Abstract
We investigate the scattering properties of an anti-parity-symmetric non-Hermitian system. The anti-parity-symmetric scattering center possesses imaginary nearest-neighbor hoppings and real onsite potentials, it has been experimentally realized through dissipative coupling and frequency detuning between atomic spin waves. We find that such anti-parity-symmetric system displays three salient features: Firstly, the reflection and transmission are both reciprocal. Secondly, the reflection and transmission probabilities satisfy R+T=1 or R-T=1, which depends on the parity of the scattering center size. Thirdly, the scattering matrix satisfies (S_z)(S_z)*=I for scattering center with even-site; for scattering center with odd-site, the dynamics exhibits Hermitian scattering behavior, possessing unitary scattering matrix SS{\dag}=I.
Highlights
The concept of parity-time (PT ) symmetry has been studied for more than two decades; researchers are interested in the peculiar effects caused by PT symmetry in non-Hermitian systems [1,2,3,4,5,6,7,8,9,10,11,12]
In 2014, PT symmetry was first experimentally demonstrated in coupled optical microcavities [15]
We have investigated the scattering behavior of a PT antisymmetric non-Hermitian scattering center Hc with imaginary nearest-neighbor couplings and real on-site potentials
Summary
The concept of parity-time (PT ) symmetry has been studied for more than two decades; researchers are interested in the peculiar effects caused by PT symmetry in non-Hermitian systems [1,2,3,4,5,6,7,8,9,10,11,12]. In this paper, inspired by the experimentally realized PT antisymmetric system, we study the scattering properties of a PT -antisymmetric non-Hermitian system, which has imaginary couplings and real on-site potentials. The parity operator P is defined as the space reflection Pj P−1 = N + 1 − j ; T is defined as the time-reversal operator T iT −1 = −i Under these definitions, the scattering center Hc possesses PT antisymmetry, which satisfies (PT )Hc(PT )−1 = −Hc. Notably, it is interesting that the PT -antisymmetric Hamiltonian Hc satisfies (PT )(±iHc)(PT )−1 = ±iHc, which indicates that Hamiltonians ±iHc are PT symmetric. |1 c and |N c are the sites of the scattering center Hc that connected to the input and output leads H− and H+, respectively Is the connection Hamiltonian. |1 c and |N c are the sites of the scattering center Hc that connected to the input and output leads H− and H+, respectively
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