Decoherence in adiabatic quantum evolution - application to Cooper pair pumping

One of the challenges of adiabatic control theory is the proper inclusion of the effects of dissipation. Here, we study the adiabatic dynamics of an open two-level quantum system deriving a generalized master equation to consistently account for the combined action of the driving and dissipation. We demonstrate that in the zero temperature limit the ground state dynamics is not affected by environment. As an example, we apply our theory to Cooper pair pumping which demonstrates the robustness of ground state adiabatic evolution.Comment: 7 pages, derivation of the master equation in the appendi

Work and its fluctuations in a driven quantum system

We analyze work done on a quantum system driven by a control field. The average work depends on the whole dynamics of the system, and is obtained as the integral of the average power operator. As a specific example we focus on a superconducting Cooper-pair box forming a two-level system. We obtain expressions for the average work and work distribution in a closed system, and discuss control field and environment contributions to the average work for an open system.Comment: 8 pages, 3 figure

Calorimetric measurement of work in a quantum system

We propose a calorimetric measurement of work in a quantumsystem. As a physical realization, we consider a superconducting two-levelsystem, a Cooper-pair box, driven by a gate voltage past an avoided levelcrossing at charge degeneracy. We demonstrate that, with realistic experimentalparameters, the temperature measurement of a resistor (environment) can detectsingle microwave photons emitted or absorbed by the two-level system. Thismethod would thus be a way to measure the full distribution of work in repeatedmeasurements, and to assess the quantum fluctuation relations.Peer reviewe

Measurement scheme for the Lamb shift in a superconducting circuit with broadband environment

Motivated by recent experiments on quantum mechanical charge pumping in a Cooper pair sluice, we present a measurement scheme for observing shifts of transition frequencies in two-level quantum systems induced by broadband environmental fluctuations. In contrast to quantum optical and related set-ups based on cavities, the impact of a thermal phase reservoir is considered. A thorough analysis of Lamb and Stark shifts within weak-coupling master equations is complemented by non-perturbative results for the model of an exactly solvable harmonic system. The experimental protocol to measure the Lamb shift in experimentally feasible superconducting circuits is analysed in detail and supported by numerical simulations.Comment: 8 pages, 4 figure

Brownian refrigeration by hybrid tunnel junctions

Voltage fluctuations generated in a hot resistor can cause extraction of heat from a colder normal metal electrode of a hybrid tunnel junction between a normal metal and a superconductor. We extend the analysis presented in [Phys. Rev. Lett. 98, 210604 (2007)] of this heat rectifying system, bearing resemblance to a Maxwell's demon. Explicit analytic calculations show that the entropy of the total system is always increasing. We then consider a single electron transistor configuration with two hybrid junctions in series, and show how the cooling is influenced by charging effects. We analyze also the cooling effect from nonequilibrium fluctuations instead of thermal noise, focusing on the shot noise generated in another tunnel junction. We conclude by discussing limitations for an experimental observation of the effect.Comment: 16 pages, 16 figure

Compressive Sensing-Based Harmonic Sources Identification in Smart Grids

Identifying the prevailing polluting sources would help the distribution system operators in acting directly on the cause of the problem, thus reducing the corresponding negative effects. Due to the limited availability of specific measurement devices, ad hoc methodologies must be considered. In this regard, compressive sensing (CS)-based solutions are perfect candidates. This mathematical technique allows recovering sparse signals when a limited number of measurements are available, thus overcoming the lack of power quality meters. In this article, a new formulation of the ell _{1} -minimization algorithm for CS problems, with quadratic constraint, has been designed and investigated in the framework of the identification of the main polluting sources in smart grids. A novel whitening transformation is proposed for this context. This specific transformation allows the energy of the measurement errors to be appropriately estimated, and thus, better identification results are obtained. The validity of the proposal is proven by means of several simulations and tests performed on two distribution networks for which suitable measurement systems are considered along with a realistic quantification of the uncertainty sources

Cooper pair current in the presence of flux noise

We study the effect of the flux noise on the Cooper pair current and pumping. We generalize the definition of the current in order to take into account the contribution induced by the environment. It turns out that this dissipative current vanishes for charge noise but it is finite in general for noise operators that do not commute with the charge operator. We discuss in a generic framework the effect of flux noise and present a way to engineer it by coupling the system to an additional external circuit. We calculate numerically the pumped charge through the device by solving the master equation for the reduced density matrix of the system and show how it depends on the coupling to the artificial environment.Comment: 10 pages, 6 figure