Shortcuts to adiabaticity with general two-level non-Hermitian systems

• URL: http://arxiv.org/abs/2404.08202v1
• Date: Fri, 12 Apr 2024 02:15:07 GMT
• Title: Shortcuts to adiabaticity with general two-level non-Hermitian systems
• Authors: T. Z. Luan, H. Z. Shen, X. X. Yi,
• Abstract summary: Adiabaticity is a fast process which reproduces the same final state as the adiabatic process in a finite or even shorter time. We propose a shortcuts to adiabaticity technique which is based on a transitionless quantum driving algorithm. We show that the general Hamiltonian the off-diagonal elements of which are not conjugate to each other can be implemented in many physical systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent years, but they are barely explored for general non-Hermitian systems where off-diagonal elements of the Hamiltonian are not Hermitian. In this paper, we propose a shortcuts to adiabaticity technique which is based on a transitionless quantum driving algorithm to realize population transfer for general two-level non-Hermitian systems and give both exact and approximate analytical solutions of the corresponding counteradiabatic driving Hamiltonian, where the latter can be extended to the zeroth-order and first-order terms by applying perturbative theory. We find that the first-order correction term is different from the previous results, which is caused by the non-Hermiticity of the off-diagonal elements. We work out an exact expression for the control function and present examples consisting of a general two-level system with gain and loss to show the theory. The results suggest that the high-fidelity population transfer can be implemented in general non-Hermitian systems by our method, which works even with strong non-Hermiticity and without rotating wave approximation. Furthermore, we show that the general Hamiltonian the off-diagonal elements of which are not conjugate to each other can be implemented in many physical systems with the present experimental technology, such as an atom-light interaction system and whispering-gallery microcavity, which might have potential applications in quantum information processing.

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