Weak and ultrastrong coupling limits of the quantum mean force Gibbs state

This is the final version. Available from the American Physical Society via the DOI in this recordThe Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the system-reservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.Engineering and Physical Sciences Research Council (EPSRC)Royal Societ

Open quantum system dynamics and the mean force Gibbs state

This is the final version. Available on open access from AIP Publishing via the DOI in this recordThe dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system’s energies alone. But at decreasing system sizes, i.e. for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system’s steady state still the Gibbs state? And if not, how may the steady state depend on the interaction details? Here we provide an overview of recent progress on answering these questions. We expand on the state-of-the-art along two general avenues: First we take the static point-of-view which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and non-equilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point-of-view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm which proves return to equilibrium, i.e. convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics, and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics and quantum optics, and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology, to magnetism and nanoscale heat management.Natural Sciences and Engineering Research Council of Canada (NSERC).Engineering and Physical Sciences Research Council (EPSRC)Royal Societ

Frontiers of open quantum system dynamics

We briefly examine recent developments in the field of open quantum system theory, devoted to the introduction of a satisfactory notion of memory for a quantum dynamics. In particular, we will consider a possible formalization of the notion of non-Markovian dynamics, as well as the construction of quantum evolution equations featuring a memory kernel. Connections will be drawn to the corresponding notions in the framework of classical stochastic processes, thus pointing to the key differences between a quantum and classical formalization of the notion of memory effects.Comment: 15 pages, contribution to "Quantum Physics and Geometry", Lecture Notes of the Unione Matematica Italiana 25,E. Ballico et al. (eds.

Overview on the phenomenon of two-qubit entanglement revivals in classical environments

The occurrence of revivals of quantum entanglement between separated open quantum systems has been shown not only for dissipative non-Markovian quantum environments but also for classical environments in absence of back-action. While the phenomenon is well understood in the first case, the possibility to retrieve entanglement when the composite quantum system is subject to local classical noise has generated a debate regarding its interpretation. This dynamical property of open quantum systems assumes an important role in quantum information theory from both fundamental and practical perspectives. Hybrid quantum-classical systems are in fact promising candidates to investigate the interplay among quantum and classical features and to look for possible control strategies of a quantum system by means of a classical device. Here we present an overview on this topic, reporting the most recent theoretical and experimental results about the revivals of entanglement between two qubits locally interacting with classical environments. We also review and discuss the interpretations provided so far to explain this phenomenon, suggesting that they can be cast under a unified viewpoint.Comment: 16 pages, 9 figures. Chapter written for the upcoming book "Lectures on general quantum correlations and their applications