Dicke States for Accelerated Two Two-Level Atoms

TL;DR

The paper investigates how Dicke states arise for two uniformly accelerated two-level atoms in the right Rindler wedge by modeling their interaction with a massless scalar field in a perturbative framework. It derives analytic one- and two-excitation amplitudes, identifying symmetric $|s⟩$ and antisymmetric $|a⟩$ Dicke components with excitation probabilities $P_s$ and $P_a$ that display the Unruh thermal factor $(e^{2π ω c / a}-1)^{-1}$ and spatial interference via separation $d$. The results extend to $N$ atoms, showing the single-excitation probability scales as $N$ times the single-atom result, and reveal joint excitation probabilities and two-photon emission amplitudes $eta_{LL}$, $eta_{RR}$, and $eta_{RL}$ that shape the final Dicke-basis state. These findings illuminate how acceleration and the Unruh effect influence collective atomic excitations, contributing to relativistic quantum information theory and enabling future exploration of diverse non-inertial configurations and field types.

Abstract

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.

Figures (3)

• Figure 1: Two atoms are moving with constant acceleration $a$ along z-axis.
• Figure 2: Initial maximum probability shows the constructive interference for the symmetric state while the blue curve determines the destructive interference for the anti-symmetric state. The parameters are $k=2\pi/\lambda$, atom-field coulping constant $\chi=10MHz$, photon frequency $\nu=0.1\omega$ and transition frequency $\omega= 1GHz$.
• Figure 3: Dicke States of two two-level atoms. The ground state $\vert b\rangle$ has both atoms in the ground state, initially. The next state has one atom excited which generates the maximally entangled symmetric $\vert s\rangle$ and anti-symmetric $\vert a\rangle$ states. This process continues until both atoms are excited $\vert e\rangle$.