Quantum trajectories and open many-body quantum systems

Abstract

The study of open quantum systems has become increasingly important in the\npast years, as the ability to control quantum coherence on a single particle\nlevel has been developed in a wide variety of physical systems. In quantum\noptics, the study of open systems goes well beyond understanding the breakdown\nof quantum coherence. There, the coupling to the environment is sufficiently\nwell understood that it can be manipulated to drive the system into desired\nquantum states, or to project the system onto known states via feedback in\nquantum measurements. Many mathematical frameworks have been developed to\ndescribe such systems, which for atomic, molecular, and optical (AMO) systems\ngenerally provide a very accurate description of the open quantum system on a\nmicroscopic level. In recent years, AMO systems including cold atomic and\nmolecular gases and trapped ions have been applied heavily to the study of\nmany-body physics, and it has become important to extend previous understanding\nof open system dynamics in single- and few-body systems to this many-body\ncontext. A key formalism that has already proven very useful in this context is\nthe quantum trajectories technique. This was developed as a numerical tool for\nstudying dynamics in open quantum systems, and falls within a broader framework\nof continuous measurement theory as a way to understand the dynamics of large\nclasses of open quantum systems. We review the progress that has been made in\nstudying open many-body systems in the AMO context, focussing on the\napplication of ideas from quantum optics, and on the implementation and\napplications of quantum trajectories methods. Control over dissipative\nprocesses promises many further tools to prepare interesting and important\nstates in strongly interacting systems, including the realisation of parameter\nregimes in quantum simulators that are inaccessible via current techniques.\n