Reverse engineering of a Hamiltonian by designing the evolution operators

TL;DR

This paper introduces a flexible scheme for reverse engineering Hamiltonians by designing evolution operators, enabling practical realization and robustness against decoherence, demonstrated through a Rydberg atom example.

Contribution

The scheme extends transitionless quantum driving by focusing on specific states and offers greater flexibility with additional free parameters.

Findings

Scheme is faster and more robust than existing methods.

Numerical simulations confirm effectiveness against decoherence.

Applicable to practical quantum systems like Rydberg atoms.

Abstract

We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD) [31], the present scheme is focus on only one or parts of moving states in a D-dimension (D > 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments