The Phase Transition in Two-Photon Rabi Model Under Mean Field Approximation

Hu, Xianlei

doi:10.1007/s10773-019-04246-w

Cited by 7 publications

(2 citation statements)

References 29 publications

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“…Recently a number of theoretical studies on the spectral collapse [28][29][30][31][32][33][34][35][36][37][38] of the model have indeed confirmed the results and observations of Ng et al 27 . Nevertheless, our understanding of the quantum two-photon Rabi model at the critical coupling ǫ c is still very limited because current theoretical approaches (both analytical and numerical) fail in dealing with the collapse point rigorously.…”

Section: Demystifying the Spectral Collapse In Two-photon Rabi Model supporting

confidence: 58%

Demystifying the spectral collapse in two-photon Rabi model

2020

Sci Rep

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We have investigated the eigenenergy spectrum of the two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”, by means of an elementary quantum mechanics approach. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in a “Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with a potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored in a straightforward manner.

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Section: Demystifying the Spectral Collapse In Two-photon Rabi Model supporting

confidence: 58%

Demystifying the spectral collapse in two-photon Rabi model

2020

Sci Rep

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“…For instance, Felicetti et al 1,4 pointed out that a trapped-ion scheme allows one to experimentally investigate two-photon interactions in unexplored regimes of light-matter coupling, and that a circuit quantum electrodynamics scheme enables us to implement a nondipolar ultrastraong two-photon interaction between a flux qubit and a bosonic mode supported by SQUID. In spite of its simplicity, the two-photon Rabi model displays a counter-intuitive feature, namely the "spectral collapse", when the coupling strength ǫ of the light-matter interaction goes beyond a critical value ǫ c [12][13][14][15][16][17][18][19][20][21][22][23] . That is, while the model has a discrete eigenenergy spectrum for ǫ < ǫ c , no normalizable eigenstate exists in the Hilbert space spanned by the photon number states for ǫ > ǫ c .…”

Section: F Lomentioning

confidence: 99%

Spectral collapse in multiqubit two-photon Rabi model

2021

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We have shown that the smallest possible singel-qubit critical coupling strength of the N-qubit two-photon Rabi model is only 1/N times that of the two-photon Rabi model. The spectral collapse can thus occur at a more attainable value of the critical coupling. For both of the two-qubit and three-qubit cases, we have also rigorously demonstrated that at the critical coupling the system not only has a set of discrete eigenenergies but also a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in the presence of a finite potential well and a nonlocal potential. The energy difference of each qubit, which specifies both the depth of the finite potential well and the strength of the nonlocal potential, determines the number of bound states available, implying that the extent of the incomplete spectral collapse can be monitored in a straightforward manner.

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Spectral collapse in two-mode two-photon Rabi model

2021

Physica A: Statistical Mechanics and its Applications

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The Phase Transition in Two-Photon Rabi Model Under Mean Field Approximation

Cited by 7 publications

References 29 publications

Demystifying the spectral collapse in two-photon Rabi model

Demystifying the spectral collapse in two-photon Rabi model

Spectral collapse in multiqubit two-photon Rabi model

Spectral collapse in two-mode two-photon Rabi model

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