If a HamiltonianH has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT . The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian ...

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the...

In this paper a practical case of a finite periodic Parity Time chain made of resonant dielectric cylinders is considered. The paper analyzes a more general case where PT symmetry is achieved by modulating both the real and imaginary part of the material refractive index along the resonator chain. The band-structure of the finite periodic PT resonator chains is compared to infinite chains in or...

A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral features of the model, specially those concerning the role of the imaginary parameters of the couplings. Analytical results as well as some numerical examples ...

We investigate the medium effect of a parity-time (PT)-symmetric bilayer on the quantum optical properties of an incident squeezed light at zero temperature (T=0 K). To do so, we use the canonical quantization approach and describe the amplification and dissipation properties of the constituent layers of the bilayer structure by Lorentz model to analyze the quadrature squeezing of the outgoing ...

We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a parity-time (PT) symmetry in the form of a purely real spectrum of modes, we...

Abstract We propose how to achieve synthetic PT $\mathcal{PT}$ symmetry in optomechanics without using any active medium. find that harnessing the Stokes process such a system can lead emergence of exceptional point (EP), i.e., coalescing both eigenvalues and eigenvectors system. By encircling EP, ...

Optical systems combining balanced loss and gain provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity–time (PT)-symmetric Hamiltonians. Such systems can be used to create synthetic materials with properties that cannot be attained in materials having only loss or only gain. Here we report PT-symmetry breaking in coupled optical resonato...

PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of pertu...