Potential-controlled filtering in quantum star graphs

TL;DR

This paper introduces a tunable quantum spectral filter based on potential-controlled scattering in star graphs with special couplings, enabling adjustable passbands and multi-mode operation.

Contribution

It presents a novel design for quantum filters using Fülöp–Tsutsui couplings, with controllable transmission properties influenced by external potentials, and discusses physical realization methods.

Findings

Identified special couplings for potential-controlled transmission.

Designed a tunable quantum band-pass filter with adjustable passbands.

Proposed physical implementation using simple graphs with δ potentials.

Abstract

We study the scattering in a quantum star graph with a F\"ul\"op--Tsutsui coupling in its vertex and with external potentials on the lines. We find certain special couplings for which the probability of the transmission between two given lines of the graph is strongly influenced by the potential applied on another line. On the basis of this phenomenon we design a tunable quantum band-pass spectral filter. The transmission from the input to the output line is governed by a potential added on the controlling line. The strength of the potential directly determines the passband position, which allows to control the filter in a macroscopic manner. Generalization of this concept to quantum devices with multiple controlling lines proves possible. It enables the construction of spectral filters with more controllable parameters or with more operation modes. In particular, we design a band-pass filter with independently adjustable multiple passbands. We also address the problem of the physical realization of F\"ul\"op--Tsutsui couplings and demonstrate that the couplings needed for the construction of the proposed quantum devices can be approximated by simple graphs carrying only $\delta$ potentials.