From sudden quench to adiabatic dynamics in the attractive Hubbard model

We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time which is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of the initial state takes place at strong coupling. We show that this is related to a sharp transition between a weak and a strong coupling quench dynamical regime, which defines the boundaries beyond which a dynamics independent from the initial state is recovered. Comparing the dynamics in the superconducting and non-superconducting phases we argue that this is due to the lack of an adiabatic connection to the equilibrium ground state for non-equilibrium superconducting states in the strong coupling quench regime.Comment: 10 pages, 5 figure

Superradiant Quantum Materials

There is currently great interest in the strong coupling between the quantized photon field of a cavity and electronic or other degrees of freedom in materials. A major goal is the creation of novel collective states entangling photons with those degrees of freedom. Here we show that the cooperative effect between strong electron interactions in quantum materials and the long-range correlations induced by the photon field leads to the stabilization of coherent phases of light and matter. By studying a two-band model of interacting electrons coupled to a cavity field, we show that a phase characterized by the simultaneous condensation of excitons and photon superradiance can be realized, hence stabilizing and intertwining two collective phenomena which are rather elusive in the absence of this cooperative effect.Comment: 5 pages, 4 figure

Non-Equilibrium Phenomena in Strongly Correlated Systems

Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field

Collective entanglement in quantum materials with competing orders

We investigate entanglement detection in quantum materials through criteria based on the simultaneous suppression of collective matter excitations. Unlike other detection schemes, these criteria can be applied to continuous and unbounded variables. By considering a system of interacting dipoles on a lattice, we show the detection of collective entanglement arising from two different physical mechanisms, namely, the ferroelectric ordering and the dressing of matter degrees of freedom by light. In the latter case, the detection shows the formation of a collective entangled phase not directly related to spontaneous symmetry breaking. These results open a new perspective for the entanglement characterization of competing orders in quantum materials, and have direct application to quantum paraelectrics with large polariton splittings.Comment: 5 pages, 3 figure

Strongly correlated exciton-polarons in twisted homo-bilayer heterostructures

We consider dressing of excitonic properties by strongly correlated electrons in gate controlled twisted homo-bilayer heterostructures. The combined effect of the moir\'e potential and the Coulomb interaction supports the formation of different strongly correlated phases depending on the filling, including charge-ordered metals or incompressible insulators at integer occupation. The coupling between excitons and electrons results in a splitting of the excitonic resonance into an attractive and a repulsive polaron peak. Analyzing the properties of the exciton-polarons across the different phases of the system, we reveal a discontinuous evolution of the spectrum with the formation of a double-peak structure in the repulsive polaron branch. The double-peak structure emerges for non-integer fillings and it is controlled by the energy separation between the quasi-particle states close to the Fermi level and the high-energy doublons excitations. Our results demonstrate that exciton-polarons carry a clear hallmark of the electronic correlations and, thus, provide a direct signature of the formation of correlation driven insulators in gate controlled heterostructures.Comment: 5 pages, 4 figure

Dissipative Dynamics of a Fermionic Superfluid with Two-Body Losses

We study the dissipative dynamics of a fermionic superfluid in presence of two-body losses. We use a variational approach for the Lindblad dynamics and obtain dynamical equations for Anderson's pseudo-spins where dissipation enters as a complex pairing interaction as well as effective, density-dependent, single particle losses which break the conservation of the pseudo-spin norm. We show that this latter has key consequences on the dynamical behavior of the system. In the case of a sudden switching of the two-body losses we show that the superfluid order parameter decays much faster than then particle density at short times and eventually slows-down, setting into a power-law decay at longer time scales driven by the depletion of the system. We then consider a quench of pairing interaction, leading to coherent oscillations in the unitary case, followed by the switching of the dissipation. We show that losses wash away the dynamical BCS synchronization by introducing not only damping but also a renormalization of the frequency of coherent oscillations, which depends strongly from the rate of two-body losses.Comment: 5 pages, 3 figure

Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures

We consider heterostructures obtained by stacking layers of two s-wave superconductors with significantly different coupling strengths, respectively in the weak- and strong-coupling regimes. The weak- and strong-coupling superconductors are chosen with similar critical temperatures for bulk systems. Using dynamical mean-field theory methods, we find an ubiquitous enhancement of the superconducting critical temperature for all the heterostructures where a single layer of one of the two superconductors is alternated with a thicker multilayer of the other. Two distinct physical regimes can be identified as a function of the thickness of the larger layer: (i) an inherently inhomogeneous superconductor characterized by the properties of the two isolated bulk superconductors where the enhancement of the critical temperature is confined to the interface and (ii) a bulk superconductor with an enhanced critical temperature extending to the whole heterostructure. We characterize the crossover between these regimes in terms of the competition between two length scales connected with the proximity effect and the pair coherence.Comment: 7 pages, 4 figure

Le aree protette: un mosaico di esperienze, pratiche e rappresentazioni

Protected Areas: a Mosaic of Experiences, Practices and Representation

Electromagnetic coupling in tight-binding models for strongly correlated light and matter

We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid, to describe sub-cycle light-driven electronic motion in the semiclassical limit, and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account, but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes