Non-Hermitian Hamiltonian for a modulated Jaynes-Cummings model withPTsymmetry

Abstract

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic rc-excitation subspace obey the same equations of motion that can be obtained from a static non-Hermitian Jaynes-Cummings Hamiltonian with V T symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of V T symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudobosons and pseudofermions, and discuss relevant mathematical and physical aspects.

Resonance Dipole-Dipole Interaction Between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

“…Changes in the spontaneous emission rate [20,[27][28][29] or in the Lamb shift of single uniformly accelerating atoms [21,22], as well as the dispersion Casimir-Polder interaction between a uniformly accelerated atom and a reflecting plate [30][31][32][33][34] or between two uniformly accelerated atoms [35,36], have been investigated, and their relation with the Unruh effect was discussed. The effect of non-equilibrium boundaries on radiative properties of atoms has been also considered [37,38].Another, albeit related, problem, recently addressed in the literature, concerns the equivalence between acceleration and temperature. For example, it has been discussed that non-thermal features (related to a uniform acceleration) manifest in the dispersion (van der Waals/Casimir-Polder) and resonance interaction between non inertial atoms in the free-space [25,26,36,39].…”

A concise review of pseudobosons, pseudofermions, and their relatives

“…This makes the situation more complicated since, in this case, neither U(z) nor V (z) are bounded, in general, at least when z = 0. Still, in [13], we have found conditions for the vectors 11) to be well defined in C. The vectors (ϕ(z), Ψ(z)) are called bi-coherent states, for the reason that will appear clear soon. This, of course, only means that ϕ 0 belongs to the domain of U(z), ϕ 0 ∈ D(U(z)), and that Ψ 0 ∈ D(V (z)), for all z ∈ C. This was proven under some assumptions on the norms of ϕ n and Ψ n :…”

“…We refer to [1] for several applications to physics of this framework, one of which is briefly reviewed in Section II.2. Other and more recent applications can be found in [10,11,12].…”

A description of pseudo-bosons in terms of nilpotent Lie algebras

“…which is non-abelian by the presence of nontrivial relations like [v4 , v 2 ] = −i sin 2θ v, and [v3 , v 2 ] = cos 2θ v. Due to (5.7) and (5.9), it is clear that a + b = s. On the other hand, a ∩ b = Z(s) shows that the condition (iii) of Definition 2.1 is not satisfied. Therefore (i) and (ii) follow.We proceed to show (iii).…”