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

International Journal of Theoretical Physics

Lewis-Riesenfeld Invariants in Two-level Quantum System Without the Rotating-Wave Approximation

Hong Li, Siqi Zhang, Meixuan Li, Xiaohan Liu

Published Oct 16, 2020• 3 citations
Publisher
DOI
10.1007/s10773-020-04621-y

Related papers

Invariant‐Based Pulse Design for Three‐Level Systems Without the Rotating‐Wave Approximation

Yi‐Hao Kang, Ye‐Hong Chen, Bi‐Hua Huang +2 more

Abstract In this paper, a scheme is put forward to design pulses which drive a three‐level system based on the reverse engineering with Lewis‐Riesenfeld invariant theory. The scheme can be applied to a three‐level system even when the rotating‐wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.

arXiv:1705.08591•Annalen der Physik•Jul 12, 2017•14 citations

Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation

C. J. Gan, H. Zheng

arXiv:0907.1180•The European Physical Journal D•Jul 2, 2010•64 citations

Dynamics of a driven open double two-level system and its entanglement generation

Wei Ma, X. L. Huang, S. L. Wu

We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant. Therefore, different driving protocols associated with corresponding Lewis-Riesenfeld invariants result in different open system dynamics and symmetries. In particular, we show that since the instantaneous steady state of the driven double two-level system is one of eigenstates of the Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse engineering method based on the Lewis-Riesenfeld invariants has a good performance in rapidly preparing the quantum state of open quantum systems. As an example, a perfect entangled state is generated by means of the inverse engineering method.

arXiv:2304.07959•Physical Review A•Mar 10, 2023•3 citations

On the ground state in rotationally invariant quantum systems

A Galindo, R. Tarrach

Annals of Physics•Feb 1, 1987•5 citations

Quantum dynamics of two-level system

M. Kira, S. W. Koch

Cambridge University Press eBooks•Nov 17, 2011•0 citations

Driven Markovian master equation based on the Lewis-Riesenfeld-invariant theory

S. L. Wu, X. L. Huang, X. X. Yi

We derive a Markovian master equation for driven open quantum systems based on the Lewis-Riesenfeld-invariants theory, which is available for arbitrary driving protocols. The role of the Lewis-Riesenfeld invariants is to help us bypass the time-ordering obstacle in expanding the propagator of the free dynamics, such that the Lindblad operators in our driven Markovian master equation can be determined easily. We also illustrate that, for the driven open quantum systems, the spontaneous emission and the thermal excitation induce the transitions between eigenstates of the Lewis-Riesenfeld invariant, but not the system Hamiltonian's. As an example, we present the driven Markovian master equation for a driven two-level system coupled to a heat reservoir. By comparing to the exactly solvable models, the availability of the driven Markovian master equation is verified. Meanwhile, the adiabatic limit and inertial limit of the driven Markovian master equation are also discussed, which result in the same Markovian master equations as those presented before in the corresponding limits.

arXiv:2304.07956•Physical Review A•Nov 29, 2022•9 citations
Abstract In this paper, a scheme is put forward to design pulses which drive a three‐level system based on the reverse engineering with Lewis‐Riesenfeld invariant theory. The scheme can be applied to a three‐level system even when the rotating‐wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.
We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant. Therefore, different driving protocols associated with corresponding Lewis-Riesenfeld invariants result in different open system dynamics and symmetries. In particular, we show that since the instantaneous steady state of the driven double two-level system is one of eigenstates of the Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse engineering method based on the Lewis-Riesenfeld invariants has a good performance in rapidly preparing the quantum state of open quantum systems. As an example, a perfect entangled state is generated by means of the inverse engineering method.
We derive a Markovian master equation for driven open quantum systems based on the Lewis-Riesenfeld-invariants theory, which is available for arbitrary driving protocols. The role of the Lewis-Riesenfeld invariants is to help us bypass the time-ordering obstacle in expanding the propagator of the free dynamics, such that the Lindblad operators in our driven Markovian master equation can be determined easily. We also illustrate that, for the driven open quantum systems, the spontaneous emission and the thermal excitation induce the transitions between eigenstates of the Lewis-Riesenfeld invariant, but not the system Hamiltonian's. As an example, we present the driven Markovian master equation for a driven two-level system coupled to a heat reservoir. By comparing to the exactly solvable models, the availability of the driven Markovian master equation is verified. Meanwhile, the adiabatic limit and inertial limit of the driven Markovian master equation are also discussed, which result in the same Markovian master equations as those presented before in the corresponding limits.