Synchronization and collective phenomena in quantum dissipative systems

The past two decades have witnessed huge experimental progress on the ability to control and engineer the dynamics of complex quantum systems. Experimental platforms range from large atomic clouds trapped in optical lattices, to few atoms trapped near photonic nanostructures, optomechanical systems, or arrays of superconducting qubits. An important driving force behind this venture has been the promise of new quantum technologies based on extended systems for computation, telecommunications, and sensing that might surpass the performance and capabilities of current ones by exploiting quantum effects. As well as the development of quantum simulation, in which highly-controllable experimental systems are aimed to study fundamental quantum phenomena currently unaddressable by other means. All these experimental platforms are unavoidably open quantum systems: the system degrees of freedom are coupled to an environment made of a continuum of modes that induces dissipation and decoherence. This coupling is inherent to our ability to observe these systems, e.g. by observing their emitted radiation, or to control them through it, and it is often an ultimate limit for quantum technologies. Still, the driven-dissipative nature of many platforms has provided a great opportunity to explore non-equilibrium dynamics in quantum systems, to study quantum phenomena that have no equilibrium counterpart, and to widen the spectrum of achievable dynamical phenomena of fundamental and applied
interest.

This thesis is devoted to the study of synchronization and related collective phenomena in dissipative quantum systems. Synchronization is a paradigmatic dynamical phenomenon of non-equilibrium classical systems, occurring in very different contexts and forms. About ten years ago a series of seminal works showed different forms of synchronization occurring in quantum systems, which gave birth to quantum synchronization. Here, we have addressed questions as how this phenomenon manifests in the quantum regime, which are the systems in which it can emerge, or whether it displays genuine quantum features. After introducing the main topics of this thesis as well as the used methods and theoretical framework, in the second part of this thesis we focus on the phenomenon of spontaneous transient synchronization, in which systems relax towards their stationary state in a synchronized fashion. As we show, this is a common and robust phenomenon: it emerges in spin systems and even in linear systems of harmonic oscillators, both in the presence of collective and independent dissipation, and in the presence of complex topologies and inhomogeneous parameters. We propose a possible implementation of transient synchronization in the low-energy physics of a one-dimensional atomic lattice, a relevant system for quantum simulation, and we identify different scenarios of synchronization. Furthermore, we establish synchronization enabled by coalescence or exceptional points in different extended systems, and we characterize specific spectral features of synchronization as narrow subradiant resonances as well as transparency windows and other interference effects. In the third part, we address the relation of quantum entrainment with other driven dissipative phenomena, considering the particular case of the squeezed quantum van der Pol oscillator. Our research shows that driven synchronization is related to quantum metastability. Moreover, as the classical limit is approached, spontaneous symmetry breaking occurs, and entrainment turns out to be related to time-crystalline order and to a dissipative phase transition. Interestingly, synchronization is here related to a discrete time-crystal, while the absence of it to a continuous one.

We conclude this thesis with final remarks and outlook. The main original results of this thesis allow us to identify new scenarios of synchronization, to establish its robustness, and to unveil its connections with other important and fundamental phenomena as coalescence, dissipative phase transitions or time-crystals.