We obtain the exceptional part of the eigenspectrum of the generalised Rabi model, also known as the driven Rabi model, in terms of the roots of a set of algebraic equations. This approach provides a product form for the wavefunction components and allows an explicit connection with recent results obtained for the wavefunction in terms of truncated confluent Heun functions. Other approaches are also compared. For particular parameter values the exceptional part of the eigenspectrum consists of doubly degenerate crossing points. We give a proof for the number of roots of the constraint polynomials and discuss the number of crossing points.
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.
The asymmetric quantum Rabi model (AQRM) has a broken Z 2 symmetry, with generally a nondegenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the Z 2 -symmetric quantum Rabi model are recovered, however, without any obvious paritylike symmetry. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. Here, we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunneling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunneling.
In our recent paper (Li and Batchelor 2015 J. Phys. A: Math. Theor. 48 454005) we obtained exceptional points in the eigenspectrum of the generalized Rabi model in terms of a set of algebraic equations. We also gave a proof for the number of roots of the constraint polynomials defining these exceptional solutions as a function of the system parameters and discussed the number of crossing points in the eigenspectrum. This approach however, only covered a subset of all exceptional points in the eigenspectrum. In this addendum, we clarify the distinction between the exceptional parts of the eigenspectrum for this model and discuss the subset of exceptional points not determined in our paper.
We present a physically motivated variational wave function for the ground state of the asymmetric quantum Rabi model (AQRM). The wave function is a weighted superposition of squeezed coherent states entangled with non-orthogonal qubit states, and relies only on three variational parameters. The variational expansion describes the ground state remarkably well in almost all parameter regimes, especially with arbitrary bias. We use the variational result to calculate various relevant physical observables of the ground state, and make a comparison with existing approximations and the exact solution. The results show that the variational expansion is a significant improvement over the existing approximations for the AQRM.
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