Decoherence in quantum bit circuits is presently a major limitation to their use for quantum computing purposes. We present experiments, inspired from NMR, that characterise decoherence in a particular superconducting quantum bit circuit, the quantronium. We introduce a general framework for the analysis of decoherence, based on the spectral densities of the noise sources coupled to the qubit. Analysis of our measurements within this framework indicates a simple model for the noise sources acting on the qubit. We discuss various methods to fight decoherence.Comment: Long paper. 65 pages, 18 Figure

Coherent superpositions of quantum states have already been demonstrated in different superconducting circuits based on Josephson junctions. These circuits are now considered for implementing quantum bits. We report on experiments in which the state of a qubit circuit, the quantronium, is efficiently manipulated using methods inspired from nuclear magnetic resonance (NMR): multipulse sequences are used to perform arbitrary operations, to improve their accuracy, and to fight decoherence.

We report an experiment on the determination of the quantum nondemolition ͑QND͒ nature of a readout scheme of a quantum electrical circuit. The circuit is a superconducting quantum bit measured by microwave reflectometry using a Josephson bifurcation amplifier. We perform a series of two subsequent measurements, record their values and correlation, and quantify the QND character of this readout.

We have mistakenly swapped the values of the Josephson and charging energies in the text and in the caption of Fig. 2 of our Letter. The correct values are E J 0:870 k B K and E C 0:655 k B K. This misprint does not affect the Letter at all.

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in other words the fact that the reduced density matrix of the system has a self-averaging property. This phenomenon, which lies in a generalized central limit theorem, justifies rigorously averaging procedures over certain classes of random interactions and can explain the absence of sensitivity to microscopic details of irreversible processes such as thermalisation. It provides more generally a new ergodic principle for embedded quantum systems.Comment: 9 pages. Accepted for publication in Phys. Rev. A. This article supersedes the part on "dynamical typicality" in arXiv:1510.0435

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.

The addition of nonlinearity to an harmonic resonator provides a route to complex dynamical behaviour of resonant modes, including coupling between them. We present a superconducting device that makes use of the nonlinearity of Josephson junctions to introduce a controlled, tunable, nonlinear inductance to a thin film coplanar waveguide resonator. Considering the device as a potential quantum optical component in the microwave regime, we create a sensitive bifurcation amplifier and then demonstrate spectroscopy of other resonant modes via the intermode coupling. We find that the sensitivity of the device approaches within a factor two quantitative agreement with a quantum model by Dykman but is limited by a noise that has its source(s) on-chip.

We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded quantum system was established for several classes of random interactions. In other words, the time evolution of its quantum state does not depend on the microscopic details of the interaction. Focusing at the long time regime, we use this property to calculate analytically a new partition function characterizing the stationary state and involving the overlaps between eigenvectors of a bare and a dressed Hamiltonian. This partition function provides a new thermodynamical ensemble which includes the microcanonical and canonical ensembles as particular cases. We check our predictions with numerical simulations.In what state of equilibrium can a quantum system be? Does this state have universal properties and what are the conditions for its emergence? These questions are not new, dating even from the very birth of quantum theory [1] and are surprisingly open [2,3]. Indeed, the foundations of statistical physics still rely today on a static Bayesian point of view assuming the equiprobability of the accessible states defining the microcanonical ensemble. Assuming temperature and chemical potential can be defined then the canonical and grand canonical ensembles can be derived, allowing to calculate all relevant macroscopic quantities in the thermodynamical limit [4][5][6]. In order to link theoretical predictions calculated with averages over these ensembles to experimental quantities measured on a single system, an assumption of ergodicity is made. Despite being broadly accepted, this assumption is not justified in a satisfactory manner (see, e.g., the discussion in Ref. [7]). Triggered by recent progress in the quantum engineering of mesoscopic systems [8,9], some theoretical progress has been achieved for attempting to explain thermodynamical equilibrium with a purely quantum point of view.From the early work of von Neumann on quantum ergodicity [1,10], most theoretical studies aiming at understanding thermalisation as a quantum and universal [11] process have focused on looking for signatures of thermalisation on physical observables of large quantum systems [12][13][14][15], for instance with the Eigenstate Thermalisation Hypothesis (ETH) surmise [16][17][18]. Instead of observables, one can also focus on the state of a system embedded in a larger one for which a "canonical typicality" property has been established: the overwhelming majority of pure quantum states of the composite system are locally [19] canonical [20][21][22]. This static "typicality" has been extended to the dynamics of embedded quantum systems (two-level [23], four-level [24] and arbitrary [25] quantum systems). We apply here this "dynamical typicality" property in order to calculate analytically and with full generality the stationary state of an embedded quantum system at long time. We find a new thermody...