Search Results (7)

We propose a versatile electronic dimer cooperatively coupled by means of mutual induction, capacitance, and resistance. In a lot of related works, the electronic dimer is inductively coupled, with one resonator characterized by positive resistance (dissipation) and the other by negative resistance (amplification). We go beyond this picture by considering capacitive and resistive coupling, and by exploring cases where both resistances are positive, as well as a case where the resonant frequencies of the individual resonators are different. Based on analytical derivation and numerical calculations, we obtain and observe the properties of parity-time (PT), quasi-PT (QPT) and quasi-anti-PT (QAPT) symmetry by adjusting the constitutive parameters of the system. This study provides a versatile and feasible platform for observing PT/anti-PT (APT) symmetry-based phenomena and provides a foundation for further studies on finding PT/APT symmetry in more sophisticated circuits. Full article

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-$\phi$-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices. Full article

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided. Full article

The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time ($\mathcal{PT}$) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry–Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-$\mathcal{PT}$-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-$\mathcal{PT}$-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-$\mathcal{PT}$-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry–Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-$\mathcal{PT}$-symmetric system and the design of associated bidirectional response prototype devices. Full article

Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future. Full article

We investigate the coherent perfect absorption laser points (CPA-LPs) in anti-parity–time-symmetric photonic crystals. CPA-LPs, which correspond to the poles of reflection and transmission, can be found in the parameter space composed of gain–loss factor and angular frequency. Discrete exceptional points (EPs) split as the gain–loss factor increases. The CPA-LPs sandwiched between the EPs are proved to be defective modes. The localization of light field and the bulk effect of gain/loss in materials induce a sharp change in phase of the reflection coefficient near the CPA-LPs. Consequently, a large spatial Goos–Hänchen shift, which is proportional to the slope of phase, can be achieved around the CPA-LPs. The study may find great applications in highly sensitive sensors. Full article

As an extension of the class of nonlinear $\mathcal{PT}$ -symmetric models, we propose a system of sine-Gordon equations, with the $\mathcal{PT}$ symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively. Full article