Eigenstate Tracking in Open Quantum Systems

TL;DR

This paper develops a systematic approach for tracking eigenstates in open quantum systems using control pulses, enabling faster adiabatic evolution without explicit counter-diabatic driving, and demonstrating robustness across various control signals.

Contribution

It introduces a projection theory-based method for transitionless evolution in open quantum systems, providing an alternative to traditional adiabatic control and analyzing its effectiveness with different control signals.

Findings

Eigenstate tracking is effective with various control signals.

The method maintains the system in the desired eigenstate during evolution.

Effectiveness is largely independent of control signal details.

Abstract

Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well established solution, but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to shortcuts to adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.