Publications

Understanding the influence of measurements on the properties of many-body systems is a fundamental problem in quantum mechanics and for quantum technologies. This paper explores how a finite density of stochastic local measurement modifies a given state’s entanglement structure. Considering various measurement protocols, we explore the typical quantum correlations of their associated projected ensembles arising from the ground state of the quantum Ising model. Using large-scale numerical simulations, we demonstrate substantial differences among inequivalent measurement protocols. Surprisingly, we observe that forced on-site measurements can enhance both bipartite and multipartite entanglement. We present a phenomenological toy model and perturbative calculations to analytically support these results. Furthermore, we extend these considerations to the non-Hermitian Ising model, naturally arising in optically monitored systems, and we show that its qualitative entanglement features are not altered by a finite density of projective measurements. Overall, these results reveal a complex phenomenology where local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.

Ensembles of identical quantum particles have statistical properties that deviate from the classical Boltzmann distribution. Quantum statistics drastically depend on the constituent particles being bosons or fermions, with tangible consequences on the properties of low-temperature quantum gases. We briefly review the properties of quantum statistics with some of their most spectacular consequences. The additional interaction between the particles enriches enormously the panorama leading to a huge variety of phenomena, two examples are magnetism or superconductivity.

We introduce the Hubbard model as the paradigmatic model of materials with strongly correlated electrons. For integer filling the model undergoes a Mott-Hubbard transition as a function of the interaction strength from a metal to a Mott insulator with localized electrons. We briefly introduce Dynamical Mean-Field Theory, a powerful nonperturbative method which provides a comprehensive picture of the Mott transition. We comment about the role of multiorbital electronic structure and the Hund's coupling.

We present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. In particular, we analyze the form of the ground state and excitations of the model, relating them to the symmetry-breaking physics, and illustrate aspects connected to calculating dynamical quantities, thermal averages, correlation functions, and entanglement entropy. A few problems provide simple applications of the techniques.

We propose a protocol for the scalable quantum simulation of SU(N)×U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices. The protocol exploits the combination of naturally occurring SU(N) pseudo-spin symmetry and strong inter-orbital interactions that is unique to such atomic species. A detailed ab initio study of the microscopic dynamics shows how gauge invariance emerges in an accessible parameter regime, and allows us to identify the main challenges in the simulation of such theories. We provide rigorous estimates about the requirements in terms of experimental stability in relation to observing gauge invariant dynamics in both one- and two-dimensional systems, a key element for a deeper analysis on the functioning of such class of theories in both quantum simulators and computers.

Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.

We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction that we describe by means of the BCS microscopic model in terms of two tunnelling superconducting systems in the strong-coupling quasi-spin formulation. Then, by means of collective observables we derive the Hamiltonian governing the quantum behaviour of the circuit in the limit of a large number N of quasi-spins. Our approach relies on suitable quantum fluctuations, i.e. on collective quasi-spin operators, different from mean-field observables, that retain a quantum character in the large-N limit. These collective operators generate the Heisenberg algebra on the circle and we show that their dynamics reproduces the phenomenological one generated by the charge qubit Hamiltonian obtained by quantizing the macroscopic classical Hamiltonian of the circuit. The microscopic derivation of the emergent, large-N behaviour provides a rigorous setting to investigate more in detail both general quantum circuits and quantum macroscopic scenarios; in particular, in the specific case of charge-qubits, it allows to explicitly obtain the temperature dependence of the critical Josephson current in the strong coupling regime, a result not accessible using standard approximation techniques.

Entanglement asymmetry is a quantity recently introduced to measure how much a symmetry is broken in a part of an extended quantum system. It has been employed to analyze the non-equilibrium dynamics of a broken symmetry after a global quantum quench with a Hamiltonian that preserves it. In this work, we carry out a comprehensive analysis of the entanglement asymmetry at equilibrium taking the ground state of the XY spin chain, which breaks the U(1) particle number symmetry, and provide a physical interpretation of it in terms of superconducting Cooper pairs. We also consider quenches from this ground state to the XX spin chain, which preserves the U(1) symmetry. In this case, the entanglement asymmetry reveals that the more the symmetry is initially broken, the faster it may be restored in a subsystem, a surprising and counter-intuitive phenomenon that is a type of a quantum Mpemba effect. We obtain a quasi-particle picture for the entanglement asymmetry in terms of Cooper pairs, from which we derive the microscopic conditions to observe the quantum Mpemba effect in this system, giving further support to the criteria recently proposed for arbitrary integrable quantum systems. In addition, we find that the power law governing symmetry restoration depends discontinuously on whether the initial state is critical or not, leading to new forms of strong and weak Mpemba effects.

Károlyházy’s original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated Károlyházy’s assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal.

We investigate the divisibility properties of the tensor products (Formula presented.) of open quantum dynamics (Formula presented.) with time-dependent generators. These dynamical maps emerge from a compound open system (Formula presented.) that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to (Formula presented.) without the same phenomenon occurring for either (Formula presented.) and (Formula presented.). We shall refer to this effect as the Superactivation of BFI (SBFI).