Detecting metrologically useful entanglement in the vicinity of Dicke states

We present a method to verify the metrological usefulness of noisy Dicke states of a particle ensemble with only a few collective measurements, without the need for a direct measurement of the sensitivity. Our method determines the usefulness of the state for the usual protocol for estimating the angle of rotation with Dicke states, which is based on the measurement of the second moment of a total spin component. It can also be used to detect entangled states that are useful for quantum metrology. We apply our method to recent experimental results.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

Effective field theories and their phenomenological applications

Effective field theories (EFTs) are ubiquitous in theoretical physics and in particular in field theory descriptions of quantum systems probed at energies much lower than one or few characterizing scales. More recently, EFTs have gained a prominent role in the study of fundamental interactions and in particular in the parametriasation of new physics beyond the Standard Model, which would occur at scales Λ, much larger than the electroweak scale. In this thesis, EFTs are employed to study three different physics cases. First, we consider light-by-light scattering as a possible probe of new physics. At low energies it can be described by dimension-8 operators, leading to the well-known Euler-Heisenberg Lagrangian. We consider the explicit dependence of matching coefficients on type of particle running in the loop, confirming the sensitiveness to the spin, mass, and interactions of possibly new particles. Second, we consider EFTs to describe Dark Matter (DM) interactions with SM particles. We consider a phenomenologically motivated case, i.e., a new fermion state that couples to the Hypercharge through a form factor and has no interactions with photons and the Z boson. Results from direct, indirect and collider searches for DM are used to constrain the parameter space of the model. Third, we consider EFTs that describe axion-like particles (ALPs), whose phenomenology is inspired by the Peccei-Quinn solution to strong CP problem. ALPs generically couple to ordinary matter through dimension-5 operators. In our case study, we investigate the rather unique phenomenological implications of ALPs with enhanced couplings to the top quark.

Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Equazioni di stato della materia in astrofisica

Le equazioni di stato (EdS) sono relazioni che permettono di descrivere sistemi termodinamici all'equilibrio. Un esempio di questi sistemi sono i gas, che si possono dividere in gas perfetti e gas degeneri, che differiscono per importanti proprietà e caratteristiche fisiche. Le proprietà dei gas degeneri cambiano in base al tipo di particelle che li compongono, il comportamento di un gas degenere di Fermioni è molto diverso da quello di un gas degenere di Bosoni. Per lo studio e la descrizione dei gas degeneri di Fermioni entrano in gioco il principio di esclusione di Pauli ed il principio di inderteminazione di Heisenberg. Attraverso le EdS si possono descrivere gli interni stellari poiché per via delle alte temperature le stelle sono formate da gas completamente ionizzato. La pressione all'interno di una stella è data dalla somma tra la pressione di radiazione, la pressione elettronica e la pressione ionica, in base al tipo di gas elettronico che si ha ed alla temperatura interna la stella può essere formata da gas perfetto o gas degenere. Lo studio del regime di pressione interno per una stella si fa con il grafico densità-temperatura, in cui una stella viene rappresentata nel piano attraverso queste due grandezze. Si vede come le stelle di sequenza principale siano formate da gas perfetto mentre i corpi compatti come le nane bianche sono formati da gas completamente degenere. Attraverso le EdS ed il principio dell'equilibrio idrostatico si possono ricavare la temperatura interna per le stelle di sequenza principale e la relazione massa-raggio per le nane bianche.