Collectively pair-driven-dissipative bosonic arrays: exotic and self-oscillatory condensates

Modern quantum platforms such as superconducting circuits provide exciting opportunities for the experimental exploration of driven-dissipative many-body systems in unconventional regimes. One of such regimes occurs in bosonic systems, where nowadays one can induce driving and dissipation through pairs of excitations, rather than the conventional single-excitation processes. Moreover, modern platforms can be driven in a way in which the modes of the bosonic array decay collectively rather than locally, such that the pairs of excitations recorded by the environment come from a coherent superposition of all sites. In this work we analyze the superfluid phases accessible to bosonic arrays subject to these novel mechanisms more characteristic of quantum optics, which we prove to lead to remarkable spatiotemporal properties beyond the traditional scope of pattern formation in condensed-matter systems or nonlinear optics alone. We show that, even in the presence of residual local loss, the system is stabilized into an exotic state with bosons condensed along the modes of a closed manifold in Fourier space, with a distribution of the population among these Fourier modes that can be controlled via a weak bias (linear) drive. This gives access to a plethora of different patterns, ranging from periodic and quasi-periodic ones with tunable spatial wavelength, to homogeneously-populated closed-Fourier-manifold condensates that are thought to play an important role in some open problems of condensed-matter physics. Moreover, we show that when any residual local linear dissipation is balanced with pumping, new constants of motion emerge that can force the superfluid to oscillate in time, similarly to the mechanism behind the recently discovered superfluid time crystals. We propose specific experimental implementations with which this rich and unusual spatiotemporal superfluid behavior can be explored.