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:2111.05091 · New Journal of Physics

Comment on ‘Parameter-dependent unitary transformation approach for quantum Rabi model’

Daniel Braak, Murray T. Batchelor, Qing‐Hu Chen

Published May 1, 2022• 0 citations
arXivHTMLPDF

Abstract

Abstract We discuss the elementary errors in Zhang’s (2021 New J. Phys. 23 093014) claimed exact solution of the quantum Rabi model. The erroneous solution is seen to be nothing more than the combined solution of the simpler Jaynes–Cummings and anti-Jaynes–Cummings models obtained by neglecting terms in the model Hamiltonian.
DOI
10.1088/1367-2630/ac6c44

Related papers

Eigenvalues and Eigenstates of Quantum Rabi Model

Andrei V. Ivanov

The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to the need for the theoretical description of the interaction of a two-level system with a quantum oscillator in the case when the rotating wave approximation fails. In this Letter, we present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. This approach is based on the properties of the Pauli operators and allows us to readily solve the stationary Schrodinger equation for a two-level system. First, we demonstrate the applicability of the approach to the Jaynes-Cummings Hamiltonian to get the well-known solution. Then, we obtain the eigenvalues and eigenstates for the quantum Rabi Hamiltonian using the proposed approach. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.

arXiv:2104.12771•Apr 26, 2021•0 citations

An approach to the time-dependent Jaynes-Cummings model without the rotating wave approximation

Jian Qi Shen

This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way.

arXiv:quant-ph/0311140•Nov 20, 2003•1 citation

The anisotropic quantum Rabi model with diamagnetic term

Jorge Andres Anaya-Contreras, I. Ramos-Prieto, Arturo Zúñiga-Segundo +1 more

We employ a squeeze operator transformation approach to solve the anisotropic quantum Rabi model that includes a diamagnetic term. By carefully adjusting the amplitude of the diamagnetic term, we demonstrate that the anisotropic Rabi model with the A2 term can be exactly reduced to either a Jaynes-Cummings or an anti-Jaynes-Cummings model without requiring any approximations.

arXiv:2501.17986•Frontiers in Physics•May 13, 2025•4 citations

A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: reply to comment

B. M. Rodríguez-Lara, Francisco Soto, Alejandro Zárate Cárdenas +1 more

We regret that such a misleading comment [Opt. Express (2013)] has been made to our paper. First Lo states in his abstract that "However, the nonlinear Rabi model has already been rigorously proven to be undefined" to later recoil and use the contradictory statement "(. . . ) regarding the BS model with the counter-rotating terms (. . . ) Lo and his co-authors have proven that the model is well defined only if the coupling stregth g is smaller than a critical value gc = ω/4". While Lo focuses on the validity of the quantum optics Hamiltonians and gives a misleading assesment of our manuscript, the focus of our paper is the method to map such a set of Hamiltonians from quantum optics to photonic lattices. Our method is valid for the given class of Hamiltonians and, indeed, precaution must be exerted on the paramater ranges where those Hamiltonians are valid and where their classical simulation is feasible. These parameter ranges have to be specified in for each particular case studied. Furthermore, we gave as example the Buck-Sukumar model including counter-rotating terms which is a valid Hamiltonian for some coupling parameters.

Optics Express•Jan 17, 2014•6 citations

Comment on ‘Initial states of qubit–environment models leading to conserved quantities’

Chi‐Fai Lo

Recently, Gardas and Dajka (2013 J. Phys. A: Math. Theor. 46 235301) proposed a theoretical scheme on how to prepare a proper initial state of a composite qubit–boson system which could assure no energy exchange between the two subsystems. For illustration, they applied the proposed scheme to both the Jaynes–Cummings model and the multi-photon Rabi model. However, it has already been rigorously proven that the k -photon Rabi model for k > 2 does not have eigenstates in the Hilbert space spanned by the eigenstates of the corresponding k -photon Jaynes–Cummings model and that the two-photon Rabi model has a discrete eigenenergy spectrum with normalizable eigenstates only if the coupling strength is smaller than a critical value. Hence, the proposed theoretical scheme is not applicable to the multi-photon Rabi model.

Journal of Physics A Mathematical and Theoretical•Apr 2, 2014•1 citation

A Comment on "Algebraic approach to the Tavis-Cummings model with three modes of oscillation" [J. Math. Phys. 59, 073506 (2018)]

Viani S. Morales-Guzman, Jorge G. Hirsch

Choreño et al. [J. Math. Phys. 59, 073506 (2018)] reported analytic solutions to the resonant case of the Tavis-Cummings model, obtained by mapping it to a Hamiltonian with three bosons and applying a Bogoliubov transformation. This comment points out that the Bogoliubov transformation employed is not unitary, cannot be inverted, and cannot enforce the symmetries of the model.

arXiv:2303.04883•Mar 8, 2023•0 citations
The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to the need for the theoretical description of the interaction of a two-level system with a quantum oscillator in the case when the rotating wave approximation fails. In this Letter, we present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. This approach is based on the properties of the Pauli operators and allows us to readily solve the stationary Schrodinger equation for a two-level system. First, we demonstrate the applicability of the approach to the Jaynes-Cummings Hamiltonian to get the well-known solution. Then, we obtain the eigenvalues and eigenstates for the quantum Rabi Hamiltonian using the proposed approach. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.
This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way.
We regret that such a misleading comment [Opt. Express (2013)] has been made to our paper. First Lo states in his abstract that "However, the nonlinear Rabi model has already been rigorously proven to be undefined" to later recoil and use the contradictory statement "(. . . ) regarding the BS model with the counter-rotating terms (. . . ) Lo and his co-authors have proven that the model is well defined only if the coupling stregth g is smaller than a critical value gc = ω/4". While Lo focuses on the validity of the quantum optics Hamiltonians and gives a misleading assesment of our manuscript, the focus of our paper is the method to map such a set of Hamiltonians from quantum optics to photonic lattices. Our method is valid for the given class of Hamiltonians and, indeed, precaution must be exerted on the paramater ranges where those Hamiltonians are valid and where their classical simulation is feasible. These parameter ranges have to be specified in for each particular case studied. Furthermore, we gave as example the Buck-Sukumar model including counter-rotating terms which is a valid Hamiltonian for some coupling parameters.
Recently, Gardas and Dajka (2013 J. Phys. A: Math. Theor. 46 235301) proposed a theoretical scheme on how to prepare a proper initial state of a composite qubit–boson system which could assure no energy exchange between the two subsystems. For illustration, they applied the proposed scheme to both the Jaynes–Cummings model and the multi-photon Rabi model. However, it has already been rigorously proven that the k -photon Rabi model for k > 2 does not have eigenstates in the Hilbert space spanned by the eigenstates of the corresponding k -photon Jaynes–Cummings model and that the two-photon Rabi model has a discrete eigenenergy spectrum with normalizable eigenstates only if the coupling strength is smaller than a critical value. Hence, the proposed theoretical scheme is not applicable to the multi-photon Rabi model.