Nonreciprocal and nonconservative forces on binary systems of identical atoms

TL;DR

The article analyzes a binary of identical two-level atoms prepared with a single excitation, focusing on time-dependent radiative dynamics, directional emission, and internal forces. Using a strong laser drive and a time-dependent QED framework with Green tensors, it derives closed-form expressions for the system's time evolution, emission spectrum, and both conservative and non-conservative forces, revealing nonreciprocal, oscillatory internal forces and a corresponding momentum exchange with the electromagnetic field. The work shows that spontaneous emission becomes directionally biased and that a net internal force arises, with momentum conservation maintained by the field; it also provides an estimate for a potentially observable center-of-mass displacement in Li Rydberg binaries, on the order of $120\,\mathrm{nm}$ over a lifetime. These results pave the way for experimental tests in strongly coupled, degenerate atomic systems and highlight measurable momentum exchanges between light and matter in a minimal quantum-optical setting.

Abstract

The dynamical and radiative features of an excited system of two identical atoms are analysed. The metastability of the system, the directionality of its emission and its internal forces are studied. Closed-form expressions are derived for the time-evolution of the system, for the angular distribution of its spontaneous emission, and for its internal dipole forces, both conservative and nonconservative. The latter reveals the presence of nonreciprocal forces, which leads to a net oscillatory force upon the system. We estimate that, for a free binary system of Li Rydberg atoms, the net internal force may cause a displacement of its center of mass as large as $120 nm$ over a lifetime.

Figures (12)

• Figure 1: Pictorial illustration of the initial setup of the system.
• Figure 2: Diagrammatic representation of the self-interaction processes contributing to the incoherent attenuation of the $\mathbb{U}_{0}(t)$ element $|A_+\rangle\langle A_+|$ with a factor $e^{-\Gamma_{0}t/2}$. Analogous diagrams hold for the element $|B_+\rangle\langle B_+|$. Note also that $\omega_{0}$ appears here implicitly 'dressed' by the Lamb-shift generated by the same sequence of self-interaction processes.
• Figure 3: Diagrammatic representation of the resonant processes (i.e, RWA) of the laser action upon atom $A$. The contribute to the $\widetilde{\mathbb{U}}_{A}$ elements $|A_+\rangle\langle A_-|$ [(a)] and $|A_-\rangle\langle A_-|$ elements [(b)], respectively. The laser photons appear depicted by dashed lines. We omit non-interacting laser photons.
• Figure 4: Diagrammatic representation of the resonant processes of the interatomic interaction which contribute to $\mathbb{U}_{B_{+}}$, in which an odd number of single photons is exchanged between both atoms. The action of the laser at the bottom of each diagram is equivalent to the sudden excitation approximation in the strong laser coupling regime.
• Figure 5: Diagrammatic representation of the resonant processes of the interatomic interaction which contribute to $\mathbb{U}_{A_{+}}$, in which an even number of single photons is exchanged between both atoms. The action of the laser at the bottom of each diagram is equivalent to the sudden excitation approximation in the strong laser coupling regime. The dashed arrows at the bottom of each diagram stands for the quasi-sadden excitation of atom $A$ by the action of the external laser.