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:2402.17881 · Journal of the Optical Society of America B

Supersymmetry journey from the Jaynes–Cummings to the anisotropic Rabi model

A. Kafuri, F. H. Maldonado-Villamizar, Alexander Moroz, B. M. Rodríguez-Lara

Published Apr 24, 2024• 4 citations
arXivHTMLPDF

Abstract

We revisit the Jaynes–Cummings and anti-Jaynes–Cummings model through the lens of the Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an underlying abstract supersymmetry, provided by the u (1|1) superalgebra, into concrete proper states and energies in the laboratory frame. Additionally, we explore the anisotropic Rabi model possessing an underlying supersymmetry, provided by the osp(2|2) superalgebra, in a squeezed reference frame, where it is possible to approximate its spectral characteristics by an effective Jaynes–Cummings model. Finally, we identify a regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced, double degenerate energy spectrum with a unique ground state energy. Our work aims to merge mathematical physics with practical quantum optics, underscoring the critical role of the Lie theory.

DOI
10.1364/josab.522504

Related papers

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

Exploring supersymmetry: Interchangeability between Jaynes-Cummings and anti-Jaynes-Cummings models

Ivan A. Bocanegra-Garay, Miguel Castillo-Celeita, J. Negro +2 more

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated. Published by the American Physical Society 2024

arXiv:2404.12438•Physical Review Research•Nov 27, 2024•11 citations

The supersymmetric Jaynes–Cummings model and its solutions

Abdulaziz D Alhaidari

The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.

arXiv:physics/0609022•Journal of Physics A Mathematical and General•Nov 30, 2006•5 citations

Analytical solutions for the Rabi model

Lixian Yu, Shiqun Zhu, Qifeng Liang +2 more

In this Brief Report, we present a perturbation theory that omits the weak multiphoton process to obtain analytical solutions for the Rabi model. Under this approximation, the Rabi model can be mapped into the solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, both the ground- and excited-state-energy spectrums and wave functions can be derived easily. Moreover, these explicit results agree well with the direct numerical simulation in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of the Bloch-Siegert shift in the circuit quantum electrodynamics with ultrastrong coupling can be explained perfectly. We believe that our results have potential applications in solid-state quantum-information processing.

arXiv:1203.5408•Physical Review A•Jul 12, 2012•78 citations

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

Guofeng Zhang, Han‐Jie Zhu

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

arXiv:1503.06538•Scientific Reports•Mar 4, 2015•22 citations

Dissecting the superradiant phase transition in the anisotropic Rabi model: Pattern competition and cavity-QED simulation

Yuan Qiu, Ke-Xiong Yan, Jun-Hao Lin +3 more

In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.

quant-pharXiv:2511.03207•Nov 6, 2025•0 citations
We revisit the Jaynes–Cummings and anti-Jaynes–Cummings model through the lens of the Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an underlying abstract supersymmetry, provided by the u (1|1) superalgebra, into concrete proper states and energies in the laboratory frame. Additionally, we explore the anisotropic Rabi model possessing an underlying supersymmetry, provided by the osp(2|2) superalgebra, in a squeezed reference frame, where it is possible to approximate its spectral characteristics by an effective Jaynes–Cummings model. Finally, we identify a regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced, double degenerate energy spectrum with a unique ground state energy. Our work aims to merge mathematical physics with practical quantum optics, underscoring the critical role of the Lie theory.
The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated. Published by the American Physical Society 2024
The super-algebraic structure of a generalized version of the Jaynes–Cummings model is investigated. We find that a Z 2 graded extension of the so (2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u (1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.
In this Brief Report, we present a perturbation theory that omits the weak multiphoton process to obtain analytical solutions for the Rabi model. Under this approximation, the Rabi model can be mapped into the solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, both the ground- and excited-state-energy spectrums and wave functions can be derived easily. Moreover, these explicit results agree well with the direct numerical simulation in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of the Bloch-Siegert shift in the circuit quantum electrodynamics with ultrastrong coupling can be explained perfectly. We believe that our results have potential applications in solid-state quantum-information processing.
The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.
In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.