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arXiv:1611.01304 · Physical Review A

Non-Hermitian interferometer: Unidirectional amplification without distortion

C. Li, L. Jin, Z. Song

Published Feb 24, 2017• 25 citations
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Abstract

A non-Hermitian interferometer can realize asymmetric transmission in the presence of imaginary potential and magnetic flux. Here, we propose a non-Hermitian dimer with an unequal hopping rate by an interferometerlike cluster in the framework of a tight-binding model. The intriguing features of this design are the wave-vector independence and unidirectionality of scattering, which amplify the wave packet without distortion and absorb the incoherent wave without reflection. The absorption relates to the system spectral singularities. The dynamical behaviors of the spectral singularities are also investigated analytically and numerically.

DOI
10.1103/physreva.95.022125

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A non-Hermitian interferometer can realize asymmetric transmission in the presence of imaginary potential and magnetic flux. Here, we propose a non-Hermitian dimer with an unequal hopping rate by an interferometerlike cluster in the framework of a tight-binding model. The intriguing features of this design are the wave-vector independence and unidirectionality of scattering, which amplify the wave packet without distortion and absorb the incoherent wave without reflection. The absorption relates to the system spectral singularities. The dynamical behaviors of the spectral singularities are also investigated analytically and numerically.
We study the possibility of asymmetric transmission induced by a non-Hermitian scattering center embedded in a one-dimensional waveguide, motivated by the aim of realizing quantum diodes in a non-Hermitian system. It is shown that a PT\mathcal{PT}PT-symmetric non-Hermitian scattering center always has symmetric transmission although the dynamics within the isolated center can be unidirectional, especially at its exceptional point. We propose a concrete scheme based on a flux-controlled non-Hermitian scattering center, which comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm flux. The analytical solution shows that such a complex scattering center acts as a diode at the resonant energy level of the spectral singularity, exhibiting perfect unidirectionality of the transmission. The connections between the phenomena of the asymmetric transmission and reflectionless absorption are also discussed.
The scattering of quantum particles by non-Hermitian (generally non-local) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. After extending the concept of symmetry for non-Hermitian potentials, eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are found. Together with generalized unitarity relations they determine selection rules for 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 pictorically 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.
We investigate the scattering properties of a parity-time-antisymmetric non-Hermitian system. The parity-time-antisymmetric scattering center possesses imaginary nearest-neighbor hoppings and real on-site potentials; it has been experimentally realized through dissipative coupling and frequency detuning between atomic spin waves. We find that such parity-time-antisymmetric system displays three salient features: First, the reflection and transmission are both reciprocal. Second, the reflection and transmission probabilities satisfy $R\ifmmode\pm\else\textpm\fi{}T=1$, which depends on the parity of the scattering center size. Third, the scattering matrix satisfies $\left(S{\ensuremath{\sigma}}_{\mathrm{z}}\right){\left(S{\ensuremath{\sigma}}_{\mathrm{z}}\right)}^{*}=I$ for a scattering center with an even site; for a scattering center with an odd site, the dynamics exhibits Hermitian scattering behavior, possessing unitary scattering matrix $S{S}^{\ifmmode\dagger\else\textdagger\fi{}}=I$.
The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied.The static properties of the model have been much studied; the complex spectrum, skin effect and its topological interpretation, etc. Effects of disorder and interparticle interaction, especially, when they coexist, may be less understood.Here, we will also focus on its dynamical properties and reveal some unique features in the wave-packet and entanglement (entropy) dynamics.For that some latest (original) results based on improved numerics (with this a system of larger system size L becomes accessible) are shown.
Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of scattering states. In practice, any physically realistic, spatially localized wave packet will generally have a nonzero overlap with the system's bound states, thereby violating this premise. While this violation is inconsequential in Hermitian systems, it can invalidate the conventional scattering picture in their non-Hermitian counterparts. The underlying cause is the emergence of time-growing bound states, which manifest as poles of the scattering matrix (SSS matrix) in the first quadrant of the complex wave-number plane. Any initial overlap with these states becomes exponentially amplified, eventually dominating the long-time dynamics. Consequently, the actual evolution of a wave packet diverges dramatically from the conventional scattering picture, rendering the transmission and reflection coefficients derived from time-independent scattering methods unphysical. Using tight-binding models with non-Hermiticity introduced via imaginary on-site potentials or asymmetric hopping, we demonstrate that parameter regimes supporting such growing states are common. We therefore conclude that an analysis of SSS-matrix poles is an indispensable step to confirm the physical relevance of time-independent scattering calculations in non-Hermitian systems.
We study the effect of PT\mathcal{PT}PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system. It is observed that the spectral singularity always occurs at $k=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ for a wide range of fluxes and imaginary potentials. Critical behavior associated with the physics of the spectral singularity is also investigated. It is demonstrated that the quasispectral singularity corresponds to a transmission maximum and the transmission phase jumps abruptly by $\ensuremath{\pi}$ when the system is swept through this point. Moreover, we find that there exists a pulselike phase lapse when the imaginary potential approaches the boundary value of the spectral singularity.