A Parafermionic Generalization of the Jaynes Cummings Model

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 $F\le 3$ 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 $\hslash$ 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.

to appear on J.Phys. A

References in corpus (2)

• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Cited by in corpus (1)

• The quantum Rabi model: solution and dynamics