Full spectrum of the Rabi model

Abstract

It is shown that in the Rabi model, for an integer value of the spectral parameter $x$, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the parameters of the problem are zeros of a certain transcendental function; in other words, there are infinitely many possible choices of parameters for which integer $x$ belongs to the spectrum. Morover, it is shown that the classical Judd eigenstates appear as degenerate cases of the confluent Heun function.Comment: 7 pages, 4 figure

Two-photon Rabi model: analytic solutions and spectral collapse

“…This is possible if the exceptional solution is not Juddian (doubly-degenerate) [32,33,34]. We shall see that also the opposite occurs: an energy level above the first pole for small g crosses the zeroth baseline at g 0 and lies below the first pole for g > g 0 .…”

A continued fraction based approach for the Two-photon Quantum Rabi Model

“…We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model. arXiv:1807.08674v2 [quant-ph] 30 Apr 2019 pansion in the basis of Heun functions, have also been proposed [20,21]. Among the many generalizations of the QRM, the Two-photon Quantum Rabi Model (2γQRM) is of particular interest.…”

The quantum Rabi model: solution and dynamics

“…The reader is also referred to the compact treatment given in [43], in which the confluent Heun functions appear naturally around the relevant singularities. As far as we are aware, the first mention of confluent Heun functions in the context of the quantum Rabi model was by D. Braak (see [41]).…”

“…Therefore the energy spectrum of the quantum Rabi model can also be obtained with the Wronskian method [42,43]. Indeed, the above Wronskians can be written in terms of the confluent Heun functions.…”

“…Subsequently this condition was reproduced via Bogoliubov transformation [41]. It was further found that the analytic solution for the quantum Rabi model can be given in terms of confluent Heun functions [42,43], with the well-known Judd isolated exact solutions [44] appearing naturally as ‡ For an early review of JC physics, the reader is referred to [7] (see also [8,9]). § One further regime is defined by the limit ω = 0, which is the relativistic Dirac regime [10].…”