Abstract An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model.Abstract An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model.

Journal of Physics A Mathematical and TheoreticalJan 10, 20171 citation

Entanglement resonance in the asymmetric quantum Rabi model

Yuqing Shi, Lei Cong, Hans-Peter Eckle

We investigate the entanglement features in the interacting system of a quantized optical field and a two-level system which is statically driven, known as the asymmetric quantum Rabi model (AsymQRM). Intriguing entanglement resonance valleys with the increase of the photon-atom coupling strength and peaks with the increase of the driving amplitude are found. It is revealed that both of these two kinds of entanglement resonance are caused by the avoided level crossing of the associated eigenenergies. In sharp contrast to the quantum Rabi model, the entanglement of the AsymQRM collapses to zero in the strong coupling regime except when the driving amplitude is equal to $m\ensuremath{\omega}/2$, with $m$ being an integer and $\ensuremath{\omega}$ being the photon frequency. Our analysis demonstrates that such entanglement reappearance is induced by the hidden symmetry of the AsymQRM. Supplying an insightful understanding of the AsymQRM, our results will be helpful in exploring the hidden symmetry and in preparing photon-atom entanglement in light-matter coupled systems.We investigate the entanglement features in the interacting system of a quantized optical field and a two-level system which is statically driven, known as the asymmetric quantum Rabi model (AsymQRM). Intriguing entanglement resonance valleys with the increase of the photon-atom coupling strength and peaks with the increase of the driving amplitude are found. It is revealed that both of these two kinds of entanglement resonance are caused by the avoided level crossing of the associated eigenenergies. In sharp contrast to the quantum Rabi model, the entanglement of the AsymQRM collapses to zero in the strong coupling regime except when the driving amplitude is equal to $m\ensuremath{\omega}/2$, with $m$ being an integer and $\ensuremath{\omega}$ being the photon frequency. Our analysis demonstrates that such entanglement reappearance is induced by the hidden symmetry of the AsymQRM. Supplying an insightful understanding of the AsymQRM, our results will be helpful in exploring the hidden symmetry and in preparing photon-atom entanglement in light-matter coupled systems.

arXiv:2109.12277Physical Review AJun 27, 202220 citations

Entanglement Measures and Their Properties in Quantum Field Theory

Stefan Hollands, Ko Sanders

arXiv:1702.04924SpringerBriefs in mathematical physicsJan 1, 201885 citations

m

being an integer and $\ensuremath{\omega}$ being the photon frequency. Our analysis demonstrates that such entanglement reappearance is induced by the hidden symmetry of the AsymQRM. Supplying an insightful understanding of the AsymQRM, our results will be helpful in exploring the hidden symmetry and in preparing photon-atom entanglement in light-matter coupled systems.