Quantum probing is a fairly wide topic deepening its roots into many fields as it can borrow tools from, and be applied to, many-body physics, open quantum systems theory, quantum information and quantum thermodynamics. Its wide range of applicability, i.e. the diverse systems under investigations and their specific properties, contributes in making a general theory of quantum probing a rather challenging, if not impossible, task. Despite the need to specialize the probing technique to the various physical systems, we have identified a leitmotiv in our probing approach. Specifically, we will consider a perturbation potential acting as the source of the probing procedure, in most cases this will be an impurity in the complex environment acting as quantum probe. We will generally quantify the information exchange between the probe and its environment, and explore the connection to the concept of non-Markovian, i.e. memoryless, quantum dynamics. This thesis aims at discussing probing protocols for atomic systems confined in optical lattices, both fermionic and bosonic species, as well as trapped ions. The systems inquired can be currently implemented in the field of ultra cold atoms, where they have attracted interest as ideal candidates for quantum simulators and quantum technologies. We will show how to design protocols in which these cold many-body systems act as an environment to a quantum probe, often designed as an impurity atom. Exploiting tools from open quantum systems theory we will discuss how to detect, from the dynamics of the probe, the characteristics of the complex environment. The key idea is to use the quantum probe as read-out device, the properties of the environment are then inferred trough measurements performed exclusively on the probe. Quantities of interest will be related to the environment energy spectrum, equilibrium properties and temperature. The quantum probing paradigm will also allow us to investigate critical phenomena such as phase transitions and orthogonality catastrophe. Finally, we will show how the memory effects induced in the reduced dynamics of an immersed quantum probe can witness, to some extent, the character of the excitations of the environment hinting to a natural link between non-Markovianity and localisation phenomena.
Quantum probing is a fairly wide topic deepening its roots into many fields as it can borrow tools from, and be applied to, many-body physics, open quantum systems theory, quantum information and quantum thermodynamics. Its wide range of applicability, i.e. the diverse systems under investigations and their specific properties, contributes in making a general theory of quantum probing a rather challenging, if not impossible, task. Despite the need to specialize the probing technique to the various physical systems, we have identified a leitmotiv in our probing approach. Specifically, we will consider a perturbation potential acting as the source of the probing procedure, in most cases this will be an impurity in the complex environment acting as quantum probe. We will generally quantify the information exchange between the probe and its environment, and explore the connection to the concept of non-Markovian, i.e. memoryless, quantum dynamics. This thesis aims at discussing probing protocols for atomic systems confined in optical lattices, both fermionic and bosonic species, as well as trapped ions. The systems inquired can be currently implemented in the field of ultra cold atoms, where they have attracted interest as ideal candidates for quantum simulators and quantum technologies. We will show how to design protocols in which these cold many-body systems act as an environment to a quantum probe, often designed as an impurity atom. Exploiting tools from open quantum systems theory we will discuss how to detect, from the dynamics of the probe, the characteristics of the complex environment. The key idea is to use the quantum probe as read-out device, the properties of the environment are then inferred trough measurements performed exclusively on the probe. Quantities of interest will be related to the environment energy spectrum, equilibrium properties and temperature. The quantum probing paradigm will also allow us to investigate critical phenomena such as phase transitions and orthogonality catastrophe. Finally, we will show how the memory effects induced in the reduced dynamics of an immersed quantum probe can witness, to some extent, the character of the excitations of the environment hinting to a natural link between non-Markovianity and localisation phenomena.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.
This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
Quantum systems are inherently open to their environment and thus they evolve under the influence of dissipation, decoherence and driving from external fields. This poses a significant theoretical challenge: how to track the dynamics of the system of interest while tracing out environmental degrees of freedom. Markovian master equations offer a longstanding solution to this problem, where under a series of assumptions the reduced density matrix of the system can be obtained. These flexible approaches provide a conceptually and numerically simple framework for describing complex many-body systems. However, the assumptions enforced by Markovian master equations create a gap in the availability of generic, simple, and analytical techniques capable of treating open quantum systems beyond the regimes of standard Markovian master equations. In this thesis, we introduce three studies addressing three regimes that are inaccessible to standard Markovian master equations and investigate their consequences in quantum thermodynamics-inspired applications. We begin by developing a Markovian embedding technique to tackle non-Markovian dynamics induced by the long correlation times of a qubit coupled to a structured environment. Subsequently, we propose an "effective" Hamiltonian theory enabling the study of equilibrium properties of strong coupling to a thermal reservoir through a dressed version of the Gibbs state. This framework can also be applied to address problems of equilibration, transport, quantum thermal machines, and quantum dynamics. Lastly, we showcase the importance of including non-secular terms in the quantum master equation, which results in a drastic separation of timescales leading to rich metastable dynamics. We apply this quantum master equation approach to temperature sensing in a nonequilibrium setting offering an alternative to standard equilibrium probes. Overall, this thesis contributes novel theoretical techniques for tackling open quantum systems beyond standard approximations with applications in quantum thermodynamics.
This thesis summarizes a course of investigation of various aspects of non-equilibrium dynamics in isolated quantum systems which can be controlled to the extent that one can speak of not just realizing but rather simulating a desired physical effect. The first subject considered concerns a general question of relaxation in a large class of physical models. It is rigorously proven that equilibration can occur for arbitrary local observables despite the entire system being perfectly isolated. Various mechanisms responsible for convergence to local equilibrium are highlighted. These involve in particular the memory loss of non-Gaussian correlations following an interaction quench, a notion of Gaussian ergodicity and a proof of the emergence of translation invariance of correlations due to the presence of this symmetry in the Hamiltonian governing the evolution. These results provide the long time and large system size asymptotics facilitating a thermodynamic limit, but at the same time are relevant for state-of-the-art quantum simulation experiments with large numbers of ultra-cold atoms: A related effect has been observed in a one-dimensional phononic quantum field simulator and additionally a method is provided to study relaxation dynamics of this type in optical lattice quantum simulators. Within the second theme explored in this thesis a novel quantum read-out method is proposed and applied in continuous field quantum simulators which allowed for the first time to measure experimentally various thermodynamical properties of one-dimensional quasi-condensates. In particular, tomographic results concerning thermal properties, non-commuting observables, momentum and time-resolved occupation numbers of phonons are presented. Finally, ideas for practical benchmarking of the dynamics of certain closed quantum systems are put forward, based on the concept of a fidelity witness. It is demonstrated that fidelity, despite being a sensitive measure for large systems, can be efficiently estimated for non-equilibrium dynamics in coherent quantum simulators implementing paradigmatic models of condensed matter physics. The method developed has already found an independent application in studies of variational quantum circuits aiming at achieving so-called quantum chemistry accuracy using the Sycamore quantum processor. The fact that all three themes of research laid out in this thesis have found an experimental realization hints at a prognosis for future developments in physics that it will become standard that quantum simulators will realize experimentally novel theoretical ideas on demand and the time between theoretical insights and experimental observations will be dramatically shortened.