Non-adiabatic effects in periodically driven-dissipative open quantum systems

We present a general method to calculate the quasi-stationary state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems -- two- and three-level models as well as the driven nonlinear cavity -- we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising non-adiabatic features in the response of these systems.Comment: 12 pages, 8 figure

Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables

To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily \emph{increase} significantly in order to reach a stationary state with \emph{smaller} occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the \emph{prohibition} of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.Comment: Submitted to The Journal of Chemical Physics, 19 pages + 14 pages of appendices with 13 figures. Significantly extended introduction and discussion, no results change

Model projections on the impact of HCV treatment in the prevention of HCV transmission among people who inject drugs in Europe"

Prevention of hepatitis C virus (HCV) transmission among people who inject drugs (PWID) is critical for eliminating HCV in Europe. We estimated the impact of current and scaled-up HCV treatment with and without scaling up opioid substitution therapy (OST) and needle and syringe programmes (NSPs) across Europe over the next 10 years. We collected data on PWID HCV treatment rates, PWID prevalence, HCV prevalence, OST, and NSP coverage from 11 European settings. We parameterised an HCV transmission model to setting-specific data that project chronic HCV prevalence and incidence among PWID. At baseline, chronic HCV prevalence varied from <25% (Slovenia/Czech Republic) to >55% (Finland/Sweden), and <2% (Amsterdam/Hamburg/Norway/Denmark/Sweden) to 5% (Slovenia/Czech Republic) of chronically infected PWID were treated annually. The current treatment rates using new direct-acting antivirals (DAAs) may achieve observable reductions in chronic prevalence (38-63%) in 10 years in Czech Republic, Slovenia, and Amsterdam. Doubling the HCV treatment rates will reduce prevalence in other sites (12-24%; Belgium/Denmark/Hamburg/Norway/Scotland), but is unlikely to reduce prevalence in Sweden and Finland. Scaling-up OST and NSP to 80% coverage with current treatment rates using DAAs could achieve observable reductions in HCV prevalence (18-79%) in all sites. Using DAAs, Slovenia and Amsterdam are projected to reduce incidence to 2 per 100 person years or less in 10 years. Moderate to substantial increases in the current treatment rates are required to achieve the same impact elsewhere, from 1.4 to 3 times (Czech Republic and France), 5-17 times (France, Scotland, Hamburg, Norway, Denmark, Belgium, and Sweden), to 200 times (Finland). Scaling-up OST and NSP coverage to 80% in all sites reduces treatment scale-up needed by 20-80%. The scale-up of HCV treatment and other interventions is needed in most settings to minimise HCV transmission among PWID in Europe. Measuring the amount of HCV in the population of PWID is uncertain. To reduce HCV infection to minimal levels in Europe will require scale-up of both HCV treatment and other interventions that reduce injecting risk (especially OST and provision of sterile injecting equipment

Quantum information & open-system dynamics : periodic driving within and complete positivity beyond the Markovian limit

In this thesis, the dynamics of generic open quantum systems is studied at the interface of quantum information and statistical field theory. Taking advantage of their synergies, we put the dynamical correlations that such systems develop with their effective environment on center stage: The key step to access the latter is a reformulation of the open system's dynamics as derived from nontrivial microscopic models in terms of Kraus operator-sums. This decomposition into physical processes conditional on measurements performed on the effective environment enables progress on three interrelated questions. How do quantum (non-)Markovian systems affect their environment? The common notion of a Markovian process entails an environment that loosely speaking retains no `memory' of its previous interactions with the system. More precisely, the dynamics is insensitive to a division at intermediate times at which the environment is reinitialized. We provide some new physical intuition for different divisibility criteria by explicitly determining the dynamics of the effective environment for a tunnel-coupled resonant level without interactions. From the time-dependence of transport currents and observable measures of information exchange between the system and its environment, we find that the details of the reinitialization matter even in this simple model. Obtaining this complete picture of the open system's dynamics not only requires an exact treatment of the problem, but also a combination of various approaches --including the Kraus operator-sum. How does periodic driving of the environment modify Markovian systems? For any but the simplest models, a detailed analysis such as the above is out of reach due to the necessity of employing approximations. The paradigmatic Born-Markov approximation is the prime example that manages to maintain a consistent yet intuitive operational understanding of the dynamics even in the presence of fast time periodic driving. We illustrate for quantum optical systems how such time-periodic driving influences the dynamical system-environment correlations and leads to driven-dissipative phase transitions which reflect a memory-effect within this originally Markovian setup. A hallmark feature of this transition is the temporary suppression of effective dissipation rates that gives rise to long-lived metastable states and interesting time-periodic steady states. We develop a new formalism for efficiently computing these periodic steady states without the need to integrate over the full transient approach. How can approximations beyond the Markovian limit be formulated? Beyond these Markovian approximations, little is known regarding the preservation of even the most fundamental properties of a reduced system state, namely its positivity and trace-normalization. Here, we focus on the stronger notion of completely positive dynamics and reorganize the real-time diagrammatic series into an operational framework of a Kraus operator-sum in which each term makes this property explicit and has a transparent physical meaning. Based on these principles, we establish for the first time the fundamental structure of the Nakajima-Zwanzig memory-kernel that guarantees the solution of a time-nonlocal quantum master equation to be completely positive. This is a crucial step towards non-Markovian approximation schemes that do not violate fundamental dynamical properties