Abstract
The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative properties of its spectrum, especially the differences to the Jaynes–Cummings model, which possesses a larger, continuous symmetry, can be understood in terms of the so-called “G-functions” whose zeroes yield the exact eigenvalues of the Rabi Hamiltonian. The special type of integrability appearing in systems with discrete degrees of freedom is responsible for the absence of Poissonian level statistics in the spectrum while its well-known “Juddian” solutions are a natural consequence of the structure of the G-functions. The poles of these functions are known in closed form, which allows drawing conclusions about the global spectrum.
Highlights
The spectacular success of quantum optics [1] is based to a considerable extent on the fact that the light quanta do not interact among themselves
The interaction of quantized radiation with matter is quite complicated because even the simplest model, an atomic two-level system coupled to a single radiation mode via a dipole term, does not conserve the excitation number
Even better known than the quantumRabi model (QRM) is a famous approximation to it, the Jaynes–Cummings model (JCM), H JC = ωa† a + g(σ+ a + σ− a† ) + ∆σz, (2)
Summary
The spectacular success of quantum optics [1] is based to a considerable extent on the fact that the light quanta do not interact among themselves. The interaction of quantized radiation with matter is quite complicated because even the simplest model, an atomic two-level system coupled to a single radiation mode via a dipole term, does not conserve the excitation number. Symmetry 2019, 11, 1259 itself for example in the vacuum Rabi splitting, observable if the coupling is larger than the cavity decay rates This was achieved in an experiment from 1992 with a ratio g/ω = 10−8 between dipole coupling and mode frequency [8]. The strong coupling regimes are fascinating from the viewpoint of fundamental research, because the light–matter system behaves in unexpected and sometimes counter-intuitive ways: the vacuum state contains virtual photons [20] and in the DSC the Purcell effect disappears [21] while the standard collapse and revival dynamics of the two-level system becomes dominated by the mode frequency [11]
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