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Bulletin of the American Physical Society

Tackling Quantum Thermodynamics via Quantum Collision Models

Francesco Ciccarello, Salvatore Lorenzo, G. Massimo Palma

Published Mar 15, 2017• 0 citations
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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 have recently presented a collision-model-based framework to tackle non-Markovian quantum dynamics (Ciccarello et al 2012 arXiv:1207.6554). As a distinctive feature, memory is introduced in a dynamical way by adding extra inter-ancillary collisions to a standard (memoryless) collision model. In this paper, we focus on the case where such intra-bath collisions are described by incoherent partial swap operations. After briefly reviewing the model, we show how to include temperature as an additional parameter by relaxing the assumption that each bath ancilla is initially in a pure state. We also calculate explicitly the dynamical map entailed by the master equation in the paradigmatic instance of a Jaynes–Cummings system–ancilla coupling.
A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.