On the fundamental level, quantum fluctuations or entanglement lead to complex dynamical behaviour in many-body systems1 for which a description as emergent phenomena can be found within the framework of quantum field theory. A central quantity in these efforts, containing all information about the measurable physical properties, is the quantum effective action2. Though non-equilibrium quantum dynamics can be exactly formulated in terms of the quantum effective action, finding solutions is in general beyond the capabilities of classical computers3. Here, we present a strategy to determine the non-equilibrium quantum effective action4 using analogue quantum simulators, and demonstrate our method experimentally with a quasi-one-dimensional spinor Bose gas out of equilibrium5,6. Spatially resolved snapshots of the complex-valued transversal spin field7 allow us to infer the quantum effective action up to fourth order in an expansion in one-particle irreducible correlation functions at equal times. We uncover a strong suppression of the irreducible four vertex emerging at low momenta in the highly occupied regime far from equilibrium where perturbative descriptions fail8. Our work constitutes a new realm of large-scale analogue quantum computing9, where highly controlled synthetic quantum systems10 provide the means for solving theoretical problems in high-energy and condensed-matter physics with an experimental approach11,12,13,14.

M. Prüfer, T. V. Zache, P. Kunkel, S. Lannig, A. Bonnin, H. Strobel, J. Berges, and M. K. Oberthaler, “Experimental extraction of the quantum effective action for a non-equilibrium  many-body system”, Nature Physics 16, 1012–1016 (2020).


Related to Project B04, A04, A03