Dissipation-induced bound states as a two-level system

TL;DR

This paper demonstrates that dissipation can induce the formation of stable two-level quantum systems in a tight-binding chain with imaginary potentials, offering a new approach for quantum device fabrication.

Contribution

It reveals how dissipation-induced bound states form a stable two-level system with orthogonal eigenstates that can be manipulated by external pulses.

Findings

Real parts of energy levels are equidistant and stable.

Imaginary parts are semi-negative and equidistant, indicating stability.

Evolved states converge to a superposition of two eigenstates.

Abstract

Potential wells are employed to constrain quantum particles into forming discrete energy levels, acting as artificial few-level systems. In contrast, an anti-parity-time ($\mathcal{PT}$) symmetric system can have a single pair of real energy levels, while all the remaining levels are unstable due to the negative imaginary part of the energy. In this work, we investigate the formation of bound states in a tight-binding chain induced by a harmonic imaginary potential. Exact solutions show that the real parts of energy levels are equidistant, while the imaginary parts are semi-negative definite and equidistant. This allows for the formation of an effective two-level system. For a given initial state with a wide range of profiles, the evolved state always converges to a superposition of two stable eigenstates. In addition, these two states are orthogonal under the Dirac inner product and can be mutually switched by applying a $\pi$ pulse of a linear field. Our finding provides an alternative method for fabricating quantum devices through dissipation.