Local controllability of generalized quantum mechanical systems

Minh Q. Phan, HERSCHEL A. RABITZ

This paper presents a general self-guided algorithm for direct laboratory learning of controls to manipulate quantum-mechanical systems. The primary focus is on an algorithm based on the learning of a linear laboratory input–output map from a sequence of controls, and their observed impact on the quantum-mechanical system. This map is then employed in an iterative fashion, to sequentially home in on the desired objective. The objective may be a target state at a final time, or a continuously weighted observational trajectory. The self-guided aspects of the algorithm are based on implementing a cost functional that only contains laboratory-accessible information. Through choice of the weights in this functional, the algorithm can automatically stay within the bounds of each local linear map and indicate when a new map is necessary for additional iterative improvement. Finally, these concepts can be generalized to include the possibility of employing nonlinear maps, as well as just the laboratory control instrument settings, rather than observation of the control itself. An illustrative simulation of the concepts is presented for the control of a four-level quantum system.

Sonia G. Schirmer, I. C. H. Pullen, A. I. Solomon

TZYH JONG TARN, John W. Clark, Garng M. Huang

Salvatore De Martino, Silvio De Siena, Fabrizio Illuminati

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.

Gabriel Turinici, HERSCHEL A. RABITZ

Qi Zhang, Xi Chen, David Guéry-Odelin

With the advent of quantum technologies, control issues are becoming increasingly important. In this paper, we address control in phase space under a global constraint provided by a minimal energylike cost function and a local (in Fourier space) constraint resulting from a robustness criterion. The inverse-engineering Lagrangian formalism developed here generalizes the formalism commonly used to describe the superoscillation phenomenon. It is applied to both nondissipative and dissipative quantum mechanics, and extended to stochastic thermodynamics. Interestingly, our approach also allows one to improve sensing capabilities by appropriate control of the system.