A Parafermionic Generalization of the Jaynes Cummings Model

TL;DR

This paper introduces a parafermionic extension of the Jaynes Cummings model, analyzing its thermodynamic behavior and crossover phenomena, including deformations like q-oscillators, revealing complex superradiance-like effects.

Contribution

It presents a novel parafermionic generalization of the Jaynes Cummings Hamiltonian and explores its semiclassical and deformed variants, uncovering new crossover behaviors.

Findings

Single crossover in bosonic number operator with standard parafermions.

Multiple crossovers in deformed (q-)oscillator cases, up to k(F-1).

Phenomenology similar to k-atoms superradiance observed.

Abstract

We introduce a parafermionic version of the Jaynes Cummings Hamiltonian, by coupling $k$ Fock parafermions (nilpotent of order $F$) to a 1D harmonic oscillator, representing the interaction with a single mode of the electromagnetic field. We argue that for $k=1$ and $F\leq 3$ there is no difference between Fock parafermions and quantum spins $s=\frac{F-1}{2}$. We also derive a semiclassical approximation of the canonical partition function of the model by assuming $\hbar$ to be small in the regime of large enough total number of excitations $n$, where the dimension of the Hilbert space of the problem becomes constant as a function of $n$. We observe in this case an interesting behaviour of the average of the bosonic number operator showing a single crossover between regimes with different integer values of this observable. These features persist when we generalize the parafermionic Hamiltonian by deforming the bosonic oscillator with a generic function $\Phi(x)$; the $q-$deformed bosonic oscillator corresponds to a specific choice of the deformation function $\Phi$. In this particular case, we observe at most $k(F-1)$ crossovers in the behavior of the mean bosonic number operator, suggesting a phenomenology of superradiance similar to the $k-$atoms Jaynes Cummings model.