Using N-point-function space-time mappings to exactly relate pairs of experiments with Markovian open quantum gases

We present an exact space-time mapping between the N-point correlation functions of two different quantum gas experiments to extend a quantum-field mapping result for closed systems[1] to the general case of open quantum systems with the Markovian property[2]. For this, we consider an open many-body system consisting of a D-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. We derive the Heisenberg evolution of any arbitrary N-point function of the system in such a regime. Our quantum field mapping for closed quantum systems is rewritten in the Schrödinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the N-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

[1] Etienne Wamba, Axel Pelster, and James Anglin, Phys. Rev. A 94, 043628 (2016)

[2] Etienne Wamba and Axel Pelster, Phys. Rev. A 102, 043320 (2020)