Directional Superradiance in a Driven Ultracold Atomic Gas in Free Space

Ultra-cold atomic systems are among the most promising platforms that have the potential to shed light on the complex behavior of many-body quantum systems. One prominent example is the case of a dense ensemble illuminated by a strong coherent drive while interacting via dipole-dipole interactions. Despite being subjected to intense investigations, this system retains many open questions. A recent experiment carried out in a pencil-shaped geometry reported measurements that seemed consistent with the emergence of strong collective effects in the form of a ``superradiant'' phase transition in free space, when looking at the light emission properties in the forward direction. Motivated by the experimental observations, we carry out a systematic theoretical analysis of the system's steady-state properties as a function of the driving strength and atom number, N. We observe signatures of collective effects in the weak drive regime, which disappear with increasing drive strength as the system evolves into a single-particle-like mixed state comprised of randomly aligned dipoles. Although the steady-state features some similarities to the reported superradiant to normal non-equilibrium transition, also known as cooperative resonance fluorescence, we observe significant qualitative and quantitative differences, including a different scaling of the critical drive parameter (from N to N). We validate the applicability of a mean-field treatment to capture the steady-state dynamics under currently accessible conditions. Furthermore, we develop a simple theoretical model that explains the scaling properties by accounting for interaction-induced inhomogeneous effects and spontaneous emission, which are intrinsic features of interacting disordered arrays in free space.