This dissertation presents theoretical and computational investigations into non-equilibrium quantum dynamics in engineered systems, with a central focus on entanglement generation for quantum metrology. The primary contributions establish the scalable and robust generation of entanglement in the form of two-mode squeezing in bilayers of power-law interacting quantum spins and uncover a novel dynamical phase transition. We develop a Floquet protocol utilizing spatio-temporal control to engineer spin-spin interactions tailored to the initial state and desired entanglement dynamics, thereby improving the standard quantum limit of 1/√N scaling of the sensitivity in system size N to approach the ultimate Heisenberg limit of 1/N. For a wide range of power-law interactions (1/rα), this approach creates exponentially fast entangled pairs of excitations between the layers. We then reveal a dynamical phase transition in the two-mode squeezing dynamics by identifying universal scaling in terms of system parameters and a divergent time-scale. We establish two distinct phases: a fully collective phase exhibiting Heisenberg-limited squeezing and a partially collective phase with scalable but sub-Heisenberg squeezing. A full set of critical exponents is derived, and a universal scaling collapse of the dynamics is demonstrated, framing entanglement generation within the theory of non-equilibrium critical phenomena. We also apply advanced computational methods to other quantum and classical engineered systems. We investigate quantum transport that maps conductivity to the disorder-driven phase diagram of two-dimensional Dirac fermions. We also design a high-efficiency, lead-free tandem photovoltaic cell. Collectively, this research provides a framework for harnessing quantum control to probe and enhance functionality in complex systems, from fundamental quantum sensing to applied materials design.
We investigate phase transitions in the nonequilibrium dynamics of power-law interacting spin-1/2 bilayer XXZ models, which have recently been shown to allow generation of entanglement in the form of two-mode squeezing. We find a transition between a collective phase characterized by Heisenberg limited squeezing and a partially collective phase with scalable squeezing. We identify universal scaling of the squeezing dynamics in terms of system parameters and a divergent timescale, establishing these as distinct dynamical phases within the framework of nonequilibrium critical phenomena. Our Letter demonstrates a novel dynamical phase transition with potential applications in quantum sensing and quantum simulation in cold-atomic, molecular, or Rydberg platforms.
Coherently controllable quantum devices have grown so large and complex that direct study of their microscopic dynamics is extremely difficult, if not infeasible. Yet, realizing the promise of quantum technologies --- such as simulation, computation and sensing --- requires a deep understanding of the structure and evolution of entanglement in these systems. Achieving this understanding challenges us to develop theoretical methods that provide insight into the dynamics of entanglement without the crutch of detailed microscopic simulations. In this thesis, we demonstrate how the tools of effective field theory and hydrodynamics can be naturally applied to meet this challenge. First, we study monitored random quantum circuits, in which random unitary dynamics are pitted against local projective measurements. The steady-state entanglement entropy of such circuits has been shown to undergo a phase transition from highly-entangled to unentangled as the measurement rate is increased. Here, we focus on the question of how the range of the entangling interactions, parametrized as a power law
r−α, affects the universality of this transition. To address this question, we develop a statistical-mechanical model of the entanglement entropy from which we derive an effective field theory governing the phase transition. Comparing to numerical simulations, we find the field theory successfully predicts the key properties of the transition, including the critical power-law exponent below which long-range interactions become relevant. Applying these same conceptual tools to finite-depth circuits, we further predict a phase transition in the teleportation fidelity between distant qubits, given projective measurements on all other qubits. We investigate several examples of this finite-time teleportation transition and demonstrate that our field-theory model accurately captures the underlying physics in each case. Second, we consider quenches of low-temperature symmetry breaking states, such as evolving the x-polarized state under an
XY model that manifests easy-plane magnetism. Typically such quenches are analyzed by first taking the thermodynamic limit
N→∞ and then finite-time evolution, which reveals the familiar process of local equilibration. However, a more relevant limit to quantum devices is that both
N and
t become large together -- that is, one has many particles that interact coherently for a long time. We analyze this limit using a combination of extensive semiclassical numerics and analytical hydrodynamics, with particular focus on the evolution of quantum fluctuations. Remarkably, under very general conditions, we find the quantum fluctuations undergo ``squeezing'' -- a pattern of entanglement useful for quantum metrology. These results lead us to the conjecture: any Hamiltonian exhibiting finite temperature, easy-plane ferromagnetism can be used to generate scalable spin squeezing. Finally, we provide experimental evidence for this conjecture using a Rydberg atom array which approximately realizes a dipolar
XY model.
The emergence of topological entanglement, a fundamental phenomenon in condensed matter physics, is often overlooked in the context of complex, non-equilibrium systems. This research proposes a novel framework, "Phase-Steering," to quantify and control the dynamics of topological entanglement within such systems. We develop a continuous, dynamically evolving algorithm that analyzes real-time feedback to actively manipulate the topological structure of entanglement, offering a fundamentally new approach to understanding and potentially engineering topological phases. The core claim is that this method can facilitate the transition between distinct topological phases and provides a pathway for designing systems exhibiting enhanced robustness and adaptability. The work presented here details the algorithm's implementation, provides preliminary results demonstrating its effectiveness in simulating a specific non-equilibrium system, and discusses potential applications in materials science and quantum computing.
Controlling the dynamics of targeted quantum correlations is a central goal across many disciplines of quantum science. For applications in nanoscale quantum sensing, nitrogen-vacancy (NV) centers in diamond have recently emerged as a leading platform due to their atom-like nature, exquisite magnetic sensitivity and well-developed coherent control techniques under ambient conditions. However, harnessing the entanglement structure required to improve this sensitivity beyond the standard quantum limit (SQL) from the native dipolar interactions between NV centers is challenging due to their strong positional disorder, three-dimensional geometry and low-fidelity readout. Coupled tightly to proof of principle experimental demonstrations, this thesis provides a theoretical blueprint to realize practical, entanglement-enhanced quantum sensing in the solid-state via far-from-equilibrium dynamics of dense ensembles of NV centers in diamond. Our most fundamental contribution is to identify a universal mechanism exploiting the thermalization of long-wavelength spin textures to generate scalable spin squeezing in the absence of finite temperature symmetry breaking. We further develop a novel sensing protocol based on asymmetric time-reversal capable of rapidly breaking the SQL without high-fidelity readout. Challenging long-standing beliefs in the field, these results open the door to a new era of entanglement-enhanced sensing under ambient conditions, with applications ranging from nanoscale imaging of biological structures to covariance magnetometry of exotic quantum materials.
Characterizing universal entanglement features in higher-dimensional quantum matter is a central goal of quantum information science and condensed matter physics. While the subleading corner terms in two-dimensional quantum systems encapsulate essential universal information of the underlying conformal field theory, our understanding of these features remains remarkably limited compared to their one-dimensional counterparts. We address this challenge by investigating the entanglement dynamics of fermionic systems along the imaginary-time evolution. We uncover a pioneering non-equilibrium scaling law where the corner entanglement entropy grows linearly with the logarithm of imaginary time, dictated solely by the universality class of the quantum critical point. Through unbiased Quantum Monte Carlo simulations, we verify this scaling in the interacting Gross-Neveu-Yukawa model, demonstrating that universal data can be accurately recovered from the early stages of relaxation. Our findings significantly circumvent the computational bottlenecks inherent in reaching full equilibrium convergence. This work establishes a direct link between the fundamental theory of non-equilibrium critical phenomena and the high-precision determination of universal entanglement properties on both classical and quantum platforms, paving the way for probing the rich entanglement structure of quantum critical systems.
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.