Quantum formalism adapted to radiation in a coherent field

A. Ben‐Reuven, Yitzhak Rabin

The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.

Masahiro Morikawa

We derive dissipative effective Hamiltonian for the unstable Lee model without any ad hoc coarse graining procedure. Generalized radiative corrections, utilizing the in-in formalism of quantum field theory, automatically yield irreversibility as well as the decay of quantum coherence. Especially we do not need to extend the ordinary Hilbert space for describing the intrinsically dissipative system if we use the generalized in-in formalism of quantum field theory.

Albert Einstein

Luis Fernando Quezada, Guo-Qing Zhang, A. Martín-Ruiz +1 more

In this work, we use a deformed version of the Heisenberg-Weyl algebra in the Dicke Model to incorporate a Kerr medium and nonlinear interaction between matter and radiation fields. The deformed algebra allows us to define two distinct nonlinear coherent states for the radiation field. These coherent states, along with the conventional Heisenberg-Weyl coherent states and their symmetry-adapted versions, are employed as trial variational states in the energy-surface minimisation method. The obtained results reveal that the Kerr medium introduces a delay in reaching the super-radiant region, with the delay becoming more pronounced as the nonlinear parameter increases. To evaluate the different approaches, we analyse the behavior of the critical coupling, ground-state energy, entropy of entanglement between matter and radiation, and fidelity between the numerical solution and the symmetry-adapted solution. We find that one particular deformed coherent state outperforms the other trial states in approximating the ground state of the system, providing an accurate description of the critical behavior in the proposed nonlinear model.

Albert Einstein