Disorder in parity-time symmetric quantum walks

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum walks.Via temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single photons.Controllable coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.

Soliton structures in the (1+1)-dimensional Ginzburg–Landau equation with a parity-time-symmetric potential in ultrafast optics

In this paper, the （l＋l）-dimensional variable-coefficient complex Ginzburg-Landau （CGL） equation with a parity- time （PT） symmetric potential U（x） is investigated. Although the CGL equations with a PT-symmetric potential are less reported analytically, the analytic solutions for the CGL equation are obtained with the bilinear method in this paper. Via the derived solutions, some soliton structures are presented with corresponding parameters, and the influences of them are analyzed and studied. The single-soliton structure is numerically verified, and its stability is analyzed against additive and multiplicative noises. In particular, we study the soliton dynamics under the impact of the PT-symmetric potential. Results show that the PT-symmetric potential plays an important role for obtaining soliton structures in ultrafast optics, and we can design fiber lasers and all-optical switches depending on the different amplitudes of soliton-like structures.

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time(PT)symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain.Here,we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits.By judiciously adjusting the resistances and inductances in the external circuits,we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility.Moreover,the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits,which represents the active control that makes the acoustic manipulation more convenient.Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Bifurcated overtones of one-way localized Fabry-Pérot resonances in parity-time symmetric optical lattices

Since the first observation of parity-time（PT） symmetry in optics, varied interesting phenomena have been discovered in both theories and experiments, such as PT phase transition and unidirectional invisibility, which turns PT-symmetric optics into a hotspot in research. Here, we report on the one-way localized Fabry-Pérot（FP） resonance, where a welldesigned PT optical resonator may operate at exceptional points with bidirectional transparency but unidirectional field localization. Overtones of such one-way localized FP resonance can be classified into a blue shifted branch and a red shifted branch. Therefore, the fundamental resonant frequency is not the lowest one. We find that the spatial field distributions of the overtones at the same absolute order are almost the same, even though their frequencies are quite different.

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes(RSAEs).Using the parameters from an ASDEXUpgrade plasma,a benchmark with the three different physical models for RSAE without and with energetic particles(EPs)is carried out.Reasonable agreement has been found for the mode frequency and the growth rate.Mode structure symmetry breaking(MSSB)is observed when EPs are included,due to the EPs’non-perturbative effects.It is found that the MSSB properties are featured by a finite radial wave phase velocity,and the linear mode structure can be well described by an analytical complex Gaussian expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number with opposite signs is generated.The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport.The parallel velocity of EPs is generated in opposite directions,due to different values of the average radial wave number,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.

Symmetry Violation of Time Reversal in Third Order Vertex Angle Renormalization Process of Electromagnetic Interaction

According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.

Seeing time-reversal transmission characteristics through kinetic anti-ferromagnetic Ising chain

As an example of our new approach to complex near-field （NF） scattering of electromagnetic waves, the timereversal （TR） transmission process on an NF current-element array is mapped to the statistical process on a kinetic Ising transmission chain. Equilibrium statistical mechanics and non-equilibrium Monte Carlo （MC） dynamics help us to find signal jamming, aging, annihilating, creating, and TR symmetry breaking on the chain with inevitable background noises; and these results are general in NF systems where complex electromagnetic scattering arises.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Extraordinary transmission and reflection in PT-symmetric two-segment-connected triangular optical waveguide networks with perfect and broken integer waveguide length ratios

By adjusting the waveguide length ratio, we study the extraordinary characteristics of electromagnetic waves propagating in one-dimensional(1D) parity-time-symmetric(PT-symmetric) two-segment-connected triangular optical waveguide networks with perfect and broken integer waveguide length ratios respectively. It is found that the number and the corresponding frequencies of the extremum spontaneous PT-symmetric breaking points are dependent on the waveguide length ratio. Near the extremum breaking points, ultrastrong extraordinary transmissions are created and the maximal can arrive at, respectively, 2.4079 × 10^14 and 4.3555 × 10^13 in both kinds of networks. However, bidirectional invisibility can only be produced by the networks with broken integer waveguide length ratio, whose mechanism is explained in detail from the perspective of photonic band structure. The findings of this work can be useful optical characteristic control in the fabrication of PT-symmetric optical waveguide networks, which possesses great potential in designing optical amplifiers,optical energy saver devices, and special optical filters.

Dynamics of Airy beams in parity–time symmetric optical lattices

We investigate the dynamics of airy beams propagating in the parity–time(PT) symmetric optical lattices in linear and nonlinear regimes, respectively. For the linear propagation, the position of the channel guided by the PT lattice can be shifted by tuning the lattice frequency. The underlying physical mechanism of this phenomenon is also discussed. An interesting phenomenon is found in the nonlinear regime in that the airy beam becomes a tilt channel with several Rayleigh lengths. These findings create new opportunities for optical steering and manipulations.

On-chip tunable parity‐time symmetric optoelectronic oscillator

Parity‐time(PT)symmetry breaking offers mode selection capability for facilitating single‐mode oscillation in the optoelectronic oscillator(OEO)loop.However,most OEO implementations depend on discrete devices,which impedes proliferation due to size,weight,power consumption,and cost.In this work,we propose and experimentally demonstrate an on-chip tunable PT‐symmetric OEO.A tunable microwave photonic filter,a PT‐symmetric mode‐selective architecture,and two photodetectors are integrated on a silicon‐on‐insulator chip.By exploiting an on‐chip Mach–Zehnder interferometer to match the gain and loss of two mutually coupled optoelectronic loops,single‐mode oscillation can be obtained.In the experiment,the oscillation frequency of the on-chip tunable PT‐symmetric OEO can be tuned from 0 to 20 GHz.To emulate the integrated case,the OEO loop length is minimized,and no extra-long fiber is used in the experiment.When the oscillation frequency is 13.67 GHz,the single‐sideband phase noise at 10-kHz offset frequency is−80.96 dBc∕Hz and the side mode suppression ratio is 46 dB.The proposed on-chip tunable PT‐symmetric OEO significantly reduces the footprint of the system and enhances mode selection.

Fundamental and dressed annular solitons in saturable nonlinearity with parity–time symmetric Bessel potential

We theoretically study the existence and stability of optical solitons in saturable nonlinearity with a two-dimensional parity–time（PT） symmetric Bessel potential.Besides the fundamental solitons,a novel type of dressed soliton,whose intensity looks like a ring dressed on an intensity hump,are presented.It is found that both the fundamental solitons and dressed solitons can exist when the propagation constant is beyond a certain critical value.The propagation stability is investigated with a linear stability analysis corroborated by a beam propagation method.All the fundamental solitons are stable,while dressed solitons are unstable for low values of saturable parameter.As the value of saturable parameter increases,the dressed solitons tend to be stable at high powers.

Reconstruction of symmetric models composed of analytic curves and surfaces from point cloud

This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, i.e., translational, reflectional and rotational symmetries are considered. The reconstruction problem is formulated as a constrained optimization, where the objective function is the sum of squared distances of points to the model, and constraints are enforced to keep geometric relationships in the model. First, the explicit representations of symmetric models are presented. Then, by using the concept of parameterized points (where the coor-dinate components are represented as functions rather than constants), the distances of points to symmetric models are deduced. With these distance functions, symmetry information, for both 2D and 3D models, is uniformly represented in the process of reconstruction. The constrained optimization problem is solved by a standard nonlinear optimization method. Owing to the explicit representation of symmetry information, the computational complexity of our method is reduced greatly. Finally, examples are given to demonstrate the application of the proposed method.

Electromagnetic retarded interaction and symmetry violation of time reversal in high order stimulated radiation and absorption processes of light

It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account,the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated,though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field,there is no such kind of symmetry violation of time reversal. In this way,the current formula on the parameters of stimulated radiation and absorption of light with time reversal sym-metry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are in-volved.

Optical resonance in inhomogeneous parity-time symmetric systems

We show that inhomogeneous waveguides of slowly varied parity-time(PT) symmetry support localized optical resonances.The resonance is closely related to the formation of exceptional points separating exact and broken PT phases.Salient features of this kind of non-Hermitian resonance, including the formation of half-vortex flux and the discrete nature,are discussed.This investigation highlights the unprecedented uniqueness of field dynamics in non-Hermitian systems with many potential adaptive applications.

Analytical Study on Propagation Dynamics of Optical Beam in Parity-Time Symmetric Optical Couplers

We present exact analytical solutions to parity-time(P T) symmetric optical system describing light transport in P T-symmetric optical couplers. We show that light intensity oscillates periodically between two waveguides for unbroken P T-symmetric phase, whereas light always leaves the system from the waveguide experiencing gain when light is initially input at either waveguide experiencing gain or waveguide experiencing loss for broken P T-symmetric phase. These analytical results agree with the recent experimental observation reported by Ru¨ter et al. [Nat. Phys.6(2010) 192]. Besides, we present a scheme for manipulating P T symmetry by applying a periodic modulation. Our results provide an efficient way to control light propagation in periodically modulated P T-symmetric system by tuning the modulation amplitude and frequency.

Enhanced absorption and electrical modulation of graphene based on the parity-time symmetry optical structure

In order to realize the ultrastrong absorption of graphene with electrical modulation properties, we designed a composite structure of graphene and parity-time(PT) symmetry photonic crystal, which is achieved by placing the graphene layer on the top layer of the PT symmetry photonic crystal. In this paper, the absorption properties of graphene and the electrical modulating properties of the structure were theoretically analyzed based on the transfer matrix method. The result shows that the proposed structure can achieve the absorption of 31.5 d B for the communication wavelength of 1550 nm;meanwhile,by setting the electric field intensity to ±0.02 V/nm, the absorption of graphene can be largely modulated to realize an electrically switchable effect, the modulation depth of graphene absorption can reach nearly 100%, and the operation speed is also close to 8.171 GHz. This investigation provides a novel approach to design graphene-based optoelectronic devices and optical communication devices.

Tunable optical second-order sideband effects in a parity-time symmetric optomechanical system

We theoretically investigate the optical second-order sideband generation(OSSG)in an optical parity-time(PT)symmetric system,which consists of a passive cavity trapping the atomic ensemble and an active cavity.Compared with the double-passive system,it is found that near the exceptional point(EP),the efficiency of the OSSG increases sharply not only for the blue probepump detuning resonant case but also for the red one.Using experimentally achievable parameters,we study the effect of the atomic ensemble on the efficiency of the OSSG in the PT-symmetric system.The numerical results show that the efficiency of the OSSG is 30%higher than that of the first-order sideband,which is realized easily by simultaneously modulating the atom-cavity coupling strength and detuning.Moreover,the efficiency of the OSSG can also be tuned effectively by the pump power,and the efficiency is robust when the pump power is strong enough.This study may have some guidance for modulating the nonlinear optical properties and controlling light propagation,which may stimulate further applications in optical communications.

Observation of Parity-Time Symmetry Breaking in Single-Photon Interferometer

We experimentally simulate a parity-time(PT)-symmetric quantum dynamics in a non-Hermitian system using a single-photon interferometer.We measure quantum final state using quantum state tomography.We observe the quantum state evolutions ranging from regions of unbroken to broken PT-symmetry using the single-photon interferometer.We experimentally prove that the eigenvalue of energy changes from real to imaginary corresponding to the non-Hermitian system from the PT-symmetry unbroken region to the PT-symmetry broken region.To the best of our knowledge,this is the first work to intuitively show the exceptional points of PT-symmetry non-unitary quantum dynamics in a single-photon interferometer from the energy perspective.

Topology in parity-time-symmetric quantum walks

The study of non-Hermitian systems with parity-time(PT)symmetry is a rapidly developing frontier in recent years?Experimentally,PT-symmetric systems have been realized in classical optics by balancing gain and loss,which holds great promise for novel optical devices and networks?Here we report experimental realization of passive PT-symmetric quantum dynamics for single photons by temporally alternating photon losses in the quantum walk(QW)interferometers.The ability to impose PT symmetry allows us to realize and investigate Floquet topological phases driven by PT-symmetric QWs.We observe topological edge states between regions with different topological invariants?Topological invariants can be defined by winding numbers,Zak phases,general geometry phases and can be calculated?Can they be detected directly?We give an answer by reporting the experimental detection of bulk topological invariants in non-unitary QWs?The topological invariant of the non-unitary quantum walk is manifested in the quantized average displacement of the walker,which is probed by monitoring the photon loss.Furthermore,we report the experimental study of dynamic quantum phase transitions(DQPTs)and photonic skyrmions using discrete-time QWs?We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics,and experimentally characterize DQPTs and emergent skyrmion structures.Our results pave the way for realizing quantum mechanical PT-synthetic devices and augurs exciting possibilities for exploring topological properties of non-Hermitian systems using discretetime QWs.