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Journal of the European Optical Society Rapid Publications

Hermitian and non-Hermitian shortcuts to adiabaticity for fast creation of maximum coherence and beam splitting

Kai Tang, Zhengfeng Hu, Xi Chen, Chengpu Liu

Published Jul 11, 2020• 3 citations
Publisher

Abstract

Abstract We theoretically exploit the shortcuts to adiabaticity (STA) technique in Hermitian and non-Hermitian quantum systems to realize the maximum coherence and beam splitting by eliminating the nonadiabatic coupling. Compared with the conventional adiabatic passage (AP) technique with the Gaussian and Allen-Eberly schemes, the operation time can be significantly shortened by three order using STA technique. This STA-based fast creation of maximum coherence or beam splitting are in use ranging from quantum sensing and metrology in a noisy environment to optical gain/loss coupled waveguides in an analogous fashion.

DOI
10.1186/s41476-020-00139-2

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Abstract We theoretically exploit the shortcuts to adiabaticity (STA) technique in Hermitian and non-Hermitian quantum systems to realize the maximum coherence and beam splitting by eliminating the nonadiabatic coupling. Compared with the conventional adiabatic passage (AP) technique with the Gaussian and Allen-Eberly schemes, the operation time can be significantly shortened by three order using STA technique. This STA-based fast creation of maximum coherence or beam splitting are in use ranging from quantum sensing and metrology in a noisy environment to optical gain/loss coupled waveguides in an analogous fashion.
The technique of shortcuts to adiabaticity (STA) has attracted broad attention due to their possible applications in quantum information processing and quantum control. However, most studies published so far have been only focused on Hermitian systems under the rotating-wave approximation (RWA). In this paper, we propose a modified shortcuts to adiabaticity technique to realize population transfer for a non-Hermitian system without RWA. We work out an exact expression for the control function and present examples consisting of two-and three-level systems with decay to show the theory. The results suggest that the shortcuts to adiabaticity technique presented here is robust for fast passages. We also find that the decay has small effect on the population transfer in the three-level system. To shed more light on the physics behind this result, we reduce the quantum three-level system to an effective two-level one with large detunings. The shortcuts to adiabaticity technique of effective two-level system is studied. Thereby the high-fidelity population transfer can be implemented in non-Hermitian systems by our method, and it works even without RWA.
Motivated by the progress on shortcuts to adiabaticity, we propose three schemes for speeding up (fractional) stimulated Raman adiabatic passage, and achieving rapid and non-adiabatic creation and transfer of maximal coherence in a triple-quantum-dot system. These different but relevant protocols, designed from counter-diabatic driving, dress-state method, and resonant technique, require their own pumping fields, applied gate voltages and varying tunneling couplings between two spatially separated dots. Such fast and reliable shortcuts not only allow for feasibly experimental realization in solid-state architectures but also may have potential applications in quantum information processing and quantum control.
We propose a non-Hermitian generalization of stimulated Raman adiabatic passage (STIRAP), which allows one to increase speed and fidelity of the adiabatic passage. This is done by adding balanced imaginary (gain and loss) terms in the diagonal (bare energy) terms of the Hamiltonian and choosing them such that they cancel exactly the nonadiabatic couplings, providing in this way an effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed Gaussian-shaped pulses in the counterintuitive scheme the imaginary terms of the Hamiltonian turn out to be time independent. A possible physical realization of non-Hermitian STIRAP, based on light transfer in three evanescently coupled optical waveguides, is proposed.
Abstract It is still a challenge to experimentally realize shortcuts to adiabaticity (STA) for a non‐Hermitian quantum system since a non‐Hermitian quantum system's counterdiabatic driving Hamiltonian contains some unrealizable auxiliary control fields. In this paper, we relax the strict condition in constructing STA and propose a method to redesign a realizable supplementary Hamiltonian to construct non‐Hermitian STA. The redesigned supplementary Hamiltonian can be eithersymmetric or asymmetric. For the sake of clearness, we apply this method to an Allen‐Eberly model as an example to verify the validity of the optimized non‐Hermitian STA. The numerical simulation demonstrates that a ultrafast population inversion could be realized in a two‐level non‐Hermitian system.
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.