Abstract
Non-Hermitian, one-dimensional potentials which are also non-local, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential imply selection rules for transmission and reflection. In particular, parity-time (PT) symmetry or the symmetry of any local potential do not allow for asymmetric transmission. We put forward a feasible quantum-optical implementation of non-Hermitian, non-local, non-PT potentials to implement different scattering asymmetries, including transmission asymmetries.
Highlights
The asymmetric response of diodes, valves, or rectifiers to input direction is of paramount importance in many different fields and technologies, from hydrodynamics to microelectronics, as well as in biological systems
This leaves us with three interesting symmetries to explore: VI, which allows for asymmetric reflection; VIII which allows for asymmetric transmission, and I, which in principle allows for arbitrary asymmetric responses, except for physical limitations imposed by the two-level model
Non-Hermitian Hamiltonians display many interesting phenomena which are impossible for a Hermitian Hamiltonian acting on the same Hilbert space
Summary
The asymmetric response of diodes, valves, or rectifiers to input direction is of paramount importance in many different fields and technologies, from hydrodynamics to microelectronics, as well as in biological systems. We expect a wealth of applications of such response asymmetries in the microscopic quantum realm, in particular, in circuits or operations carrying or processing quantum information with moving atoms. Asymmetric transmission and reflection probabilities for one-dimensional (1D) particle scattering off a potential center are not possible if the Hamiltonian is Hermitian [12,13]. Off a potential center, the different Hamiltonian symmetries imply selection rules for asymmetric transmission and reflection [26,28].1. After a lightning review of Hamiltonian symmetries and the corresponding scattering selection rules in Sec. II, we shall explain in Sec. III how to generate different NH symmetries in a quantum optical setting of an atom impinging on a laser illuminated region.
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