Ensemble control of n-level quantum systems with a scalar control

TL;DR

This paper presents a control strategy for steering finite-dimensional n-level quantum systems between eigenstates using bilinear control, spectral gap conditions, and approximations, with numerical validation.

Contribution

It introduces an explicit control law for quantum state manipulation under spectral gap and dispersion conditions, combining rotating wave and adiabatic approximations.

Findings

Control law effectively achieves population inversion.

Spectral gap and dispersion conditions are critical for success.

Numerical tests confirm the theoretical conditions' sharpness.

Abstract

In this paper we discuss how a general bilinear finite-dimensional closed quantum system with dispersed parameters can be steered between eigenstates. We show that, under suitable conditions on the separation of spectral gaps and the boundedness of parameter dispersion, rotating wave and adiabatic approximations can be employed in cascade to achieve population inversion between arbitrary eigenstates. We propose an explicit control law and test numerically the sharpness of the conditions on several examples.