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

JOURNAL OF ADVANCES IN PHYSICS

Application of the Magnus and Fer expansions to a perturbative study of the time dependent Jaynes Cummings Model

T.P. Das

Published Dec 19, 2018• 0 citations
Publisher

Abstract

We apply the Magnus and Fer perturbation methods to Jaynes Cummings Model (JCM) with linear time dependence and show that the perturbation methods yield results which are appreciably close to the results obtained by Wei-Norman method, leading to exact solution when the Hamiltonian under consideration is an element of su(2), thus making the perturbation methods important for Hamiltonians for which a method of exact solution is not available.

DOI
10.24297/jap.v15i0.7965

Related papers

Exploring the Solvability of the Jaynes-Cummings and Jaynes-Cummings-like Models: Implementing Quantum Control

Austen Couvertier

In this paper we aim to explore the dynamics and overall solvability of the Jaynes-Cummings \& Jaynes-Cummings-Like models. As a lens to understand these dynamics, we focused on cases where the parameters of the system were made time-dependent. All previous work on solving the dynamics of the Jaynes-Cummings models has relied heavily on the use of differential methods and setting the parameters as time-independent constants which were zero or one. To account for this, we utilized the Wei-Norman method which allowed us to analytical solve the time-dependent Hamiltonian. Through the use of this method, we can understand the more general characteristics of the dynamics associated with the Jaynes-Cummings model. This research related back to the field of Quantum information and control as the model highlights interactions with qubits and our time-dependent parameters can force certain transitions.

•Jan 1, 2017•0 citations

An analytically solvable time-dependent Jaynes-Cummings model

Ananda Dasgupta

Using the underlying SU (2) algebra of the Jaynes-Cummings model, we construct a time-dependent interaction term that allows analytical solution for even off-resonance conditions. Exact solutions for the time evolution of any state have been found. The effect of detuning on the Rabi oscillations and the collapse and revival of inversion is indicated. It is also shown that at resonance, the time-dependent Jaynes-Cummings model is analytically solvable for an arbitrary interaction term.

arXiv:quant-ph/9808004•Journal of Optics B Quantum and Semiclassical Optics•Jan 1, 1999•16 citations

An operational perspective on the Magnus–Fer conundrum in time-dependent quantum mechanics

Kuntal Mukherjee, Shreyan Ganguly, Ramesh Ramachandran

The development of analytic methods for studying quantum systems driven by periodic Hamiltonians has remained an active pursuit for gaining insights into physical phenomena in spectroscopy and other related areas in chemical physics. From a theoretical perspective, the success of a given analytic method relies on the operational aspects as well as its exactness in replicating (known) experimental results. While analytic methods built around the Magnus expansion (ME) scheme have been preferred in time-evolution studies, the splitting of the time-propagator into a product of exponential operators in the Fer expansion (FE) scheme has gained wider attention in recent years. To this end, the operational advantages of one scheme over the other have always remained contentious and form the basis for the present report. Employing periodic Hamiltonians as examples, the operational aspects and the relative merits/demerits of the two methods are analyzed, and their long-term/short-term behavior is discussed through analytic expressions in experimentally verifiable systems.

The Journal of Chemical Physics•Apr 2, 2025•0 citations

QUASI-EXACTLY SOLVABLE APPROACH TO THE JAYNES–CUMMINGS MODEL WITHOUT ROTATION WAVE APPROXIMATION

N. Debergh, A. B. Klimov

The Jaynes–Cummings model (JCM) is studied in the frame of methods of quasi-exactly solvable problems. First, we apply these methods to the JCM under RWA and anti-RWA approximations and then, we analyze the possibility of solving the whole model.

International Journal of Modern Physics A•Sep 30, 2001•5 citations

Convergence of the Magnus expansion

Francisco Marcelo Fernández

The convergence of the Magnus expansion in the Schr\"odinger representation is investigated with the aid of two exactly solvable models. A baffling observation regarding the dynamics of a spin-(1/2 system driven by a superposition of a constant and a rotating magnetic field is elucidated. Perturbation theory is applied to the exponential solution to the Schr\"odinger equation for a time-dependent harmonic oscillator. The first terms of the perturbation expansion for the singularity of the exponent are exactly calculated. The scope and limitations of perturbation theory in obtaining the range of validity of the Magnus expansion are discussed.

Physical Review A•Mar 1, 1990•31 citations

Revisiting the applications of Floquet–Magnus and Fer expansion approaches in physics and solid-state NMR

Eugene Stephane Mananga, Thibault Charpentier

In this paper, we revisit, from different perspectives, the applications of Floquet–Magnus expansion (FME) and Fer expansion (FE) in NMR and physics. We use these expansion schemes for the calculation of effective Hamiltonians and propagators. We found that the FME is related to the FE. While both approaches are powerful methods, there are subtle differences between them. To understand the differences, we performed explicit calculation on various problems, namely, Bloch–Siegert shift, Cross Polarization (CP) and Continuous Waves (CW). We put the work in a prospect that is related to spin physics in order to make the calculation more general. As the propagator from the FME takes the form of the evolution operator, which removes the constraint of a stroboscopic observation, we appreciated the effects of time-evolution under Hamiltonians with different orders separately.

International Journal of Modern Physics B•Jul 24, 2018•5 citations
We apply the Magnus and Fer perturbation methods to Jaynes Cummings Model (JCM) with linear time dependence and show that the perturbation methods yield results which are appreciably close to the results obtained by Wei-Norman method, leading to exact solution when the Hamiltonian under consideration is an element of su(2), thus making the perturbation methods important for Hamiltonians for which a method of exact solution is not available.
In this paper we aim to explore the dynamics and overall solvability of the Jaynes-Cummings \& Jaynes-Cummings-Like models. As a lens to understand these dynamics, we focused on cases where the parameters of the system were made time-dependent. All previous work on solving the dynamics of the Jaynes-Cummings models has relied heavily on the use of differential methods and setting the parameters as time-independent constants which were zero or one. To account for this, we utilized the Wei-Norman method which allowed us to analytical solve the time-dependent Hamiltonian. Through the use of this method, we can understand the more general characteristics of the dynamics associated with the Jaynes-Cummings model. This research related back to the field of Quantum information and control as the model highlights interactions with qubits and our time-dependent parameters can force certain transitions.
The development of analytic methods for studying quantum systems driven by periodic Hamiltonians has remained an active pursuit for gaining insights into physical phenomena in spectroscopy and other related areas in chemical physics. From a theoretical perspective, the success of a given analytic method relies on the operational aspects as well as its exactness in replicating (known) experimental results. While analytic methods built around the Magnus expansion (ME) scheme have been preferred in time-evolution studies, the splitting of the time-propagator into a product of exponential operators in the Fer expansion (FE) scheme has gained wider attention in recent years. To this end, the operational advantages of one scheme over the other have always remained contentious and form the basis for the present report. Employing periodic Hamiltonians as examples, the operational aspects and the relative merits/demerits of the two methods are analyzed, and their long-term/short-term behavior is discussed through analytic expressions in experimentally verifiable systems.
The convergence of the Magnus expansion in the Schr\"odinger representation is investigated with the aid of two exactly solvable models. A baffling observation regarding the dynamics of a spin-(1/2 system driven by a superposition of a constant and a rotating magnetic field is elucidated. Perturbation theory is applied to the exponential solution to the Schr\"odinger equation for a time-dependent harmonic oscillator. The first terms of the perturbation expansion for the singularity of the exponent are exactly calculated. The scope and limitations of perturbation theory in obtaining the range of validity of the Magnus expansion are discussed.
In this paper, we revisit, from different perspectives, the applications of Floquet–Magnus expansion (FME) and Fer expansion (FE) in NMR and physics. We use these expansion schemes for the calculation of effective Hamiltonians and propagators. We found that the FME is related to the FE. While both approaches are powerful methods, there are subtle differences between them. To understand the differences, we performed explicit calculation on various problems, namely, Bloch–Siegert shift, Cross Polarization (CP) and Continuous Waves (CW). We put the work in a prospect that is related to spin physics in order to make the calculation more general. As the propagator from the FME takes the form of the evolution operator, which removes the constraint of a stroboscopic observation, we appreciated the effects of time-evolution under Hamiltonians with different orders separately.