Driven-dissipative phenomena in quantum many-body systems

Abstract

Quantum simulation provides an arena for investigating complex quantum many-body phenomena, which are otherwise inaccessible through conventional techniques like analytical calculations and numerical simulations. One intriguing platform is ultracold atomic gases driven by external lasers and coupled to lossy optical cavities. Its ease of controllability and tunability endowed by tremendous technology advances has led to its great success in simulating a large variety of quantum many-body Hamiltonians and associated phenomenology not easily implemented in traditional condensed matter systems. Specifically, cavity-boson systems have also provided the first experimental realisation of the renowned Dicke model and related models, whose simplicity and tractability offer the opportunity for a more profound insight into driven-dissipative processes. Nevertheless, a fundamental distinction between quantum gases subject to driving and dissipation as simulators and condensed matter systems as simulatees is that the former is inherently out of equilibrium. Recently, an increasing number of studies manifest unique and exotic behaviours in out-of-equilibrium systems, which potentially obscures the role of quantum gases as faithful quantum simulators. This doctoral thesis addresses the interplay between drive and dissipation, as well as their impact on the physics of quantum many-body systems through two perspectives. On the one hand, using cavity-boson systems as examples, this thesis thoroughly investigates a plethora of many-body phenomena of inherently driven-dissipative nature, and demonstrates the emergence of many peculiar phenomena, including limit cycles and chaotic behaviours, a continuous family of multistable steady states, and a uni-directional atomic current on synthetic momentum lattice. On the other hand, a framework is sought for a better clarification of quantum driven-dissipative dynamics, which captures and categorises the underlying mechanisms leading to the aforementioned phenomena in ultracold atomic systems. The acquired understandings, as reformulated in the Floquet and Keldysh formalisms, are finally harnessed and applied to condensed matter systems. Specifically, it reveals an unexploited mechanism where the interplay between drive and dissipation is shown to generate a substantial enhancement of superconductivity at finite temperatures. In summary, this thesis elucidates the role of quantum-optical ultracold-atomic systems as quantum simulators. They go far beyond the simulators of static systems via effective stroboscopic Hamiltonians, and are intrinsically capable of emulating thermal environmental effects ubiquitous to quantum many-body systems of both quantum gases and condensed matter. This thesis thus sheds light on a novel paradigm for driven-dissipative engineering of quantum many-body systems, which potentially has broad applications in the realms of, e.g., quantum critical phenomena, quantum many-body phase preparation, and quantum information processing.