Prof Dieter Jaksch

Abstract:

Understanding spatial and temporal order in many-body systems is a key challenge, particularly in out-of-equilibrium settings. A major hurdle is developing controlled model systems to study these phases. We propose an experiment with a driven quantum gas coupled to a dissipative optical cavity, realizing a non-equilibrium phase diagram featuring both spatial and temporal order. The system’s control parameter is the detuning between the drive frequency and cavity resonance. Negative detunings yield a spatially ordered phase, while positive detunings produce phases with both spatial order and persistent oscillations, forming dissipative spatio-temporal lattices. We also identify a phase where the dynamics dephase, leading to chaotic behavior. Numerical and analytical evidence supports these superradiant phases, showing that the spatio-temporal lattice originates from cavity dissipation. The atoms experience accelerated transport, either via uniform acceleration or abrupt momentum transitions. Our work provides insights into temporal phases of matter not possible at equilibrium.

Abstract:

Predicting the dynamics of turbulent fluids has been an elusive goal for centuries. Even with modern computers, anything beyond the simplest turbulent flows is too chaotic and multiscaled to be directly simulatable. An alternative is to treat turbulence probabilistically, viewing flow properties as random variables distributed according to joint probability density functions (PDFs). Such PDFs are neither chaotic nor multiscale, yet remain challenging to simulate due to their high dimensionality. Here, we overcome the dimensionality problem by encoding turbulence PDFs as highly compressed "tensor networks" (TNs). This enables single CPU core simulations that would otherwise be impractical even with supercomputers: for a 5 + 1 dimensional PDF of a chemically reactive turbulent flow, we achieve reductions in memory and computational costs by factors of [Formula: see text] and [Formula: see text], respectively, compared to standard finite-difference algorithms. A future path is opened toward something heretofore thought infeasible: directly simulating high-dimensional PDFs of both turbulent flows and other chaotic systems that can usefully be described probabilistically.