Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1804.03626 · Physical Review Letters

Eigenstates Transition without Undergoing an Adiabatic Process

Fatemeh Mostafavi, Luqi Yuan, Hamidreza Ramezani

Published Feb 8, 2019• 10 citations
arXivHTMLPDF

Abstract

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to a shortcut to adiabaticity (DASA). In particular, in our proposed 2×2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of eigenvalues helps us to exponentially decay the population in an undesired eigenfunction or amplify the population in the desired state while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonians have a much simpler form with a lower thermodynamic cost. Furthermore, we show that DASA can be extended to higher dimensions using the parameters associated with our 2×2 Hamiltonians. Our proposed Hamiltonians not only have application in DASA but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics.

DOI
10.1103/physrevlett.122.050404

Related papers

Dynamical approach to shortcuts to adiabaticity for general two-level non-Hermitian systems

T. Z. Luan, Jia-Zheng Sun, H. Z. Shen

Abstract In this Letter, we apply a class of general two-level non-Hermitian Hamiltonians whose off-diagonal elements are neither equal nor conjugate of each other to study the dynamical approach to shortcut to adiabaticity which is based on engineering the Hamiltonian and dynamical properties of the system to remove any unwanted probability amplitude or implant the desired probability amplitude. Using the special characteristics that one of the eigenvalues of the general two-level non-Hermitian Hamiltonian is real and the other is complex, we can decay (amplify) the population exponentially in the undesired (desired) eigenstate, and maintain the conservation of probability amplitude of the other eigenstate. Applying this approach to general two-level non-Hermitian systems, we find that the efficient population transfer can be achieved by our method, which works even in almost instantaneous manner and has a lower cost compared with the common approach of shortcut to adiabaticity.

Europhysics Letters (EPL)•May 15, 2023•5 citations

A dynamical approach to low-cost shortcut to adiabaticity

Hamidreza Ramezani, Fatemeh Mostafavi

By introducing a class of non-Hermitian Hamiltonians we propose an approach to low-cost shortcut to adiabaticity. Our approach focuses on dynamical properties of the system and has application in STIRAP, tunable mode filtering.

Frontiers in Optics•Jan 1, 2018•0 citations

Shortcuts to adiabaticity

E. Torrontegui, M. Modugno B, E D. Guéry-odelin F +4 more

Quantum adiabatic processes—that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian—are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.

•Aug 16, 2016•338 citations

Shortcuts to adiabaticity in non-Hermitian quantum systems without rotating-wave approximation

Hong Li, H. Z. Shen, S. L. Wu +1 more

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.

arXiv:1710.05129•Optics Express•Nov 16, 2017•19 citations

Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms

Ye‐Hong Chen, Yan Xia, Qi‐Cheng Wu +2 more

We propose an efficient method to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocols' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms---even only some of them---have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of fast population inversion. The results show that in both Hermitian and non-Hermitian systems, we can design different additional Hamiltonians to replace the traditional counterdiabatic driving Hamiltonian to speed up the process. This method provides many choices for designing additional terms of the Hamiltonian such that one can choose a realizable model in practice.

arXiv:1604.06301•Physical Review A•May 13, 2016•114 citations

Shortcuts to adiabaticity for non-Hermitian systems

Sara Ibañez, S. Martínez-Garaot, Xi Chen +2 more

Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on counter-diabatic (transitionless driving) algorithms or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator.

arXiv:1106.2776•Physical Review A•Aug 29, 2011•123 citations
We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to a shortcut to adiabaticity (DASA). In particular, in our proposed 2×2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of eigenvalues helps us to exponentially decay the population in an undesired eigenfunction or amplify the population in the desired state while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonians have a much simpler form with a lower thermodynamic cost. Furthermore, we show that DASA can be extended to higher dimensions using the parameters associated with our 2×2 Hamiltonians. Our proposed Hamiltonians not only have application in DASA but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics.
Abstract In this Letter, we apply a class of general two-level non-Hermitian Hamiltonians whose off-diagonal elements are neither equal nor conjugate of each other to study the dynamical approach to shortcut to adiabaticity which is based on engineering the Hamiltonian and dynamical properties of the system to remove any unwanted probability amplitude or implant the desired probability amplitude. Using the special characteristics that one of the eigenvalues of the general two-level non-Hermitian Hamiltonian is real and the other is complex, we can decay (amplify) the population exponentially in the undesired (desired) eigenstate, and maintain the conservation of probability amplitude of the other eigenstate. Applying this approach to general two-level non-Hermitian systems, we find that the efficient population transfer can be achieved by our method, which works even in almost instantaneous manner and has a lower cost compared with the common approach of shortcut to adiabaticity.
Quantum adiabatic processes—that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian—are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.
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.
We propose an efficient method to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocols' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms---even only some of them---have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of fast population inversion. The results show that in both Hermitian and non-Hermitian systems, we can design different additional Hamiltonians to replace the traditional counterdiabatic driving Hamiltonian to speed up the process. This method provides many choices for designing additional terms of the Hamiltonian such that one can choose a realizable model in practice.