Inverse techniques and evolution of systems

Jean-Louis Basdevant

Marco Enríquez, Alfonso Jaimes-Nájera

Abstract The dynamics of a two-level system interacting with a new class of analytically solvable driving fields is analyzed. Such fields are obtained using an inverse-engineering approach, which allows to exactly factorize the correspondent time-evolution operator via the Wei-Norman theorem. This technique is presented as an algorithm and using an example we show that the free parameters involved can be used to tune some aspects of the dynamics on demand such as the atomic population inversion.

T. Kiran, M. Ponmurugan

In general, the conventional Lewis-Riesenfeld invariant-based inverse engineering is a nonadiabatic process that results in the adiabatic final states to achieve the shortcut to adiabaticity, which does not provide complete suppression of non-adiabaticity throughout the evolution. We propose a new method to accomplish the shortcut to adiabaticity through an entirely adiabatic path. This new method is developed using the number operator as an invariant of the Hamiltonian. This paper discusses the mathematical framework of the new method in two-level quantum system and analyzes its performance compared to the conventional Lewis-Riesenfeld invariant-based inverse engineering method.

Jean-Louis Basdevant

W. Peier

Shuo‐Yen Tseng

Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.