Electric Circuits for the Investigation of Non-Hermitian Lattice Physics

A general paradigm within quantum mechanics is that a system’s Hamiltonians are described by Hermitian operators. However, this description fails to explain the non-unitary evolution of quantum states observed experimentally. An alternative approach to quantum mechanics that fixes this problem and eventually accounts for a simple form of coupling to the environment is based on the so-called non-Hermitian Hamiltonians [1], where non-Hermitian Hamiltonian operators are used. This approach gives rise to a new set of fascinating phenomena. One of these is the non-Hermitian skin effect. Here, a piling of the system eigenstates is observed on the boundary of a finite-size system. This phenomenon breaks one of the important pillars of topological lattice physics, the bulk-boundary correspondence. It is possible to realize classical electric circuits that mimic one- and two-dimensional non-Hermitian lattice Hamiltonians [2]. In this project, we will investigate how to implement a circuit mimicking the non-Hermitian implementation of the diamond chain [3].

[1] Bergholtz et al., Rev. Mod. Phys. 93, 015005 (2021).
[2] Liu et al., Research 5608038 (2021).
[3] Martinez et al., Adv Quantum Technol. 2300225 (2023).