Open system probes can provide an efficient means to characterize quantum many-body systems by employing them as engineered environments. The key idea is to map long-range spatial correlations of the environment onto dynamical correlations in the evolution of a simple quantum probe. Using the example of a qubit coupled to a transverse-field Ising model, we show how the non-Markovian rate or spectral flow can be used to identify stable and unstable fixed points, infer scaling dimensions of relevant fields, and deduce the renormalization group flow induced by deformations around any fixed point.
Open system probes can provide an efficient means to characterize quantum many-body systems by employing them as engineered environments. The key idea is to map long-range spatial correlations of the environment onto dynamical correlations in the evolution of a simple quantum probe. Using the example of a qubit coupled to a transverse-field Ising model, we show how the non-Markovian rate or spectral flow can be used to identify stable and unstable fixed points, infer scaling dimensions of relevant fields, and deduce the renormalization group flow induced by deformations around any fixed point.
The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fixed-point manifold, while the flow preserves the target unitary and monotonically reduces the Hamiltonian weight outside this subspace. Exploiting the freedom in constructing the flow, we introduce flow-equation engineering to enhance the versatility of the framework for diverse control problems, including time-periodic and open-interval smooth protocols with prescribed endpoints. We provide two disparate applications to exhibit the utility of our approach: (i) Nonperturbative Floquet engineering beyond the regime of validity of high-frequency expansions, which we demonstrate by constructing an implementable time-periodic protocol for the Haldane model; (ii) Accessible fast-forward driving from unit-fidelity counterdiabatic evolution, which we showcase for large transverse-field Ising chains away from the adiabatic regime by compressing the long-range multibody adiabatic gauge potential into the original time-dependent Ising control schedules. Our control RG framework reveals a unifying perspective on Hamiltonian engineering and unitary quantum control, and can serve as an organizing principle behind seemingly disparate nonequilibrium quantum dynamics.
We present a renormalization-group (RG) method which allows for an analytical study of the transient dynamics of open quantum systems on all time scales. Whereas oscillation frequencies and decay rates of exponential time evolution follow from the fixed point positions, the long-time behavior of preexponential functions is related to the scaling behavior around the fixed points. We show that certain terms of the RG flow are only cut off by inverse time, which leads to a difference between infrared and ultraviolet scaling. An evaluation for the Ohmic spin boson model at weak damping reveals significant deviations from previous predictions in the long-time regime. We propose that weak-coupling problems for stationary quantities can in principle turn into strong-coupling ones for the determination of the long-time behavior.
We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.
Abstract Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.
In this paper, we provide a complete description of the life cycle of entanglement during the real-time motion of open quantum systems. The quantum environment can have arbitrary (e.g., structured) spectral density. The entanglement can be seen constructively as a Lego: its bricks are the modes of the environment. These bricks are connected to each other via operator transforms. The central result is that during each infinitesimal time interval one new (incoming) mode of the environment gets coupled (entangled) to the open system, and one new (outgoing) mode gets irreversibly decoupled (disentangled from the future). Moreover, each moment of time, only a few relevant modes (three to four in the considered cases) are non-negligibly coupled to the future quantum motion. These relevant modes change (flow or renormalize) with time. As a result, the temporal entanglement has the structure of a matrix-product operator. This allows us to pose a number of questions and to answer them in this paper: What is the intrinsic quantum complexity of a real time motion? Does this complexity saturate with time or grow without bounds? How does one do the real-time renormalization group in a justified way? How do the classical Brownian stochastic trajectories emerge from the quantum evolution? How does one construct the few-mode representations of non-Markovian environments? We provide illustrative simulations of the spin-boson model for various spectral densities of the environment: semicircle, subohmic, ohmic, and superohmic.
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.