Analytical solution for the anisotropic Rabi model: effects of counter-rotating terms

Scientific Reports
Guofeng Zhang, Hanjie Zhu

Abstract

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.

References

Jan 15, 2011·Physical Review Letters·J CasanovaE Solano
Oct 11, 2011·Physical Review Letters·D Braak
Jun 7, 2013·Physical Review Letters·H S NguyenJ Bloch

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Citations

Mar 16, 2019·Scientific Reports·Gangcheng WangKang Xue

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Software Mentioned

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