Recent advances in coherent manipulation and control have led to new opportunities to study non-equilibrium dynamics in quantum many-body systems. Using a variety of experimental platforms ranging from cold atoms and ions to solid-state spin defects, small building blocks of fully controllable quantum systems can be assembled into a strongly interacting many-body system. With this approach, one can gain new insights into fundamental questions in basic science such as the mechanism of quantum thermalization or the existence of exotic phases of matter out of equilibrium. At the same time, a fully controllable large-scale quantum device has promising applications for high precision sensing, secure communication, and quantum information processing.\nThis thesis describes recent progress in engineering quantum dynamics that is robust against various imperfections such as environmental noise, disorder, or imprecise controls. We find that non-equilibrium quantum states of strongly interacting systems can be protected from imperfections upon appropriate external manipulations such as time-dependent periodic controls, engineered coherent or dissipative interactions, or an introduction of strong quenched disorder. Furthermore, under certain conditions, these imperfections can be utilized to stabilize non-trivial quantum states. Our results challenge conventional wisdom of statistical mechanics, shedding light on the microscopic mechanisms of thermalization.\nWe also discuss how engineered dynamics can be harnessed for applications such as quantum metrology, simulations, or information processing.
Recent advances in coherent manipulation and control have led to new opportunities to study non-equilibrium dynamics in quantum many-body systems. Using a variety of experimental platforms ranging from cold atoms and ions to solid-state spin defects, small building blocks of fully controllable quantum systems can be assembled into a strongly interacting many-body system. With this approach, one can gain new insights into fundamental questions in basic science such as the mechanism of quantum thermalization or the existence of exotic phases of matter out of equilibrium. At the same time, a fully controllable large-scale quantum device has promising applications for high precision sensing, secure communication, and quantum information processing.\nThis thesis describes recent progress in engineering quantum dynamics that is robust against various imperfections such as environmental noise, disorder, or imprecise controls. We find that non-equilibrium quantum states of strongly interacting systems can be protected from imperfections upon appropriate external manipulations such as time-dependent periodic controls, engineered coherent or dissipative interactions, or an introduction of strong quenched disorder. Furthermore, under certain conditions, these imperfections can be utilized to stabilize non-trivial quantum states. Our results challenge conventional wisdom of statistical mechanics, shedding light on the microscopic mechanisms of thermalization.\nWe also discuss how engineered dynamics can be harnessed for applications such as quantum metrology, simulations, or information processing.
Isolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.
All real-world quantum systems interact with their surrounding environment to some extent. No matter how weak the coupling that prevents the system from being isolated, the evolution of an open quantum system is eventually plagued by non-unitary features, such as decoherence and dissipation. Decoherence is a quantum effect where the system loses its ability to exhibit coherent behavior. Nowadays, decoherence stands as a serious obstacle in quantum information processing. As the manipulation of quantum coherence in experiments has progressed, the need to better understand, control, and utilize dissipative non-equilibrium dynamics of quantum systems has grown in importance. This has ranged from fundamental questions associated with the quantum-to-classical transition and quantum thermodynamics innovation in quantum optics and cavity/circuit quantum electrodynamics. Current studies of many-body dynamics, ultracold atoms in optical lattices, trapped ions, superconducting systems, nanoelectro-mechanical systems, and quantum fields under the influence of external conditions offer new challenges to address questions regarding quantum systems far from equilibrium. On the theoretical side, quantum trajectory-based methods could be the key to both quantum nanodevice design and exploration of new regimes of quantum mechanics and quantum measurement, as well as applications to various quantum technologies.
The study of quantum mechanics, together with the ability to coherently control and manipulate quantum systems in the lab has led to a myriad of discoveries and real world applications. In this thesis we present experiments demonstrating precise control of an individual long-lived spin qubit as well as sensing applications for biology and investigation of quantum many-body dynamics.\n\nStable quantum bits, capable both of storing quantum information for macroscopic time scales and of integration inside small portable devices, are an essential building block for an array of potential applications. In the second chapter of this thesis we demonstrate high-fidelity control of a solid-state qubit, which preserves its polarization for several minutes and features coherence lifetimes exceeding 1 second at room temperature.\n\nSensitive probing of temperature variations on nanometer scales is an outstanding challenge in many areas of modern science and technology. In chapter three we show how nitrogen vacancy centers in diamond can be used as a robust, high sensitivity temperature probe. We furthermore demonstrate biological compatibility by introducing nano-sized diamonds into living cells and measuring externally induced sub-cellular temperature gradients.\n\nUnderstanding the dynamics of interacting many-body quantum systems with on-site potential disorder has proven one of the biggest challenges in quantum physics to investigate both in theory and experiment. In chapter four we demonstrate how coherent control techniques can be utilized to probe the many-body dynamics of a strongly interacting NV spin ensemble. Specifically, we show how a long-range interacting dipolar spin system exhibits characteristically slow thermalization in the presence of tunable disorder.\n\nThe presented works offer up many new areas to investigate, including complex quantum many-body effects of large, disordered spin systems, as well as applications of NV centers as bio-compatible nano-scale temperature probes.
Improved control and manipulation of quantum systems lies at the heart of modern quantum science and technology, with broad applications ranging from quantum metrology to quantum information science and many-body physics. In this thesis, I will introduce a novel framework for robust Hamiltonian engineering in interacting spin systems, which enables the efficient design of Floquet engineering pulse sequences for qubit and qudit systems that out-perform state-of-the-art control methods by orders of magnitude. As applications of this framework, we utilize a high density ensemble of nitrogen vacancy (NV) centers in diamond, and demonstrate significantly improved control over the disordered, interacting many-body spin system. This enabled the first solid state spin ensemble quantum sensor operating beyond the sensitivity limit imposed by interactions between sensing particles, as well as the observation and understanding of novel dynamical many-body phenomena, including discrete time crystalline order and thermalization dynamics in long-range interacting XXZ spin models.