Universal quantum control by non-Hermitian Hamiltonian

TL;DR

This paper introduces a novel approach to quantum control using non-Hermitian Hamiltonians, enabling universal, robust, and automatic normalization of quantum states in finite-dimensional systems.

Contribution

It develops a framework for universal quantum control with non-Hermitian Hamiltonians, treating system geometry and constraints equally, and demonstrates robustness and applicability to multi-level systems.

Findings

Achieves automatic normalization of target states during control.

Demonstrates robustness against parametric deviations.

Validates protocol with population transfer in two- and three-level systems.

Abstract

Conventional manipulations over quantum systems for such as coherent population trapping and unidirectional transfer focus on Hamiltonian engineering while regarding the system's manifold geometry and constraint equation as secondary causes. Here we treat them on equal footing in controlling a finite-dimensional quantum system under a time-dependent non-Hermitian Hamiltonian, which is inspired by the D'Alembert principle of regarding active force, constraint force, and inertial force in an unbiased way. Under the biorthogonal condition, the non-Hermitian Hamiltonian could be triangularized in a constraint picture spanned by a set of completed and orthonormal basis states, which is found to be a sufficient condition to construct at least one universal nonadiabatic passage in both bra and ket spaces. The passage ends up with a desired target state that is automatically normalized without artificial normalization in the existing treatments for non-Hermitian quantum systems. Moreover, the passage is found to be robust against the parametric deviation when the real part of its global phase is rapidly varying with time. Our protocol is explicitly verified for the perfect population transfer in the two-level system and the chiral population transfer in the three-level system. It generalizes our framework of universal quantum control to the field of the biorthogonal quantum mechanics.