Quantum Jump Approach for Work and Dissipation in a Two-Level System

We apply the quantum jump approach to address the statistics of work in a driven two-level system coupled to a heat bath. We demonstrate how this question can be analyzed by counting photons absorbed and emitted by the environment in repeated experiments. We find that the common nonequilibrium fluctuation relations are satisfied identically. The usual fluctuation-dissipation theorem for linear response applies for weak dissipation and/or weak drive. We point out qualitative differences between the classical and quantum regimesPeer reviewe

Electron-phonon coupling and longitudinal mechanical-mode cooling in a metallic nanowire

We investigate electron-phonon coupling in a narrow suspended metallic wire, in which the phonon modes are restricted to one dimension but the electrons behave three-dimensionally. Explicit theoretical results related to the known bulk properties are derived. We find out that longitudinal vibration modes can be cooled by electronic tunnel refrigeration far below the bath temperature provided the mechanical quality factors of the modes are sufficiently high. The obtained results apply to feasible experimental configurations.Comment: 4+ pages, 3 figure

Frequency-dependent current correlation functions from scattering theory

We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal with arbitrary correlation functions. The formalism proves useful, e.g., in view of recent developments in full counting statistics of charge transfer, where detecting schemes have been proposed for measurement of frequency dependent spectra of higher moments. Some of these schemes are different from the well-known fictitious spin detector and therefore generally involve calculation of non-Keldysh-contour-ordered correlation functions. As an illustration of the approach we consider various third order correlation functions of current, including the usual third cumulant of current statistics. We investigate the frequency dependence of these correlation functions explicitly in the case of energy-independent scattering. The results can easily be generalized to the calculation of arbitrary nth order correlation functions, or to include the effect of interactions.Peer reviewe

Observation of transition from escape dynamics to underdamped phase diffusion in a Josephson junction

We have investigated the dynamics of underdamped Josephson junctions. In addition to the usual crossover between macroscopic quantum tunnelling and thermally activated (TA) behaviour we observe in our samples with relatively small Josephson coupling E_J, for the first time, the transition from TA behaviour to underdamped phase diffusion. Above the crossover temperature the threshold for switching into the finite voltage state becomes extremely sharp. We propose a (T,E_J) phase-diagram with various regimes and show that for a proper description of it dissipation and level quantization in a metastable well are crucial.Comment: 4 pages, 3 figure

Limitations in cooling electrons by normal metal - superconductor tunnel junctions

We demonstrate both theoretically and experimentally two limiting factors in cooling electrons using biased tunnel junctions to extract heat from a normal metal into a superconductor. Firstly, when the injection rate of electrons exceeds the internal relaxation rate in the metal to be cooled, the electrons do no more obey the Fermi-Dirac distribution, and the concept of temperature cannot be applied as such. Secondly, at low bath temperatures, states within the gap induce anomalous heating and yield a theoretical limit of the achievable minimum temperature.Comment: 4 pages, 4 figures, added Ref. [6] + minor correction

Measurement scheme of the Berry phase in superconducting circuits

We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. The experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.Comment: 19 pages, 5 figure

One-Shot Quantum Measurement Using a Hysteretic dc SQUID

We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.Peer reviewe

Competition between electronic cooling and Andreev dissipation in a superconducting micro-cooler

We discuss very low temperature experiments on superconducting micro-coolers made of a double Normal metal - Insulator - Superconductor junction. We investigate with a high resolution the differential conductance of the micro-cooler as well as of additional probe junctions. There is an explicit crossover between the single quasi-particle current and the phase-coherent Andreev current. We establish a thermal model by considering the thermal contribution due to the Andreev current. The related increase of the electron temperature is discussed, including the influence of several parameters like the phase-coherence length or the tunnel junction transparency

Optimal Control of Superconducting N-level quantum systems

We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic potential, subject to external time-dependent control fields, {\it i.e.} a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed

Leakage current of a superconductor–normal metal tunnel junction connected to a high-temperature environment

We consider a voltage-biased normal metal-insulator-superconductor (NIS) tunnel junction, connected to a high-temperature external electromagnetic environment. This model system features the commonly observed subgap leakage current in NIS junctions through photon-assisted tunneling which is detrimental for applications. We first consider a NIS junction directly coupled to the environment and analyze the subgap leakage current both analytically and numerically; we discuss the link with the phenomenological Dynes parameter. Then, we focus on a circuit where a low-temperature lossy transmission line is inserted between the NIS junction and the environment. We show that the amplitude of the transmitted frequencies relevant for the photon-assisted tunneling is exponentially suppressed as the length ℓ and the resistance per unit length R0 of the line are increased. Consequently, the subgap current is reduced exponentially as well. This property can not be obtained by means of lumped circuit elements. We finally discuss our results in view of the performance of NIS junctions in applications.Peer reviewe