Measuring the quantum dynamics of a mechanical system, when few phonons are involved, remains a challenge. We show that a superconducting microwave resonator linearly coupled to the mechanical mode constitutes a very powerful probe for this scope. This new coupling can be much stronger than the usual radiation pressure interaction by adjusting a gate voltage. We focus on the detection of phonon blockade, showing that it can be observed by measuring the statistics of the light in the cavity. The underlying reason is the formation of an entangled state between the two resonators. Our scheme realizes a phonotonic Josephson junction, giving rise to coherent oscillations between phonons and photons as well as a self-trapping regime for a coupling smaller than a critical value. The transition from the self-trapping to the oscillating regime is also induced dynamically by dissipation.

In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. In order to test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the non-adiabatic case.Comment: 9 page

We study a gated quantum wire contacted to source and drain electrodes in the Fabry-Pérot regime. The wire is also coupled to a third terminal ͑tip͒, and we allow for an asymmetry of the tip tunneling amplitudes of right-moving and left-moving electrons. We analyze configurations where the tip acts as an electron injector or as a voltage probe and show that the transport properties of this three-terminal setup exhibit very rich physical behavior. For a noninteracting wire we find that a tip in the voltage-probe configuration affects the source-drain transport in different ways, namely, by suppressing the conductance, by modulating the Fabry-Pérot oscillations, and by reducing their visibility. The combined effect of electron-electron interaction and finite length of the wire, accounted for by the inhomogeneous Luttinger liquid model, leads to significantly modified predictions as compared to models based on infinite wires. We show that when the tip injects electrons asymmetrically the charge fractionalization induced by interaction cannot be inferred from the asymmetry of the currents flowing in source and drain. Nevertheless interaction effects are visible as oscillations in the nonlinear tipsource and tip-drain conductances. Important differences with respect to a two-terminal setup emerge, suggesting new strategies for the experimental investigation of Luttinger liquid behavior.

We show that the dynamics of a driven quantum system weakly coupled to the environment can exhibit two distinct regimes. While the relaxation basis is usually determined by the system þ drive Hamiltonian (system-governed dynamics), we find that under certain conditions it is determined by specific features of the environment, such as, the form of the coupling operator (environment-governed dynamics). We provide an effective coupling parameter describing the transition between the two regimes and discuss how to observe the transition in a superconducting charge pump. Introduction.-Understanding how quantum systems interact with the environment [1] is of paramount importance in quantum information science. While unveiling how the classical world emerges from the quantum one [2], it can also lead to a better protection against decoherence effects on the way towards the realization of a quantum computer [3].A standard approach to the dynamics of open quantum systems boils the problem down to the measurement of decoherence rates, distinguishing between coherence loss, or dephasing, and relaxation. While this approach has successfully described a variety of quantum systems, it only offers a limited insight into the dynamics of decoherence. A promising line of work developed in the last decade exploits the possibility of coupling the system to an engineered reservoir [4][5][6][7][8][9][10][11][12].As new and more accurate ways are found of harnessing the dynamic evolution of quantum systems, it becomes increasingly important to understand how the interaction with the environment is affected by a time-dependent modulation of the system parameters. Indeed, the study of dissipation in driven quantum systems is a longestablished topic [13] that keeps finding new applications to quantum pumping [14][15][16], quantum computation [17,18], and possibly even biological systems [19,20].In this Letter, we consider a periodically driven quantum system in the presence of a weakly coupled environment. We show that under certain conditions decoherence takes place in a preferred basis determined by specific features of the environment, such as, the type of noise, rather than of the system. We label this unusual regime as environmentgoverned dynamics (EGD), as opposed to the more familiar system-governed dynamics (SGD). We introduce an effective coupling parameter that presides over the transition between SGD and EGD. This parameter can be tuned by changing the properties of the drive. Our analysis is general and applies to optical and solid-state systems alike.

We investigate the dynamics of a superconducting rectifying circuit, namely, a three-junction superconducting quantum interference device ͑SQUID͒, where one arm of the superconducting loop consists of a nanomechanical resonator. We find that the dc characteristic curve of the system displays features that are directly related to the frequency and amplitude of the mechanical oscillations; these effects can be further enhanced by biasing the SQUID with an ac current. We discuss potential future developments of this idea in the field of ultrasensitive position detection, and assess their feasibility in current setups.