust for misalignment of the coils. Our results open up opportunities for the robust operation of motors via wireless power transfer in dynamic scenarios towards autonomous vehicles.

Defect modes in defective one dimensional parity-time symmetric photonic crystal

The introduction of defect layers into one-dimensional parity-time (PT) symmetric photonic crystals gives rise to resonances within the photonic bandgaps. These resonances can be effectively explained by our generalized temporal coupled mode theory. The scattering properties and dispersion relation of defect modes exhibit distinct characteristics compared to conventional one-dimensional Hermitian photonic crystals with defect layers. By tuning the non-Hermiticity or other model parameters, the modulus of the generalized decay rate can be reduced, consequently, the electric field concentrated within the defect layer strengthens. This arises due to the unique band structure of one-dimensional PT-symmetric photonic crystals, which differs significantly from that of traditional one-dimensional Hermitian photonic crystals. Furthermore, the interaction between multiple resonances is investigated through the introduction of multiple defect layers. Our study not only provides insights into resonance phenomena in defective non-Hermitian systems but also contributes to the design of relevant optical resonance devices.

Acoustic coherent perfect absorption based on a PT symmetric coupled Mie resonator system

Parity-time (PT) symmetric coupled resonator systems have exhibited intriguing and unexpected properties in optics and electronics. Here, we extend it to acoustics and report a coupled Mie resonators (MRs) system respecting PT symmetry. The system is constructed with two parallel waveguides connected by an aperture and two MRs placed symmetrically at both sides of the aperture. Instead of using active elements or complex refractive index modulation without gain, we exploit the incident waves of the waveguide as an effective gain so that PT symmetry with balanced loss and gain is realized by only passive materials. Coherent perfect absorption (CPA), which can completely absorb the in-phase excitations with the same intensity provided from two opposite directions, is observed in the PT symmetric phase and at the exceptional point but not in the broken phase. In addition, by varying the relative phase between the two incident waves, the coherent absorption can be tuned from CPA to zero. Our design may provide a flexible platform to research PT symmetry in acoustics and may have applications in tunable noise control, acoustic modulators, and switches.

Parity time symmetry in two dimensional chiral optical lattice, via positive and negative refraction

The parity time symmetry and positive/negative refraction is investigated in chiral optical lattice. Significant parity time symmetry is reported in five level chiral optical lattice which satisfied the conditions Re(nr(±)(x,y))=Re(nr∗(±)(−x,−y) and Im(nr(±)(x,y))=−Im(nr∗(±)(−x,−y) for left and right circularly polarized beams. The related group indices, phase shifts and divergent angle are also satisfied the parity time symmetry conditions ng(±)(x,y))=ng∗(±)(−x,−y), ϕ(±)(x,y))=ϕ∗(±)(−x,−y) and θd,g(x,y)=θd,g∗(−x,−y) for left and right circularly polarized beams. Maximum negative group index is calculated to −25000. The maximum phase and group divergent angles are reported to 0.001 radian and −0.9 radian. The phase shifts in LCP and RCP beams are investigated to ±0.004 radian at a length L=10λ. The modified results have potential application in nanotechnology.

Controllable flatbands via non-Hermiticity

We propose a flexible way to design and control flatbands in photonic systems with balanced gain and loss. We investigate a lattice model constructed from two parity-time (PT)-symmetric dimer systems, which give rise to two flatbands. By tuning the non-Hermiticity in this composite lattice, the flatbands can be manipulated into the regime of the dispersive bands and remain completely flat, which is protected by the PT symmetry. When reaching the exceptional point (EP), where two flatbands merge into one flatband, and surpassing the EP, one of the flatbands transforms into a partial flatband, while the imaginary parts of the band structure also appear in the form of multiple flatbands. We also discover that dimensionality plays an important role in controlling flatbands in a non-Hermitian manner. Our results could be potentially important for manipulating the dynamics and localization of light in non-Hermitian open systems.

Arbitrary Wireless Energy Distribution within an Epsilon Near‐zero Environment

AbstractEfficient power distribution to multiple receivers with controlled amounts is critical for wireless communication and sensing systems. Previous efforts have attempted to improve power transfer efficiency through strong coupling and parity‐time (PT) symmetry, providing attractive opportunities for flexible energy flow control. In this study, a novel method for achieving arbitrary power distribution is proposed and numerically demonstrated by leveraging the unique properties inside an epsilon near‐zero (ENZ) environment. Specifically, it shows that the power from a single source can be transferred to multiple receivers inside an ENZ medium with negligible loss by modifying optical properties of receivers rather than introducing sophisticated active control modules. Importantly, full power transfer is independent of the size and shape of the ENZ medium, as well as the positions of the receivers and source. A realizable system is further designed with effective zero index at microwave frequencies to confirm the high efficiency of energy transfer. The innovative approach, employing photonic doping for advanced and efficient wireless power transfer, may shed light on the new generation of energy efficient communication/sensing systems with versatile control functionalities.

Multi-peak solitons in parity-time symmetry composite Mathieu lattices

This paper numerically investigates the existence, stability, and transmission characteristics of multi-peak solitons in parity-time (PT) symmetric composite Mathieu lattices in self-focusing Kerr nonlinear media. These multi-peak solitons are highly sensitive to the incident light power, position, and phase. Different incident lights generate solitons with different transmission characteristics, especially the generation of breather soliton transmission characteristics. These findings have significant theoretical and practical implications for the fields of photonics and nonlinear optics.

Exceptional points for crack detection in non-Hermitian beams

We study exceptional points (EPs) in parity-time (PT) symmetric non-Hermitian beams and explore their applications in crack detection. The EPs are formed by coupling different beam modes under feedback-controlled forces. The variations of the required non-Hermitian coefficient for the achievement of EPs are studied as a function of the separations and center positions of the applied force pairs. Then, a 3D cuboid-shaped crack is introduced at the center of the top surface of the beam, and results in the square-root behaviors of the frequency splitting under different crack geometries and force polarizations. This supports the enhanced sensitivity based on EPs as compared to the usual linear sensing methods. Using several polarizations allows access to different types of waves propagating in the beam and their modifications in the presence of the crack, therefore providing combined means of testing. Furthermore, a practical and feasible feedback control design is realized via replacing the applied forces by piezoelectric patches on the beam surface, exhibiting highly sensitive responses of the EPs to minor cracks. The studied results provide a new platform for crack or perturbation detection in elastic media.

A Three-Coil Constant Output Wireless Power Transfer System Based on Parity–Time Symmetry Theory

In a three-coil wireless power transfer system with relay coils, the transmission efficiency and output power of the system decreases with changes in the adjacent coupling coefficients. Controlling the power of three-coil wireless power transfer systems is also a significant challenge. To solve these issues, a three-coil wireless power transfer system based on parity–time symmetry is proposed in this paper. First, a three-coil parity–time wireless power transfer system was modeled based on a circuit model. Then, the transmission and gain characteristics of the three-coil parity–time wireless power transfer system were analyzed. It was found that when the system is in a parity–time-exact region, it can maintain a constant transmission efficiency and output power, and its output power is independent of the coupling coefficient. In addition, based on the output characteristics of the three-coil parity–time wireless power transfer system, a power control method and a working range detection method were proposed to attain a constant power output. Finally, a three-coil parity–time wireless power transfer system was experimentally tested.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.

A Symmetric Parity–Time Coupled Optoelectronic Oscillator Using a Polarization–Dependent Spatial Structure

We propose and experimentally investigate a symmetric parity-time (PT) coupled optoelectronic oscillator (COEO) based on a polarization-dependent spatial structure. In such a COEO system, the gain/loss and coupling coefficients of two orthogonal polarization optical waves can be controlled by adjusting the polarization controller (PC) and the bias voltage of a Mach-Zehnder modulator (MZM). The single-mode selection of a microwave signal can be implemented by the PT symmetry breaking of a special mode. The performance of the proposed COEO is experimentally examined, and a 10.0 GHz microwave signal with a phase noise of −109.1 dBc/Hz @ 10 kHz and a side mode suppression ratio of 51.4 dB is generated. Moreover, an optical frequency comb with a comb tooth spacing of 10.0 GHz and a bandwidth of 100 GHz within a 10 dB amplitude variation can be simultaneously generated.