Dicke superradiance in ordered lattices: dimensionality matters

Abstract

Many-body superradiance in ordered atomic arrays is a phenomenon where atomic synchronization gives rise to a burst in photon emission. This superradiant burst only occurs if there is one -or just a few -dominant decay channels. By mapping the question of whether many-body superradiance occurs into a simple algebraic equation, we demonstrate that it exists in arrays of any dimensionality, as interference in photon emission leads to the preeminence of certain channels over others. In atomic chains superradiance occurs only below a critical interatomic distance, which we derive analytically. Increasing the array dimensionality leads to a critical distance that scales with system size: sublogarithmically for 2D, and seemingly faster than that for 3D lattices. We perform calculations for both infinite and finite systems, the latter by employing a highly-efficient algorithm with a computational complexity that scales only linearly with system size, which enables us to study very large arrays. Our results provide a guide to explore this many-body phenomenon in state-of-the art experimental setups.

Superradiance and subradiance in inverted atomic arrays

“…The spacing d crit depends on the size of the array, such that larger samples can sustain superradiance at larger lattice constants. Note that these values are much lower than those reported in other references [35][36][37] and have to be understood as a very conservative estimate. This is due to the self-consistent procedure used to compute the cooperative rate Γ, which considers interactions and cooperativity to be present from the beginning.…”

“…3(a), which qualitatively matches those reported in Refs. [35][36][37]. For both phase diagrams, we obtain a critical spacing that scales as d crit ∝ √ N rad [37], as shown by the black dashed fitted curves.…”

“…As opposed to the formalism used in Refs. [35][36][37], which perfectly captures the photon emission at zero time, our method overestimates the initial cooperative effects in the array and consequently does not provide accurate estimates of the superradiant phase diagrams. However, it satisfactorily captures the mid-and long-term behavior of the atomic system.…”

“…While * orubies@mit.edu these systems have been extensively studied in the case where only one excitation is present in the lattice [27][28][29][30][31][32][33][34], the behavior of inverted lattices is poorly understood. Recent theoretical studies have shown that the appearance of the superradiant burst in inverted samples is determined by the statistics of the first two photons [35,36], or alternatively by the Taylor series expansion of the photon emission rate at time t = 0 [37]. While these methods allow to determine the superradiant phase diagram and the initial slope of the emitted radiation, they provide no information about the scaling of the superradiant peak or the nature of the subsequent time evolution.…”

“…We hereby confirm the appearance of a superradiant burst in two-dimensional and three-dimensional atomic arrays with small enough inter-particle spacing and extend the results in Refs. [35][36][37] by characterizing the scaling of the superradiant peak for both dimensionalities and by studying the long-time dynamics of the system-which exhibit a subradiant behavior.…”