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Wave packet methods in cavity QED

Jonas Larson

Published Aug 5, 2013• 2 citations
OpenAlex

Abstract

Abstract. The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, reminiscent of coupled bound electronic potential curves of diatomic molecules. Using the knowledge of such models, this approach of the problem gives new insight of the dynamics. The effect of the rotating wave approximation is discussed. The collapse-revival phenomenon is especially analyzed in a non-standard manner. Extensions of the method is briefly mentioned in terms of a three-level atom and the Dicke model. 1.

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Wave packet methods in cavity QED

Jonas Larson

The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, reminiscent of coupled bound electronic potential curves of diatomic molecules. Using the knowledge of such models, this approach of the problem gives new insight of the dynamics. The effect of the rotating wave approximation is discussed. The collapse-revival phenomenon is especially analyzed in a non-standard manner. Extensions of the method is briefly mentioned in terms of a three-level atom and the Dicke model.

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Exact Solution for Phenomenon of atomic Collapse and Revival under Rotating Wave and Anti-Rotating Wave Approximation

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An accurate method to solve the Jaynes—Cummings (J—C) Hamiltonian has been investigated here. The phenomenon of atomic collapse and revival predicted by Jaynes—Cummings model is demonstrated. Solutions are consistent with the precious such as using the operator method. Furthermore, the Jaynes—Cummings Hamiltonian including the anti-rotating term is also solved precisely using this accurate way so that results agree with experiments better. Essences of the anti-rotating term are revealed. We discuss the relations of the phenomenon of atomic collapse and revival with the average photons number, the light field phase angle, the resonant frequency, and the size of coupling constant. The discussions may make one select suitable conditions to carry out experiment well and study the virtual light field effect on cavity quantum electrodynamics.

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Jorge Casanova, Guillermo Romero, Ion Lizuain +2 more

We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω≳1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wave packets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.

arXiv:1008.1240•Physical Review Letters•Dec 20, 2010•535 citations
Abstract. The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, reminiscent of coupled bound electronic potential curves of diatomic molecules. Using the knowledge of such models, this approach of the problem gives new insight of the dynamics. The effect of the rotating wave approximation is discussed. The collapse-revival phenomenon is especially analyzed in a non-standard manner. Extensions of the method is briefly mentioned in terms of a three-level atom and the Dicke model. 1.
The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, reminiscent of coupled bound electronic potential curves of diatomic molecules. Using the knowledge of such models, this approach of the problem gives new insight of the dynamics. The effect of the rotating wave approximation is discussed. The collapse-revival phenomenon is especially analyzed in a non-standard manner. Extensions of the method is briefly mentioned in terms of a three-level atom and the Dicke model.
By using a wave packet approach, this paper reviews the Jaynes-Cummings model with and without the rotating wave approximation in a non-standard way. This gives new insight, not only of the two models themselves, but of the rotating wave approximation as well. Expressing the models by field quadrature operators, instead of the typically used boson ladder operators, wave packet simulations are presented. Several known phenomena of these systems, such as collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed and explained in this new picture, either in an adiabatic or diabatic frame. The harmonic shape of the potential curves that the wave packets evolve on and the existence of a level crossing make these results interesting in a broader sense than only for models in quantum optics, especially in atomic and molecular physics.
By using a wavepacket approach, this paper reviews the Jaynes–Cummings model with and without the rotating wave approximation (RWA) in a non-standard way. This gives new insight, not only of the two models themselves, but of the RWA as well. Expressing the models by field quadrature operators, instead of the typically used boson ladder operators, wavepacket simulations are presented. Several known phenomena of these systems, such as collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed and explained in this new picture, either in an adiabatic or diabatic frame. The harmonic shape of the potential curves that the wavepackets evolve on and the existence of a level crossing make these results interesting in a broader sense not only for models in quantum optics, but especially in atomic and molecular physics.
This paper numerically studies the Jaynes-Cummings model with and without the rotating wave approximation in a non-standard way. Expressing the models with field quadrature operators, instead of the typically used boson ladder operators, a wave packet propagation approach is applied. The obtained evolved wave packets are then used to calculate various quantities, such as, Rabi oscillations, squeezing and entanglement. Many of the phenomenon can be explained from the wave packet evolution, either in the adiabatic or diabatic frames. Different behaviours of the two models are discussed.
An accurate method to solve the Jaynes—Cummings (J—C) Hamiltonian has been investigated here. The phenomenon of atomic collapse and revival predicted by Jaynes—Cummings model is demonstrated. Solutions are consistent with the precious such as using the operator method. Furthermore, the Jaynes—Cummings Hamiltonian including the anti-rotating term is also solved precisely using this accurate way so that results agree with experiments better. Essences of the anti-rotating term are revealed. We discuss the relations of the phenomenon of atomic collapse and revival with the average photons number, the light field phase angle, the resonant frequency, and the size of coupling constant. The discussions may make one select suitable conditions to carry out experiment well and study the virtual light field effect on cavity quantum electrodynamics.
We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω≳1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wave packets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.