Dicke States for Accelerated Two Two-Level Atoms

We explore the formation of Dicke states. A system consisting of two two-level atoms located in the right Rindler wedge, has investigated to determine the conditions under which the superradiant or subradiant state can be formed. The dynamics of N two-level atoms forming symmetric state has also been analyzed and showed that the probability to excite any one atom of a collection of N atoms is related to the probability of exciting a single atom. We derive the analytical expression for the joint excitation probability which demonstrates the the interference effect. These findings provide new insights into the behavior of quantum systems in non-inertial frames and contribute to the broader understanding of relativistic quantum information theory.

💡 Research Summary

The paper investigates how Dicke states—collective symmetric (super‑radiant) and antisymmetric (sub‑radiant) superpositions—emerge when two identical two‑level atoms undergo uniform acceleration in the right Rindler wedge and interact with a massless scalar field. Starting from the Rindler trajectories for each atom, the authors write the atom‑field interaction Hamiltonian in terms of the atomic lowering/raising operators and the field operator evaluated along the worldlines. The initial state is taken as both atoms in the ground state and the field in the Minkowski vacuum.

Using time‑ordered perturbation theory, the evolution operator is expanded to first and second order in the coupling constant χ. The first‑order term describes the excitation of a single atom together with the emission of a single photon. By evaluating the relevant integrals, the authors obtain analytic expressions for the probability amplitudes of creating the symmetric state |s⟩=(|e₁g₂⟩+|g₁e₂⟩)/√2 and the antisymmetric state |a⟩=(|e₁g₂⟩−|g₁e₂⟩)/√2. The amplitudes contain a phase factor e^{ikd_i} that depends on the spatial separation d between the atoms, and a thermal factor (e^{2π ωc/a}−1)^{-1} that originates from the Unruh temperature T_U=ℏa/2πck_B. Consequently, the excitation probabilities are

P_s ∝ cos²(kd/2) ·