  Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and
natural sciences. In the classical limit the dipoles can be described as
damped-driven oscillators, which are able to spontaneously synchronize and
collectively lock their phases. Here we investigate the correspond- ing
phenomenon in the quantum regime with arrays of quantized two-level systems
coupled via long-range and anisotropic dipolar interactions. Our calculations
demonstrate that the dipoles may overcome the decoherence induced by quantum
fluctuations and inhomogeneous couplings and evolve to a synchronized
steady-state. This steady-state bears much similarity to that observed in
classical systems, and yet also exhibits genuine quantum properties such as
quantum correlations and quan- tum phase diffusion (reminiscent of lasing). Our
predictions could be relevant for the development of better atomic clocks and a
variety of noise tolerant quantum devices.
