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We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from the mean-field equations, we explain the emergence of chaos by way of quasiperiodicity -- presence of two or more incommensurate frequencies. This is known as the Ruelle-Takens-Newhouse route to chaos. The equations of motion have a $mathbb{Z}_{2}$-symmetry with respect to the interchange of the two ensembles. However, some of the attractors of these equations spontaneously break this symmetry. To understand the emergence and subsequent properties of various attractors, we concurrently study the mean-field trajectories, Poincar{e} sections, maximum and conditional Lyapunov exponents, and power spectra. Using Floquet analysis, we show that quasiperiodicity is born out of non $mathbb{Z}_{2}$-symmetric oscillations via a supercritical Neimark-Sacker bifurcation. Changing the detuning between the level spacings in the two ensembles and the repump rate results in the synchronization of the two chaotic ensembles. In this regime, the chaotic intensity fluctuations of the light radiated by the two ensembles are identical. Identifying the synchronization manifold, we understand the origin of synchronized chaos as a tangent bifurcation intermittency of the $mathbb{Z}_{2}$-symmetric oscillations. At its birth, synchronized chaos is unstable. The interaction of this attractor with other attractors causes on-off intermittency until the synchronization manifold becomes sufficiently attractive. We also show coexistence of different phases in small pockets near the boundaries.
We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two paramet
We study nonlinear cavity arrays where the particle relaxation rate in each cavity increases with the excitation number. We show that coherent parametric inputs can drive such arrays into states with commensurate filling that form non-equilibrium ana
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped non
We discuss a hybrid quantum system where a dielectric membrane situated inside an optical cavity is coupled to a distant atomic ensemble trapped in an optical lattice. The coupling is mediated by the exchange of sideband photons of the lattice laser,
We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population of the cav