Collective effects in many-body systems: the case of quantum batteries and photon condensation

This thesis studies problems concerning light-matter interaction in the context of many-body systems and the exploitation of these systems in the context of the emerging field of quantum batteries (QBs). We start by introducing the necessary theoretical concepts and tools forming the basis of this manuscript. Among these, the Dicke Hamiltonian, a paradigmatic model which describes an ensemble of N atoms interacting with the same electromagnetic mode, is introduced. This model represents a key concept on which the thesis is developed. The remaining chapters contain original results and can be conceptually split into two parts. The first one deals with the study of many-body QBs, quantum mechanical systems with many degrees of freedom which can be used to store energy and that display fast charging. The second part studies equilibrium superradiant quantum phase transition, (which we dub, to avoid confusion with many superradiant phenomena, systems “photon condensation”), in the context of many-body strongly-correlated system. Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of QBs made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model (“Dicke QB”), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode (“Rabi QB”). By employing exact diagonalization, we demonstrate the emergence of a collective advantage in the charging power of Dicke QBs, which scales like pN for N 1. We study a simplified version of a Dicke QB, where non energy-conserving interactions are neglected. In such so-called Tavis-Cummings QB, we quantify the fraction E(N) B of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that E(N) B is highly reduced by the presence of correlations between the charger and the battery or between the two-level systems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the chargerbattery system is asymptotically free of such locking correlations in the N ! 1 limit. At this point, the physics behind fast charging in a Dicke QB is still unclear. Is this just due to the collective behavior of the underlying interacting many-body system or does it have its roots in the quantum mechanical nature of the system itself? We address these questions by studying three examples of quantum-mechanical many-body batteries with rigorous classical analogs. We find that quantum and classical models perform with the same scaling with the number of battery units N. Within these models it is possible to find only parametric advantages (i.e. advantages independent of N), which are model dependent and, even within the same model, depend on the value of the coupling constant that controls the interaction between the charger and the battery itself. We introduce a different model of charging, which relies on a quantum quench base on the Sachdev-Ye-Kitaev (SYK) model. The exactly-solvable SYK model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. Here, we examine SYK-based charging protocols of quantum batteries with N quantum cells. The complexity of the SYK problem prevents us from employing analytic techniques and thus we rely on a fully numerical approach. Extensive calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuine quantum mechanical effects. To the best of our knowledge, this is the first quantum many-body battery model where fast charging occurs due to the maximally-entangling underlying quantum dynamics. Lastly, we study photon condensation in strongly-interacting many-body systems. Despite decades of work it has remained unclear whether or not photon condensation can occur an equilibrium. We first show that when a non-relativistic quantum many-body system is coupled to a spatially-uniform quantum cavity field, gauge invariance forbids photon condensation. We then present a microscopic theory of the cavity quantum electrodynamics of an extended Falicov-Kimball model, showing that, in agreement with the general theorem, its insulating ferroelectric and exciton condensate phases are not altered by the cavity and do not support photon condensation. Finally, we show that the no-go theorem does not apply to spatially-varying quantum cavity fields. We find a criterion for occurrence of photon condensation that depends solely on the static, non-local orbital magnetic susceptibility orb(q), of the electronic system (ES) evaluated at a cavity photon momentum ~q. Only 3D ESs satisfying the Condon inequality orb(q) > 1=(4) can harbor photon condensation. For the experimentally relevant case of two-dimensional (2D) ESs embedded in quasi-2D cavities the criterion again involves orb(q) but also the vertical size of the cavity. We use these considerations to identify electronic properties that are ideal for photon condensation. Our theory is non-perturbative in the strength of electron-electron interaction and therefore applicable to strongly correlated ESs. We conclude the Thesis with a number of Appendices reporting useful technical details.