Abstract Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the dynamics and thermodynamics of quantum systems. Significant effort has been invested in developing various methods for tackling this issue and in this Perspective paper we focus on one such technique, namely collision models, which have emerged as a remarkably flexible approach. We discuss their application to understanding non-Markovian dynamics and to studying the thermodynamics of quantum systems, two areas in which collision models have proven to be particularly insightful. Their simple structure endows them with extremely broad applicability which has spurred their recent experimental demonstrations. By focusing on these areas, our aim is to provide a succinct entry point to this remarkable framework.
Abstract Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the dynamics and thermodynamics of quantum systems. Significant effort has been invested in developing various methods for tackling this issue and in this Perspective paper we focus on one such technique, namely collision models, which have emerged as a remarkably flexible approach. We discuss their application to understanding non-Markovian dynamics and to studying the thermodynamics of quantum systems, two areas in which collision models have proven to be particularly insightful. Their simple structure endows them with extremely broad applicability which has spurred their recent experimental demonstrations. By focusing on these areas, our aim is to provide a succinct entry point to this remarkable framework.
We study the applicability of collisional models for non-Markovian dynamics of open quantum systems. By allowing interactions between the separate environmental degrees of freedom in between collisions we are able to construct a collision model that allows us to study quantum memory effects in open system dynamics. We also discuss the possibility to embed non-Markovian collision model dynamics into Markovian collision model dynamics in an extended state space. As a concrete example we show how, using the proposed class of collision models, we can discretely model non-Markovian amplitude damping of a qubit. In the time-continuous limit, we obtain the well-known results for spontaneous decay of a two-level system into a structured zero-temperature reservoir.
Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a p-impurity model is non-Markovian, then the corresponding (p+1)-impurity model is also non-Markovian, implying the existence of a critical p at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical p, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.
The paradigm of considering open quantum systems—i.e., focusing only on the system of interest, and treating the rest of the world as an effective environment—has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this Perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.
Collision models provide a simple and versatile setting to capture the dynamics of open quantum systems. The standard approach to thermalization in this setting involves an environment of independent and identically prepared thermal qubits, interacting sequentially for a finite duration Δ t with the system. We compare this to a two-bath scenario in which collisional qubits are prepared in either their ground or excited states and the environment temperature is encoded in system-environment couplings. The system reaches the same thermal steady state for both settings, although even in this limit they describe fundamentally different physical processes, with the two-bath setup yielding a nonequilibrium state with finite heat currents. Non-Markovian dynamics arises when intraenvironment interactions in either setting are introduced. Here the system in the single-bath setup again reaches a steady state at the canonical temperature of the bath, but the nonequilibrium steady state of the two-bath setup tends to a different temperature due to the generation of strong system-environment and intraenvironment correlations. The two-bath setting is particularly suited to studying quantum trajectories, which are well defined also for the non-Markovian case. We showcase this with a trajectory analysis of the heat currents within a two-point measurement scheme. Finally, we consider how our results are impacted when the system-environment interaction leads to strict homogenization. Our results provide insights into the dynamics and thermodynamics of thermalization towards nonequilibrium steady states and the role of non-Markovian interactions.
Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test experimentally various theoretical, mathematical, and physical concepts related to non-Markovian quantum dynamics. This includes experimental characterization and quantification of non-Markovian memory effects and proof-of-principle demonstrations how to use them for certain quantum communication and information tasks. We describe here recent experimental advances for open system studies, focussing in particular to non-Markovian dynamics including the applications of memory effects, and discuss the possibilities for ultimate control of decoherence and open system dynamics.
The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling open quantum systems is via a Collision Model. For instance, one could model the environment as being composed of many small quantum systems (ancillas) which interact with the target system sequentially, in a series of "collisions". In this thesis I will discuss a novel method for constructing a continuous-time master equation from the discrete-time dynamics given by any such collision model. This new approach works for any interaction duration, δt, by interpolating the dynamics between the time-points t=nδt. I will contrast this with previous methods which only work in the continuum limit (as δt→0). Moreover, I will show that any continuum-limit-based approach will always yield unitary dynamics unless it is fine-tuned in some way. For instance, it is common to find non-unitary dynamics in the continuum limit by taking an (I will argue unphysical) divergence in the interaction strengths, g, such that g2δt is constant as δt→0.