Emergent coherent phenomena in many-body quantum systems - time-crystals and synchronization

• Applicant: Dr. Albert Cabot, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 519847240

One of the frontiers of many-body physics is the study of collective phenomena in far-from-equilibrium quantum systems. In such systems novel phases of matter can be observed, which have no equilibrium counterpart. This is the case for time crystals, in which time-translation symmetry is spontaneously broken, that is, a many-body system converges towards a stable oscillatory state. In the presence of such oscillations another intrinsically non-equilibrium phenomenon is possible: that of quantum synchronization. This occurs when coupled oscillatory systems mutually lock their frequency and phase. In this project, we will study these two phenomena and their effects on the emitted light in many-body quantum optical systems. The motivation behind considering such platforms is twofold: (i) they are highly tuneable and controllable experimental platforms; (ii) their many-body dynamics shape the properties of the emitted light. In fact, our project will place especial emphasis on characterizing the emitted light, as this is a crucial analysis for assessing the potential of these phenomena for many-body enhanced metrology. The project is divided in the following two objectives: - Characterization of the emergence of time-crystals and quantum synchronization beyond the mean-field approximation. The emergence of these phenomena in many-body scenarios arranged in low-dimensional lattice geometries and with short-ranged interactions have remained elusive beyond the mean-field approximation. This is a basic level of approximation in which quantum correlations and fluctuations are neglected. Going beyond it is crucial for being able to assess the properties of the emitted light. Here we will tackle this open problem focusing on two research directions, first exploring the effects of the geometry of the arrays and then those of the local dimension of the systems. - Conception and development of schemes for quantum optics platforms that allow to realize time-crystals and synchronization. Quantum optical platforms are particularly promising for the observation of non-equilibrium quantum phenomena due to their high controllability and tunability, while the many-body dynamics is imprinted in the properties of the emitted light. Here, we will focus on the study and conception of engineered arrays of coupled collective spin systems. The objective is to conceive and study which system configurations can display time-crystal phases, and whether and how synchronization is possible. We will focus on atomic-waveguide systems, as they allow for several types of many-body arrays and also provide a rich toolkit to engineer their interaction. A crucial advantage of this kind of systems is that the waveguide already collects the emitted light. Our analysis of the dynamics will place emphasis on characterizing this light in order to assess the potential of time-crystalline/synchronized phases for time-keeping and metrology applications.

• DFG Programme: WBP Position