Energy landscape and conical intersection points of the driven Rabi model

Abstract

We examine the energy surfaces of the driven Rabi model, also known as the biased or generalised Rabi model, as a function of the coupling strength and the driving term. The energy surfaces are plotted numerically from the known analytic solution. The resulting energy landscape consists of an infinite stack of sheets connected by conical intersection points located at the degenerate Juddian points in the eigenspectrum. Trajectories encircling these points are expected to exhibit a nonzero geometric phase.

Symmetry of asymmetric quantum Rabi models

“…Using this Z 2 -symmetry, D. Braak [3] has shown the integrability of the quantum Rabi model in 2011. In the present paper, we study the spectrum of the following asymmetric quantum Rabi model [34] (called "generalized" quantum Rabi model in [3,19], "biased" in [2] and "driven" in [21]) with broken Z 2 -symmetry. This asymmetric model provides actually a more realistic description of circuit QED experiments employing flux qubits than the QRM itself [24]: H ǫ Rabi = ωa † a + ∆σ z + gσ x (a † + a) + ǫσ x .…”

Generalized adiabatic approximation to the quantum Rabi model

“…The corresponding constraint polynomials and their properties have been explored in detail [31,37,39]. We expect the present GAA can approximate the AQRM and, importantly, recover the conical intersections in the spectrum [40].…”

General symmetry operators of the asymmetric quantum Rabi model

“…Theoretically, the AQRM does not possess any obvious symmetry. So the observed double degeneracy in the asymmetric model is certainly due to unknown hidden symmetries, which have attracted a lot of attentions in the past decade [11][12][13][14][15][16][17][18][19][20][21]. On the other hand, since the AQRM is ubiquitous in the modern solid devices, many celebrated properties described in conventional quantum optics, where the static bias is usually lacking, would appear in the artificial superconducting qubit setups if the hidden symmetry is generated by manipulating the static bias.…”