Dynamic transition from insulating state to eta-pairing state in a composite non-Hermitian system

TL;DR

This paper investigates a non-Hermitian Hubbard system where a dynamic transition from an insulating state to an eta-pairing state occurs via probability flow, with the transition speed influenced by the exceptional point's order.

Contribution

It introduces a novel non-Hermitian system model demonstrating a controlled transition to eta-pairing states, highlighting the role of exceptional points in quantum dynamics.

Findings

Transition speed depends on the order of the exceptional point.

The scheme's fidelity is robust against lattice irregularities.

The transition involves probability flow from subsystem A to B.

Abstract

The dynamics of Hermitian many-body quantum systems has long been a challenging subject due to the complexity induced by the particle-particle interactions. In contrast, this difficulty may be avoided in a well-designed non-Hermitian system. The exceptional point (EP) in a non-Hermitian system admits a peculiar dynamics: the final state being a particular eigenstate, coalescing state. In this work, we study the dynamic transition from a trivial insulating state to an {\eta}-pairing state in a composite non-Hermitian Hubbard system. The system consists of two subsystems, A and B, which are connected by unidirectional hoppings.We show that the dynamic transition from an insulating state to an {\eta}-pairing state occurs by the probability flow from A to B: the initial state is prepared as an insulating state of A, while B is left empty. The final state is an {\eta}-pairing state in B but empty in A. Analytical analyses and numerical simulations show that the speed of relaxation of the off-diagonal long-range order pair state depends on the order of the EP, which is determined by the number of pairs and the fidelity of the scheme is immune to the irregularity of the lattice.