A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. In practice, the main difficulty is to derive the equations analytically, which is usually a very tedious and error-prone task. In this talk, I present our open-source framework QuantumCumulants.jl that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After briefly explaining the cumulant expansion approach, I introduce the main concepts of the framework and demonstrate its usefulness with some example problems.

Christoph Hotter is a postdoctoral researcher in the Cavity-QED theory group of Helmut Ritsch at the University of Innsbruck. He received his PhD from the University of Innsbruck in June 2023. During his PhD he worked on collective quantum phenomena for large ensembles of clock atoms in optical cavities. His main research focuses on simulating large open quantum systems and quantum-enhanced metrology, especially in the context of squeezing, sub- and superradiance.