Universal perspective on nonadiabatic quantum control

TL;DR

This paper introduces a universal control framework for nonadiabatic quantum control, enabling stable, fast state transitions and unifying various existing methods through an ancillary picture approach.

Contribution

It develops a novel, universal control framework using an ancillary picture that unifies multiple quantum control techniques and applies to finite-dimensional systems.

Findings

Framework reduces to known control methods under certain conditions

Enables cyclic transfer of system populations

Provides a full-rank time-evolution operator for finite systems

Abstract

A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path is also fundamental to the exact solution of the time-dependent Schr\"odinger equation. We construct a universal control framework using an ancillary picture, in which the time-dependent Hamiltonian can be diagonalized. Multiple desired paths can be derived by the von Neumann equation for parametric ancillary projection operators. No transition exists among the ancillary basis states during the time evolution. Under various conditions, our control framework reduces to the nonadiabatic holonomic transformation, the Lewis-Riesenfeld theory for invariants, and counterdiabatic driving methods. In addition, it is applicable to the cyclic transfer of system populations that could be a hard problem for existing methods. Our work can provide a full-rank time-evolution operator for a time-dependent quantum system with a finite number of dimensions.