We have designed and operated a superconducting tunnel junction circuit that behaves as a twolevel atom: the "quantronium". An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout sub-circuit. The measured quality factor of quantum coherence Qϕ ≃ 25000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.Can we build machines that actively exploit the fundamental properties of quantum mechanics, such as the superposition principle or the existence of entangled states? Applications such as the transistor or the laser, often quoted as developments based on quantum mechanics, do not actually answer this question. Quantum mechanics enters into these devices only at the level of material properties but their state variables such as voltages and currents remain classical. Proposals for true quantum machines emerged in the last decades of the 20th century and are now being actively explored: quantum computers [1], quantum cryptography communication systems [2] and detectors operating below the standard quantum limit [3]. The major difficulty facing the engineer of a quantum machine is decoherence [4]. If a degree of freedom needs to be manipulated externally, as in the writing of information, its quantum coherence usually becomes very fragile. Although schemes that actively fight decoherence have recently been proposed [5,6], they need very coherent quantum systems to start with. The quality of coherence for a two-level system can be quantitatively described by the quality factor of quantum coherence Q ϕ = πν 01 T ϕ where ν 01 is its transition frequency and T ϕ is the coherence time of a superposition of the states. It is generally accepted that for active decoherence compensation mechanisms, Q ϕ 's larger than 10 4 ν 01 t op are necessary, t op being the duration of an elementary operation [7].Among all the practical realizations of quantum machines, those involving integrated electrical circuits are particularly attractive. However, unlike the electric dipoles of isolated atoms or ions, the state variables of a circuit like voltages and currents usually undergo rapid quantum decoherence because they are strongly coupled to an environment with a large number of uncontrolled * To whom correspondence should be addressed; E-mail: vion@drecam.saclay.cea.fr † Member of CNRS. ‡ Present address: Applied Physics, Yale University, New Haven, CT 6520, USA degrees of freedom [8]. Nevertheless, superconducting tunnel junction circuits [9,10,11,12,13] have displayed Q ϕ 's up to several hundred [14] and temporal coherent evolution of the quantum state has been observed on the nanosecond time scale [10,15] in the case of the single Cooper pair box [16]. We report here a new circuit built around the Cooper pair box with Q ϕ in excess of 10 4 , whose main feature is the separation of the write and readout ports [17,18]. This circuit, which behaves as a tunable ar...

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

A metallic electrode connected to electron reservoirs by tunnel junctions has a series of charge states corresponding to the number of excess electrons in the electrode. In contrast with the charge state of an atomic or molecular ion, the charge states of such an ""islandÏÏ involve a macroscopic number of conduction electrons of the island. Island charge states bear some resemblance with the photon number states of the cavity in cavity QED, the phase conjugate to the number of electrons being analogous to the phase of the Ðeld in the cavity. For a normal island, charge states decay irreversibly into charge states of lower energies. However, the ground state of a superconducting island connected to superconducting reservoirs can be a coherent superposition of charge states di †ering by two electrons (i.e. a Cooper pair). We describe an experiment in which this Josephson e †ect involving only one Cooper pair is measured.

We have determined the individual transmission coefficients of Al quantum point contacts containing up to six conduction channels. The determination is based on a comparison of the highly nonlinear current-voltage characteristics in the superconducting state with the predictions of the theory for a single channel superconducting contact. We find that at least two channels contribute to the transport even for contacts with conductance lower than the conductance quantum. [S0031-9007(97) PACS numbers: 73.40. Jn, 74.50.+r, 73.20.Dx In mesoscopic structures electrical transport takes place through independent "conduction channels" which are characterized by a transmission coefficient t i and whose contribution to the total conductance G is G 0 t i , where G 0 2e 2 ͞h is the conductance quantum [1]. An atomicsize constriction between two metallic electrodes can accommodate only a small number of such channels. The contact is thus fully described by a set ͕t i ͖ ͕t 1 , t 2 , . . .͖, which depends both on the chemical properties of the atoms forming the contact and on their geometrical arrangement [2][3][4]. Experimentally, contacts consisting of even a single atom have been obtained using both scanning tunnel microscope and break-junction techniques [5,6]. The total transmission T P N i1 t i of the contacts is deduced from their measured conductance G using the Landauer formula G G 0 T . Experiments on a large ensemble of metallic contacts have demonstrated the statistical tendency of atomic-size contacts to have a conductance G close to integer multiples of G 0 [7][8][9]. Does this mean that each channel of the set is either fully open ͑t i 1͒ or completely closed ͑t i 0͒, i.e., that there is an underlying "transmission quantization"? This question cannot be answered solely by conductance measurements which provide no information whatsoever on the individual channels. We show in this Letter that the full set ͕t i ͖ is amenable to measurement in the case of superconducting materials.Several authors [10][11][12] have calculated the currentvoltage characteristics i͑V , t͒ for a single channel superconducting contact with arbitrary transmission t. The upper left inset of Fig. 1 shows their numerical results [13]. A precise determination of the channel content of any superconducting contact is thus possible if one assumes that the total current I͑V ͒ results from the contributions of N independent channels,The i͑V , t͒ curves present a series of sharp current steps at voltage values V 2D͞ne, where n is a positive integer and D is the superconducting gap. The well-known process of single quasiparticle transport corresponds to n 1. The common phenomenon behind the other steps is multiple Andreev reflection (MAR) of quasiparticles between the two superconducting banks [14]. The order n 2, 3, . . . , of a step corresponds to the number of electronic charges transferred in the underlying MAR process. As the transmission of the channel rises from 0 to 1, the higher order processes grow stronger and the subgap current increas...

Carbon nanotubes (CNTs) are not intrinsically superconducting but they can carry a supercurrent when connected to superconducting electrodes 1-4. This supercurrent is mainly transmitted by discrete entangled electron-hole states confined to the nanotube, called Andreev bound states (ABS). These states are a key concept in mesoscopic superconductivity as they provide a universal description of Josephson-like effects in quantum-coherent nanostructures (for example molecules, nanowires, magnetic or normal metallic layers) connected to superconducting leads 5. We report here the first tunnelling spectroscopy of individually resolved ABS, in a nanotubesuperconductor device. Analysing the evolution of the ABS spectrum with a gate voltage, we show that the ABS arise from the discrete electronic levels of the molecule and that they reveal detailed information about the energies of these levels, their relative spin orientation and the coupling to the leads. Such measurements hence constitute a powerful new spectroscopic technique capable of elucidating the electronic structure of CNT-based devices, including those with well-coupled leads. This is relevant for conventional applications (for example, superconducting or normal transistors, superconducting quantum interference devices 3 (SQUIDs)) and quantum information processing (for example, entangled electron pair generation 6,7 , ABS-based qubits 8). Finally, our device is a new type of d.c.measurable SQUID. First conceived of four decades ago 9 , ABS are electronic analogues of the resonant states in a Fabry-Pérot resonator. The cavity is here a nanostructure and its interfaces with superconducting leads play the role of the mirrors. Furthermore, these 'mirrors' behave similarly to optical phase-conjugate mirrors: because of the superconducting pairing, electrons in the nanostructure with energies below the superconducting gap are reflected as their time-reversed particle-a process known as Andreev reflection. As a result, the resonant standing waves-the ABS-are entangled pairs of timereversed electronic states, which have opposite spins (Fig. 1a); they form a set of discrete levels within the superconducting gap (Fig. 1b) and have fermionic character. Changing the superconducting phase difference ϕ between the leads is analogous to moving the mirrors and changes the energies E n (ϕ) of the ABS. In response, a populated ABS carries a supercurrent (2e/h)(∂E n (ϕ)/∂ϕ) through the device, whereas states in the continuous spectrum (outside the superconducting gap) have negligible or minor contributions in most common cases 5. Therefore, the finite set of ABS generically determines Josephson-like effects in such systems. As such, ABS

Metallic point contacts and tunnel junctions with a small and adjustable number of conduction channels have been obtained in the last few years using scanning tunneling microscope and break junction techniques. For conventional break junctions, the reported drift of the interelectrode spacing in the tunnel regime is typically of the order of 0.5 pm/min ͑1 pmϭ10 Ϫ12 m͒. We have nanofabricated break junctions which display a drift smaller than 0.2 pm/h. The improvement results from the scaling down by two orders of magnitude of the device dimensions. We describe the nanofabrication process, which can be adapted to most metals. We have performed measurements on Al, Cu, and Nb devices. The results illustrate the ability of the technique to explore phenomenalike conductance quantization and two level fluctuations. These new adjustable atomic size contacts and tunnel junctions can be integrated in complex circuits.

We explore the photonic (bright) side of dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated to the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory. PACS numbers: 74.50+r, 73.23Hk, 85.25Cp Dynamical Coulomb blockade (DCB) of tunneling is a quantum phenomenon in which tunneling of charge through a small tunnel junction is modified by its electromagnetic environment [1][2][3][4]. This environment is described as an impedance in series with the tunnel element (see Fig. 1a). The sudden charge transfer associated with tunneling can generate photons in the electromagnetic modes of the environment. In a normal metal tunnel junction, biased at voltage V , the energy eV of a tunneling electron can be dissipated both into quasiparticle excitations in the electrodes and into photons. At low temperature energy conservation forbids tunneling processes emitting photons with total energy higher than eV . This suppression reduces the conductance at low bias voltage [1, 2, 4]. In a Josephson junction, DCB effects are more prominent since at bias voltages smaller than the gap voltage 2∆/e quasiparticle excitations cannot take away energy. Therefore, as shown in Fig. 1a, the entire energy 2eV of tunneling Cooper pairs has to be transformed into photons in the impedance for a dc current to flow through the junction [3,4]. Experiments have confirmed the predictions of DCB theory for the tunneling current, both in the normal [5][6][7] and superconducting case [8,9] but the associated emission of photons into the environment has never been investigated. The aim of this work is precisely to fill this gap by exploring the photonic side of DCB. We do so by embedding a Josephson junction into a well controlled electromagnetic environment provided by a microwave resonator. The resonator in turn leaks photons into an amplifier, allowing to measure the rate and spectrum of photons emitted by the junction.The experimental setup is represented in Fig. 1b. A small SQUID acts as a tunable Josephson junction with Josephson energy E J = E J0 | cos(eΦ/ )| adjustable via the magnetic flux Φ threading its loop. The microwave resonator is made of two quarter-wave transformers and its fundamental mode has frequency ν 0 6.0 GHz and quality factor Q 0 9.4. Higher modes of the resonator appear at ν n (2n + 1)ν 0 (n = 1, 2, . . .) with the same lineshape up to small deviations caused by the junction

Abstract:Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here, we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasiparticle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup we perform single-shot readout of this "Andreev qubit". We determine its excited state lifetime and coherence time to be in the microsecond range.Quantum jumps and parity switchings are observed in continuous measurements. In addition to possible quantum information applications, such Andreev qubits are a testbed for the physics of single elementary excitations in superconductors. 2The ground state of a uniform superconductor is a many-body coherent state. Microscopic excitations of this superconducting condensate, which can be created for example by the absorption of photons of high enough energy, are delocalized and incoherent because they have energies in a continuum of states. Localized states arise in situations where the superconducting gap Δ or the superconducting phase undergo strong spatial variations: examples include Shiba states around magnetic impurities (1), Andreev states in vortices (2) or in weak links between two superconductors (3). Because they have discrete energies within the gap, Andreev states are expected to be amenable to coherent manipulation (4,5,6,7,8). In the simplest weak link, a single conduction channel shorter than the superconducting coherence length  , there are only two Andreev levels, governed by the transmission probability  of electrons through the channel and the phase difference  between the two superconducting condensates (3). Despite the absence of actual barriers, quasiparticles (bogoliubons) occupying these Andreev levels are localized over a distance  around the weak link by the gradient of the superconducting phase, and the system can be considered an "Andreev quantum dot " (5,6). Figure 1 EE (13,14). The e state can also be reached directly from g by absorption of a photon of energy 2.A EHere we demonstrate experimentally the manipulation of coherent superpositions of states g and , e even if parasitic transitions to o are also observed.3 Atomic-size contacts are suitable systems to address the Andreev physics because they accommodate a small number of short conduction channels (15). We create them using the microfabricated break-junction technique (16). (Fig. 3D). The analysis (23) of this real-time trace yields a parity switching rate of 50kHz (20). 5The coherent manipulation at   of the two-level system formed by g and e is illustrated in Fig. 4. Figure 4A shows the Rabi oscillations between g and e obtained by varying the duration of a driving pulse at frequency 1 ( , )A ff   (Movie S1). Figure 4B shows how the populations of g and e change when the driving pulse frequency ...