We review the most recent developments in the theory of open quantum systems focusing on situations in which the reservoir memory effects, due to long-lasting and non-negligible correlations between system and environment, play a crucial role. These
systems are often referred to as non-Markovian systems. After a brief summary of different measures of non-Markovianity that have been introduced over the last few years we restrict our analysis to the investigation of information flow between system and environment. Within this framework we introduce an important application of non-Markovianity, namely its use as a quantum probe of complex quantum systems. To illustrate this point we consider quantum probes of ultracold gases, spin chains, and trapped ion crystals and show how properties of these systems can be extracted by means of non-Markovianity measures.
The Landau-Zener formula provides an analytical expression for the final excitation of a quantum system after passage of an avoided crossing of two energy levels. If the two levels correspond to a ground state, and to an excited state which is subjec
t to radiative decay, the probability of exciting the system by adiabatic passage of the level crossing is reduced. In this article we use a stochastic master equation to study the level crossing dynamics when the system is subject to continuous probing of the emitted radiation. The measurement backaction on the system associated with the fluctuating homodyne detection record alters the level crossing dynamics, leading to significant excitation in spite of decay and imperfect transfer.
We present a detailed investigation of the dynamics of two physically different qubit models, dephasing under the effect of an ultracold atomic gas in a Bose-Einstein condensed (BEC) state. We study the robustness of each qubit probe against environm
ental noise; even though the two models appear very similar at a first glance, we demonstrate that they decohere in a strikingly different way. This result holds significance for studies of reservoir engineering as well as for using the qubits as quantum probes of the ultracold gas. For each model we study whether and when, upon suitable manipulation of the BEC, the dynamics of the qubit can be described by a (non-)Markovian process and consider the the effect of thermal fluctuations on the qubit dynamics. Finally, we provide an intuitive explanation for the phenomena we observe in terms of the spectral density function of the environment.
We study the effect of thermal fluctuations on a probe qubit interacting with a Bose-Einstein condensed (BEC) reservoir. The zero-temperature case was studied in [Haikka P et al 2011 Phys. Rev. A 84 031602], where we proposed a method to probe the ef
fects of dimensionality and scattering length of a BEC based on its behavior as an environment. Here we show that the sensitivity of the probe qubit is remarkably robust against thermal noise. We give an intuitive explanation for the thermal resilience, showing that it is due to the unique choice of the probe qubit architecture of our model.
We study non-Markovianity and information flow for qubits experiencing local dephasing with an Ohmic class spectrum. We demonstrate the existence of a temperature-dependent critical value of the Ohmicity parameter s for the onset of non-Markovianity
and give a physical interpretation of this phenomenon by linking it to the form of the reservoir spectrum. We demonstrate that this link holds also for more general spectra. We unveil a class of initial states for which discord is forever frozen at a positive value. We connect time invariant discord to non-Markovianity and propose a physical system in which it could be observed.
A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Losc
hmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.
We study quantum information flow in a model comprising of an impurity qubit immersed in a Bose-Einstein condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold res
ervoir within experimentally realistic limits. We place a particular emphasis on non-Markovian dynamics, characterized by a reversed flow of information from the background gas to the qubit and identify a controllable crossover between Markovian and non-Markovian dynamics in the parameter space of the model.
We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation of this study is twofold: on one hand, we study the differences
and analogies of the non-Markovianity measures and on the other hand, we investigate the effect of the driving force on the dissipative dynamics of the qubit. In particular we ask if the drive introduces new channels for energy and/or information transfer between the system and the environment, or amplifies existing ones. We show under which conditions the presence of the drive slows down the inevitable loss of quantum properties of the qubit.
We study a driven two-state system interacting with a structured environment. We introduce the non-Markovian master equation ruling the system dynamics, and we derive its analytic solution for general reservoir spectra. We compare the non-Markovian d
ynamics of the Bloch vector for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic timescales of phase diffusion and relaxation processes.
We present a detailed microscopic derivation for a non-Markovian master equation for a driven two-state system interacting with a general structured reservoir. The master equation is derived using the time-convolutionless projection operator techniqu
e in the limit of weak coupling between the two-state quantum system and its environment. We briefly discuss the Markov approximation, the secular approximation and their validity.
