Spontaneous formation of persistent square pattern in a driven superfluid

The emergence of patterns from simple physical laws belongs to the most striking topics in natural science. In particular, the spontaneous formation of structures from an initially homogeneous state can eventually lead to stable, non-homogeneous states of matter. Here we report on the spontaneous formation of square lattice patterns in a rotationally symmetric and driven Bose-Einstein condensate, confined in a two-dimensional box potential with absorptive boundaries. The drive is realized by globally modulating the two-particle interaction periodically in time. After a primary phase of randomly oriented stripes that emerge as a consequence of the Faraday instability, we observe the subsequent formation of persistent square lattice patterns in the highly occupied regime, where phonon-phonon interactions become relevant. We show theoretically that this state can be understood as an attractive fixed point of coupled nonlinear amplitude equations. Establishing the existence of this fixed point opens the perspective for engineering new, highly correlated states of matter in driven superfluids.Comment: 9 pages, 5 figure

Square Pattern Formation as Stable Fixed Point in Driven Two-Dimensional Bose-Einstein Condensates

We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by temporal periodic modulation of the interatomic interaction. Temporal modulation of the interaction causes the so-called Faraday instability in the condensate, which we show generically leads to a stable square grid density pattern. We take the amplitudes in each of the two directions spanning the two-dimensional density pattern as order parameters in pattern formation and derive a set of simultaneous time evolution equations for those order parameters from the Gross--Pitaevskii (GP) equation with a time-periodic interaction. We identify the fixed points of the time evolution and show by stability analysis that the inhomogeneous density exhibits a square grid pattern as a stable fixed point.Comment: 7 pages, 3 figures. Supplemental material: 9 page

Bose-Einstein condensate experiment as a nonlinear block of a machine learning pipeline

Physical systems can be used as an information processing substrate and, with that, extend traditional computing architectures. For such an application, the experimental platform must guarantee pristine control of the initial state, the temporal evolution, and readout. All these ingredients are provided by modern experimental realizations of atomic Bose-Einstein condensates. By embedding a quantum gas experiment in a machine learning pipeline, one can represent nonlinear functions while only linear operations on classical computers of the pipeline are necessary. We demonstrate successful regression and interpolation of a nonlinear function using an elongated cloud of potassium atoms and characterize the performance of our system