Asymmetric scattering by non-hermitian potentials

Abstract

The scattering of quantum particles by non-hermitian (generally nonlocal) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. Eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are used together with generalized unitarity relations to determine the possible and/or forbidden scattering asymmetries. Six basic device types are identified when the scattering coefficients (squared moduli of scattering amplitudes) adopt zero/one values, and transmission and/or reflection are asymmetric. They can pictorially be described as a one-way mirror, a one-way barrier (a Maxwell pressure demon), one-way (transmission or reflection) filters, a mirror with unidirectional transmission, and a transparent, one-way reflector. We design potentials for these devices and also demonstrate that the behavior of the scattering coefficients can be extended to a broad range of incident momenta.

References in corpus (12)

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Cited by in corpus (13)

• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Unitary Scattering Protected by Pseudo-Hermiticity
• Non-Hermitian invisibility in tight-binding lattices
• Coherent scattering from semi-infinite non-Hermitian potentials
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
• Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Symmetries and invariants for non-Hermitian Hamiltonians
• Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries
• Quantifying Algebraic Asymmetry of Hamiltonian Systems
• Balancing gain and loss in symmetrised multi-well potentials
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states