CAREER: New Algorithms to Simulate Ultracold Matter Out of Equilibrium and Redefine the Low-Temperature Frontier

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Understanding and controlling the dynamics of quantum systems which are out of equilibrium is a fundamental challenge for science in the 21st century. Systems which are not in equilibrium display phenomena that "break the rules" that govern equilibrium phases. Such phenomena are intrinsically interesting and potentially useful for applications. Gases that have been cooled to nano-Kelvin temperatures provide an exciting new platform for the study of non-equilibrium systems. Experiments with ultracold gases flexibly manipulate and image matter using unique and precise tools provided by optics. While such experiments are rapidly advancing, new theoretical techniques are also needed to aid the investigations. This project will develop numerical algorithms to solve a range of previously intractable, experimentally important problems. The new algorithms will be used to design experimental schemes to cool ultracold matter to even lower temperatures (a grand challenge of the field), thereby redefining the low-temperature frontier. This would realize long-sought and previously inaccessible phases of matter, including phases which simulate high-temperature superconductivity. The project will train graduate, undergraduate, and high school students in the use of the new algorithms, facilitating their future use in other areas of non-equilibrium physics. In addition, publicly accessible educational materials will be developed which unify concepts in non-equilibrium dynamics that are used regularly by physicists, but which are taught only inexplicitly, if at all, in typical physics curricula. These lessons will include videos, reading, and exercises that can be used for self-study or in a classroom, and will include multiple versions, each designed for students of different levels of expertise, from non-physicists to practicing researchers.This project will develop two algorithms, a dynamical numerical linked cluster expansion (NLCE) and a cluster truncated Wigner approximation (cl-TWA), which potentially can accurately calculate important ultracold dynamics in minutes on a laptop for cases that are currently inaccessible to even the largest supercomputers. The algorithms achieve their accuracy by recognizing and exploiting special physical structures that underlie many ultracold dynamics experiments. The project will focus on applying these new algorithms to design and optimize new protocols for cooling ultracold matter that fall into three categories: entropy management, adiabatic preparation, and engineered dissipation. It will also partner with experiments to address fundamental questions of nonequilibrium physics, selected to align the strengths of the algorithms with emerging experimental directions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.