Over the last decade and a half, superconducting circuits have advanced to the point where we can generate and detect highly-entangled states, and perform universal quantum gates. These macroscopic, artificial systems now allow us to tailor-make interesting Hamiltonians with several interacting degrees of freedom. Meanwhile, the coherence properties of these systems have improved more than 10,000-fold. I will describe recent experiments, such as the most recent advance in coherence using a three-dimensional implementation of qubits and cavities (3D circuit QED) and the implementation of rudimentary error-correction protocols. I will also discuss the prospects for the future of this rapidly advancing field.
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That an object can be in two distinct places simultaneously is a consequence of quantum theory and a fact routinely invoked to account for the behavior of electrons and atoms. Nevertheless, these superpositions are in conflict with our everyday experience. What is the largest and most tangible object that can be prepared in such a superposition? This question has motivated researchers to fabricate micron-scale mechanical resonators and coax them towards the regime of quantum behavior. Indeed micro-mechanical devices recently reached the quantum regime.
In this talk, I will describe how we use electricity to achieve the exquisite control and measurement of micro-mechanical resonators necessary to reach the quantum regime. Having entered this regime, we are now able to pursue many exciting ideas. We endeavor to use mechanical resonators as long-lived memories for the quantum states of electrical circuits. In addition, we are developing the technology to transfer quantum states between two incompatible systems via a mechanical intermediary. In the future, it may even be possible to test quantum theory itself in an unexplored region of mass and size scales.
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A single Nitrogen Vacancy (NV) center hosted in a diamond nanocrystal is positioned at the extremity of a SiC nanowire. This novel hybrid system couples the degrees of freedom of two radically different systems, i.e. a nanomechanical oscillator and a single quantum object. The dynamics of the nano-resonator is probed through time resolved nanocrystal fluorescence and photon correlation measurements. Moreover, by immersing the system in a strong magnetic field gradient, we obtain a clear signature of a magnetic coupling between the nanomechanical oscillator position and the NV electronic spin.
This represents a first step toward the realization of a hybrid nanomechanical system whose both components can be monitored and controlled.
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Thanks to their reduced inertial mass, small-scale mechanical resonators (micro and nanoscale) are subject to the mechanical action of light. Radiation pressure, photothermal pressure, electrostriction or optoelectronic forces, can actuate and control the vibration of these resonators, cool their mechanical motion to reveal its quantum behavior, modify its dynamics for amplification or mechanical sensing applications. I will present several optical/mechanical systems of decreasing dimensions, and show that nanoscale optomechanical platforms now allow reaching an unprecedented level of coupling between photons and phonons. This will be illustrated by the case of miniature GaAs optomechanical resonators, which combine exquisite nano-optomechanical features with the possibility of III-V semiconductor photonics integration.
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Great progress had been made in understanding mesoscopic electron systems coupled to the environment through leads by considering them as scattering systems and characterizing their physical properties in terms of the properties of a corresponding scattering matrix. Often the electronic device functions as a kind of resonant cavity with a complex or random geometry. Lasers are paradigmatic devices based on electromagnetic resonators, and modern research on micro and nano lasers has led to the development of totally new types of lasers such as photon crystal, chaotic and random lasers, with complicated cavity geometries. Such novel laser structures pose a challenge to conventional laser theory, which typically assumes simple one-dimensional resonators, such as the Fabry-Perot. Following the “mesoscopic approach”, we have formulated a scattering theory of lasing, which describes arbitrarily complex lasers in terms of a non- linear and non-unitary scattering matrix. Steady-state Ab initio Laser Theory (SALT) predicts all of the stationary properties of multi-mode lasers; it treats the openness of the cavity exactly and the non-linear modal interactions to infinite order, in a well-satisfied approximation. It leads to a novel computational algorithm that is many orders of magnitude faster than previous methods, as well as providing much physical insight into complex lasers. The key difference from mesoscopic electron systems is the non- hermitian nature of the system, due to the presence of gain or loss. Our reformulation of laser theory as a scattering theory suggested the possibility of constructing a time-reversed or “anti-laser”, which we term a coherent perfect absorber (CPA). This is a linear device in which the gain medium of the laser is replaced with a loss medium such that the cavity will perfectly absorb the incoming (time-reversed) modes of the corresponding laser at threshold. Recently we have experimentally demonstrated such a device in a simple silicon cavity, which acts as an absorptive interferometer, in which narrow-band absorption can be both increased to ~ 99% and reduced to ~30%. Theoretical extensions of this concept indicate that an appropriately prepared input radiation pattern can be made to penetrate deeply into an opaque elastic scattering medium, where it can be completely captured by a “buried absorber”.
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The mutual coupling of optical and mechanical degrees of freedom via radiation pressure has been a subject of interest in the context of quantum limited displacements measurements for Gravity Wave Detection for many decades, however light forces have remained experimentally unexplored in such systems. Recent advances in nano- and micro-mechanical oscillators have for the first time allowed the observation of radiation pressure phenomena in an experimental setting and constitute the emerging research field of cavity optomechanics [1].
Using on-chip micro-cavities that combine both optical and mechanical degrees of freedom in one and the same device [2], radiation pressure back-action of photons is shown to lead to effective cooling [3-6] of the mechanical oscillator mode using dynamical backaction, which has been predicted by Braginsky as early as 1969 [4]. This back-action cooling exhibits many close analogies to atomic laser cooling. With this novel technique the quantum mechanical ground state of a micromechanical oscillator has been prepared with high probability using both microwave and optical fields. In our research this is reached using cryogenic precooling to ca. 700 mK in conjunction with laser cooling, allowing cooling of micro-mechanical oscillator to only 1.7 quanta. – implying the oscillator resides more than 1/3 of its time in the quantum ground state. Moreover it is possible in this regime to observe quantum coherent coupling in which the mechanical and optical mode hybridize and the coupling rate exceeds the mechanical and optical decoherence rate [7]. This accomplishment enables a range of quantum optical experiments, including state transfer from light to mechanics using the phenomenon of optomechanically induced transparency [8].
From a broader perspective the described experiments that exploit optomechanical coupling are motivated both by the effort to realize quantum measurement schemes on mechanical systems in an experimental setting as well as to explore the behavior of nanomechanical systems at low temperatures.

[1] T. J. Kippenberg, K. J. Vahala, Cavity Optomechanics: Backaction at the mesoscale. Science 321, 1172 (2008, 2008).
[2] T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, K. J. Vahala, Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity. Physical Review Letters 95, 033901 (2005).
[3] V. B. Braginsky, S. P. Vyatchanin, Low quantum noise tranquilizer for Fabry-Perot interferometer. Physics Letters A 293, 228 (Feb 4, 2002).
[4] V. B. Braginsky, Measurement of Weak Forces in Physics Experiments. (University of Chicago Press, Chicago, 1977).
[5] A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, T. J. Kippenberg, Radiation pressure cooling of a micromechanical oscillator using dynamical backaction. Physical Review Letters 97, 243905 (Dec 15, 2006).
[6] A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, T. J. Kippenberg, Resolved-sideband cooling of a micromechanical oscillator. Nature Physics 4, 415 (May, 2008).
[7] E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, T.J. Kippenberg, Nature (2012)
[8] S. Weis et al., Optomechanically Induced Transparency. Science 330, 1520 (Dec, 2010).
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The electromagnetic environment of a tunnel junction can modify the current through the junction because the sudden charge transfer associated with a tunnel event can generate photons in the environment. This dissipation process, called dynamical Coulomb blockade (DCB), tends to reduce the current through a normal metal junction at low bias and in the case of a Josephson junction allows for a Cooper pair current at non-zero bias voltage [1]. DCB has been extensively studied and is well understood [2], yet the radiation emitted into the electromagnetic environment has never been observed. With the advent of circuit quantum electrodynamics, the quantum properties of the photons emitted could now become useful.
We explore this bright (photonic) side of DCB by measuring the radiation emitted by a voltage-biased Josephson junction embedded in a microwave resonator. 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.
[1] T. Holst et al. Effect of a transmission line resonator on a small capacitance tunnel junction. Phys. Ref. Lett. 73, 3455 (1994)
[2] H. Grabert and M. H. Devoret (editors). Single charge tunneling. Plenum Press (1992). In particular chapter 2 by G.-L. Ingold and Y. V. Nazarov.
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As early as 1974 Aviram and Ratner proposed a device in which organic molecules serve as electronic components, rectifying the current. It has taken more than twenty years before experimental attempts were made to address the transport properties of single molecules. While we are still far from being able to produce reliable device structures, much progress has been made in the techniques of attaching metallic wires to individual molecules, and in the study and understanding of the electronic transport properties of the molecular junctions. Even three-terminal transistor-like devices have been reported. I will briefly review the various experimental techniques and some important results obtained in recent research towards molecular electronics. I will discuss some of the interesting open problems that have not yet been addressed, and give my view of where the field will be heading.
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Great advances have been made in superconducting qubit technology since the first demonstration of coherent oscillations more than 10 years ago. Coherence times have improved by several orders of magnitude, basic gate operations and three qubit entanglement have been demonstrated, but the continuous, high-fidelity monitoring of the qubit state has remained an elusive target. This functionality can play a key role in quantum state feedback, and in particular qubit error correction. We realize such a readout using a wide bandwidth, phase-sensitive parametric amplifier operating near the quantum noise limit. With this level of sensitivity, quantum jumps between the qubit states in a transmon and in a flux qubit are readily resolved in real time. I will discuss the statistics of the quantum jumps as well as the evolution of the qubit under simultaneous measurement and excitation.
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Quantum information theory provides a very challenging but well defined goal for the further development of solid state qubits: achieve high enough fidelity so that fault-tolerant, error corrected quantum computation in networks of these qubits becomes possible. I will review the development and essential textbook facts about quantum error correcting codes, but will discuss developments not yet found in the books that make solid state fault tolerance much more tangible: gate transversality is replaced by code deformation, and concatentation (with the concomitant requirement for long-distance couplings) is replaced by regular, extendable lattice structures of locally interacting qubits. This new point of view points us to a concrete concept of the solid state structure that we need, and indicates fidelity targets, around 99%, which do not appear as unreachable as they once were.
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Superconducting quantum bits and quantum integrated circuits have made significant progress over the past decade. The performance of the individual qubits is now sufficient to begin exploring the fundamentals of quantum mechanics in new experimental systems. In this talk I will present a description of recent experiments at UC Santa Barbara in which superconducting qubits were used to demonstrate the coherent control of individual quanta of light in the microwave band, with the quantum states stored in superconducting resonators. These experiments include the on-demand generation of photon Fock (number) states, with up to about 15 photons, and the synthesis of arbitrary quantum superpositions of these states. More recent experiments have allowed us to shuttle photons between different resonators, and to build entangled states across two resonators, including the generation of NOON states, with N photons in one resonator and zero in the other, superposed with the state where the occupations are reversed.
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In the last decade, superconducting circuits have seen their coherence time increased by three orders of magnitude and can now rival with atomic systems for the implementation of quantum information processors. Microwave photons carry the readout information from the circuit to a macroscopic measurement apparatus. An amplifier is needed to boost the energy of these weak quantum signals to the proper energy level required by standard commercial signal processing instruments. The quantum limit of detection, where the noise added is less than one photon, is still far from being reached in the best commercial amplifiers where about 20 to 40 quanta of noise are added. On the other hand, several important quantum information protocols like state tomography and feedback control of quantum states require the measurement of quantum bit signals to be done with the strict minimum of added noise. I will present our experimental work on a new type of Josephson amplifier implementing the op-amp type of amplifier known as the non-degenerate parametric amplifier. Using a ring of four Josephson junctions, and microwave superconducting resonators, this device is a practical amplifier for qubit readout and operates close to the quantum limit. Our recent advances on the stability and bandwidth tunability of this amplifier will be described.
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One of the bizarre predictions of quantum mechanics is that physical objects can actually be in two places at the same time, or in two physical states at the same time (for instance, a light switch could be both “on” and “off” simultaneously). This clearly contradicts our everyday experience. In this talk, I will illustrate what conditions must be met in order that such quantum effects can be made apparent, and describe a series of experiments that were completed at UC Santa Barbara, in which quantum effects were observed in a mechanical system about the diameter of a human hair. While the conditions for detecting quantum effects are fairly stringent, size does not appear to matter.
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In this talk I will describe two experiments carried out in our group which illustrate the modern view of the Josephson effect in terms of Andreev Bound States.
In the first experiment[1], the current-phase relation is measured on the simplest of the weak links, namely a one-atom contact between two superconducting banks.
In the second one[2], direct observation of individual Andreev Bound States is achieved by tunneling spectroscopy in a carbon nanotube connected to superconducting electrodes.
[1] M. L. Della Rocca, M. Chauvin, B. Huard, H. Pothier, D. Esteve, and C. Urbina, « Measurement of the current-phase relation of superconducting atomic contacts », Phys. Rev. Lett. 99, 127005 (2007).
[2] J.-D. Pillet, C. H. L. Quay, P. Morfin, C. Bena, A. Levy Yeyati and P. Joyez, submitted.
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En physique statistique, les symétries globales (et leurs brisures spontanées) jouent un rôle essentiel pour la description des différentes phases possibles de systèmes macroscopiques. Les symétries locales (ou symétries de jauge) sont surtout associées aux théories fondamentales de la physique (électromagnétisme, interactions faibles et fortes). Je montrerai comment des réseaux de jonctions Josephson permettent de simuler de telles symétries locales. La réalisation la plus simple est celle d’une symétrie discrète à deux éléments. Je montrerai dans ce cas que l’on stabilise ainsi des états supraconducteurs inhabituels, dans lesquels le condensat de paires de Cooper n’existe que localement, car des interférences quantiques le détruisent à grande échelle, laissant la place à un condensat de paires de paires de Cooper. Un tel état possède une dégénérescence dite topologique. Ceci signifie que toute perturbation locale ne lève la dégénérescence qu’à des ordres élevés en théorie des perturbations, typiquement supérieurs à la taille du réseau. Je discuterai des applications possibles de tels réseaux à la réalisation de mémoires quantiques.
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L’asymétrie de diffusion entre les spins + et les spins – à l’interface entre un métal ferromagnétique et un métal non-magnétique est au coeur du principe de fonctionnement des jonctions tunnel ou des multicouches magnétiques qui ont valu le prix Nobel à A. Fert et P. Grünberg en 2007. Bien que ces dispositifs utilisent l’effet tunnel et le spin de l’électron, ils n’exploitent pas un degré de liberté crucial autorisé par la mécanique quantique : la phase de la fonction d’onde. En effet, le plus souvent, cet aspect reste confidentiel et le transport électronique à travers de tels objets est très bien décrit par des lois essentiellement classiques.
Dans la première partie de l’exposé, je présenterai nos observations récentes de transport polarisé en spin dans des dispositifs à base de nanotubes de carbone à plusieurs contacts ferromagnétiques. Je montrerai qu’elles réalisent un pont entre la physique mésoscopique et l’électronique de spin et ouvrent la voie vers la réalisation de composants de la nano-électronique utilisant le degré de liberté quantiques de spin et de phase de la fonction d’onde électronique sur un pied d’égalité.
Dans la deuxième partie de l’exposé, je montrerai comment on peut envisager d’utiliser ce « couplage spin-orbite artificiel » dans des systèmes multi-boîte pour contrôler électriquement l’état de spin d’un seul électron. La possibilité d’utiliser de tels systèmes dans le cadre de l’électrodynamique quantique en cavité sur circuit et, notamment, d’obtenir le régime de couplage fort entre un spin électronique unique et des photons d’une cavité supraconductrice sera discutée.
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This seminar will be devoted to circuit quantum electrodynamics (QED) in the ultrastrong coupling regime. Such an unconvential limit is achieved when the vacuum Rabi frequency (quantifying the light-matter interaction) is comparable or larger than the two-level transition coupled to the bosonic field of a resonator. In particular, quantum properties of a chain of Josephson atoms in a transmission line resonator will be described, both in the case of inductive[1] and capacitive coupling with the resonator field. In the ‘thermodynamic’ limit of a large number of artificial atoms, predictions and constraints will be presented for the occurrence of ‘superradiant’ quantum phase transitions, with a doubly degenerate vacuum (ground state) above a quantum critical coupling. In the finite-size case, the robustness and protection of the vacuum degeneracy in the ultrastrong coupling regime will be explained. Moreover, fundamental analogies and differences with atomic and semiconductor cavity QED will be highlighted. [1] P. Nataf, C. Ciuti, Phys. Rev. Lett. 104, 023601 (2010) and references therein.
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Entanglement has traditionally played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled quantum particles exhibits results at odds with classical behavior. With quantum mechanical predictions now amply confirmed in experiment, entanglement has evolved from a philosophical conundrum to a key resource for quantum-based computation. This seminar will be devoted to the preparation and measurement of two- and three-qubit entanglement in circuit quantum electrodynamics. In this versatile architecture for quantum information processing, a microwave transmission-line resonator couples multiple engineered qubits, enhances their coherence, and allows their readout. Bell and Greenberger-Horne-Zeilinger states are created with simple sequences of one-qubit rotations and two-qubit conditional phase gates. This entanglement is detected using the resonator to directly measure correlations in the qubit register. We discuss both thorough (quantum state tomography) and scalable (witnesses, Mermin-Bell inequalities) means of detection. While control of two-qubit entanglement allows the realization of simple quantum algorithms, a recent extension to three qubits opens the door to exploration of basic quantum error correction.
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The Fluxonium artificial atom consists of a small capacitance Josephson tunnel junction shunted by a long array of large area junctions to form a superconducting loop. With an adequate choice of parameters for both the small and the large junctions, the low energy spectrum of the Fluxonium is quite unique: it almost corresponds to the inductive energy of the loop threaded with an integer number of flux quanta, or fluxons. The external magnetic field tunes the inductive energy of the loop in exactly the same way as an external electric field tunes the electrostatic energy of a single Cooper pair box. Remarkably, we find that transitions between fluxon states show coherence quality factor not worse than in all previously reported conventional superconducting qubits. This is despite the fact that here transition energy is shared equally between 43 junctions of the array. The rich spectrum of the fluxonium could offer new solutions to an efficient quantum information processing schemes involving many qubits as well as quantum non-demolition state monitoring. It will also serve a tool to diagnose intrinsic decoherence sources in Josephson circuits. More generally, our experiment proves that chains of Josephson junctions could be used in designs of complex yet highly coherent superconducting circuits.
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La mise au point d’une architecture capable d’implémenter un processeur quantique d’information requiert des qubits avec des temps de cohérence suffisamment longs pour enchaîner des portes quantiques, d’effectuer ces dernières avec précision, et de lire l’état du registre de qubits en effectuant une mesure projective avec une grande fidélité. Des progrès appréciables sur le front de la cohérence quantique ont été récemment obtenus dans le domaine des qubits Josephson en plaçant une version modifiée de la boîte à paires de Cooper, appelée transmon, dans une cavité microonde résonnante. Ce circuit conceptuellement très proche de l’électrodynamique quantique en cavité manquait toutefois d’une méthode de lecture assez performante pour tester réellement un algorithme quantique même élémentaire ou les inégalités de Bell sur une paire de qubits intriqués. La méthode de lecture par la transmission de la cavité ne permet en effet pas la discrimination fidèle et rapide des états du qubit en raison du bruit encore trop important de l’électronique de mesure. Pour surmonter cette difficulté, nous avons utilisé une cavité non-linéaire dont la transition de bifurcation entre deux états dynamiques peut discriminer rapidement les deux états d’un qubit comme déjà démontré pour d’autres qubits Josephson. Le transmon offre de plus à cette méthode des avantages intrinsèques qui laissent espérer des performances supérieures. L’observation d’oscillations de Rabi avec un contraste atteignant 94% confirme la très bonne fidélité de la lecture réalisée. En effectuant des mesures répétées, nous testons par ailleurs la fidélité de projection de la mesure, et montrons qu’elle n’induit pas de relaxation supplémentaire. Nous discuterons les perspectives ouvertes par ces résultats pour les circuits à plusieurs qubits.
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On montrera simplement les conséquences de la statistique de Fermi dans des conducteurs balistique, comme les gaz d’électrons bidimensionnels, et ses possibilités d’observation expérimentales. Si les conséquences les plus spectaculaires, comme la quantification de la conductance et l’absence de bruit de conducteurs parfaitement balistiques, sont bien connues, un champ d’expérimentation important concerne les corrélations d’échanges, ou intrication, entre électrons provenant de réservoirs indépendants ou d’états d’énergie différente. On discutera plusieurs approches expérimentales pour observer ces effets, l’une en cours et les deux autres en projet : la manipulation d’électrons uniques à la demande ouvrant la porte à l’équivalent électronique de l’expérience Hong-Ou-Mandel avec des photons ; la manipulation de petit nombre d’électrons qui devrait montrer d’importantes déviations aux théories ’classiques’ de statistique de comptage dues à l’indiscernabilité des particules; enfin, la mesure bruit de charge associé à la connexion subite de deux réservoirs comme mesure d’entropie d’intrication.
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‘Circuit QED’ [1] explores quantum optics and cavity quantum electrodynamics in electrical circuits. Josephson junction ‘atoms’ placed inside an on-chip resonant cavity can strongly interact with microwave photons. In addition to being a new test bed for quantum mechanics and quantum optics in the ultra-strong coupling regime, this system has many promising features for quantum computation. This talk will discuss recent experimental progress in the Schoelkopf and Devoret lab at Yale and the Martinis lab at UCSB and present detailed theoretical modeling of the non-linear response of vacuum Rabi peaks to strong microwave driving. Recent progress in developing direct readout of two qubits will be explained. If time permits, the demonstration of the two-qubit Grover search and Deutsch-Josza algorithms by the Schoelkopf group will also be briefly discussed.
[1] ‘Wiring up quantum systems,’ R.J. Schoelkopf and S.M. Girvin, Nature 451, 664 (2008).
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Our fascination with the paradoxical world of quantum physics has evolved, lately, into an effort to apply the most counterintuitive aspects of quantum theory toward a new generation of information processing machines. A variety of approaches have appeared in the last decade, each with its merits and challenges. In all instances, the task for the quantum technologist is hard, but seemingly, frustratingly, not impossible. In this talk, I will review recent progress in the use of the spin of electrons, confined in semiconductor quantum dots, as the basis of the quantum bit (qubit). As in all cases, the challenge of this approach is to maintain control over the qubits through selective, deliberate coupling to the classical world, while guarding against inadvertent coupling, which destroys the subtle coherence that powers quantum information devices. The path forward depends on identifying the inadvertent environmental couplings, which itself turns out to be a very interesting physics problem.
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L’effet Hall quantique est l’un des phénomènes les plus remarquables découverts dans la seconde moitié du 20ème siècle. Observé pour la première fois en 1980, il fait toujours l’objet d’intenses recherches. Une analogie fructueuse avec l’optique quantique permet notamment d’envisager des applications pour le traitement quantique de l’information. Nous nous intéresserons ici à la détermination expérimentale et au contrôle des mécanismes inélastiques qui limitent le temps de vie quantique et déterminent la dynamique du retour vers l’équilibre dans le régime Hall quantique.
Lorsqu’un gaz d’électrons confiné à deux dimensions est soumis à un champ magnétique perpendiculaire, la quantification des orbites cyclotrons conduit à la discrétisation des états électroniques en niveaux de Landau. A chaque niveau de Landau occupé au cœur du système correspond un canal de bord qui porte les excitations électroniques de basse énergie, jouant ainsi un rôle crucial sur la thermodynamique. La théorie effective du régime Hall quantique entier suggère que les canaux de bords sont assimilables à des systèmes 1D de fermions libres chiraux (se propageant selon une direction unique). Pourtant des mesures récentes de la longueur de cohérence de phase sur laquelle des interférences quantiques se produisent, montrent que celle ci est plus faible qu’initialement attendue, de l’ordre de 20µm à 20mK et diminuant comme l’inverse de la température. Le mécanisme de décohérence responsable de ce comportement fait actuellement l’objet de vifs débats.
Lors de ce séminaire sera présentée une série d’expériences très récentes apportant un éclairage expérimental nouveau par la mesure direct de la relaxation en énergie le long d’un canal de bord placé en situation hors d’équilibre. Dans un premier temps, on montrera qu’il est possible d’effectuer la spectroscopie en énergie de la fonction de distribution des excitations électroniques. Ceci en utilisant les niveaux discrets d’une boite quantique comme filtres à énergie. Ensuite, nous déterminerons les mécanismes inélastiques à l’œuvre en analysant l’effet de la longueur de propagation sur la distribution en énergie. Finalement, nous verrons qu’il est possible de réduire considérablement les échanges d’énergie en utilisant une géométrie adaptée.
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I review the theoretical models of the Josephson arrays that form logical qubits protected from local noises, discuss experimental constraints on their designs and the challenges of their implementation. I will discuss optimal geometries that provide best compromise between the level of protection and complexity of their design. I will also present the results of the measurements of several array designs performed by Rutgers group in different setups. These results show that quantum fluctuations protect the resulting qubit from the effect of the static noise in a full agreement with the theoretical predictions. This demonstrates that the parameter scattering of the Josephson junctions available experimentally is sufficiently small to provide us with the topologically protected arrays.
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The Cooper pair box (CPBs) is a simple superconducting circuit that behaves as an artificial atom whose two lowest energy levels can be used to define a quantum bit. Modified CPBs as the quantronium or the transmon developed at CEA-Saclay and Yale University have coherence times sufficiently long to do many atomic physics experiments with them. In the transmon case, the qubit is measured by coupling it to an electromagnetic mode of a coplanar waveguide cavity. The photons stored in the cavity progressively extract information about the quantum state of the qubit, and correlatively dephase it. This information is carried by the phase of the electromagnetic field leaking out of the cavity and being measured by homodyne detection. By continuously applying the measuring field during Rabi oscillations of the circuit, we revisit the quantum measurement problem of a mesoscopic quantum electrical circuit. By increasing the average number of photons in the cavity, we observe the transition between the weak measurement and Zeno regimes, both in the time and frequency domains. In the latter case, we discuss how far the experimental results provide a proof of the quantum behavior of the circuit.
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Dans les mesures dites de « bruit » du courant électrique on détecte la variance des fluctuations i(f) du courant dans un conducteur autour d’une fréquence f, i.e. la quantité < i²(f)>. Après un rappel sur les propriétés générales du bruit hors d’équilibre dans le domaine quantique hf > eV, kT (où V est la tension aux bornes de l’échantillon et T la température), nous nous intéresserons à deux expériences qui visent à sonder les fluctuations de courant au-delà des mesures de bruit habituelles :
-Dynamique du bruit : si l’on applique une tension lentement variable, le bruit va « suivre » l’excitation adiabatiquement. Qu’advient-il lorsque la tension appliquée varie rapidement ? Autrement dit, quel est le temps de réponse du bruit ? Nous discuterons des mesures sur une jonction tunnel dans le régime quantique, lorsque le bruit détecté provient du mouvement de point zéro des électrons.
-Troisième moment des fluctuations : en appliquant une tension finie on brise l’invariance par renversement du sens du temps, entraînant l’apparition d’un courant continu. Il en résulte que les fluctuations du courant peuvent devenir asymétriques, ce qui se traduit par l’existence d’un troisième moment < i³> non nul. Nous discuterons la mesure de ce corrélateur, dans le régime classique puis dans le régime quantique.
Enfin nous verrons comment ces deux concepts sont étroitement reliés en présence d’un environnement électromagnétique, en particulier comment la dynamique du bruit influence la statistique du courant électrique, que ce soit le troisième moment ou plus simplement le courant moyen, un phénomène communément appelé blocage de Coulomb dynamique.
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On propose une description des effets de cohérence de phase sur la propagation des électrons et des ondes électromagnétiques dans les milieux désordonnés. La représentation utilisée est simple mais elle décrit fidèlement les résultats obtenus par des méthodes sophistiquées. On insistera sur la séparation des échelles de longueur dans le régime diffusif, et la distinction entre les phénomènes de diffusion à longue portée et d’interférences quantiques à courte portée. Pour les électrons, ces effets de cohérence définissent le domaine communément appelé celui de la Physique Quantique Mésoscopique, qui concerne des échelles de longueur intermédiaires entre la physique atomique et celles du monde macroscopique. Par extension, cette dénomination couvre aussi les effets d’interférence liés à la propagation dans des milieux complexes des ondes de toute nature, en particulier de la lumière. A l’aide de la représentation proposée, on décrira de façon simple les propriétés physiques, conséquences de la cohérence de phase : localisation faible des électrons, rétrodiffusion cohérente, fluctuations universelles de conductance ou de speckle, dont on rappellera les principales caractéristiques.
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In the physic of quantum conductors, one of the very basic length scales which gives a limitation to the manifestation of quantum effects, is the so-called quantum coherence length Lphi. It characterizes the length on which an excitation exchanges information with other degrees of freedom and hence looses its phase coherence. Lphi has been extensively studied in quasi-1D diffusive wires in the last decade. It has been shown to result from electron electron interaction as predicted by Altshuler-Aronov-Khmelnitsky, leading to a T^-1/3 temperature dependence of Lphi in quasi-1D diffusive wires. Surprisingly, very little has been known about the actual coherence length in the Integer Quantum Hall Regime (IQHE), where transport occurs through one dimensional chiral wires localized on the edge of the sample (the edge states); the number of these edge states being equal to the filling factor (the number of electron per quantum of flux). In principle, for such ballistic wires, one expects the chirality to prevent momentum conserving energy exchange processes and lead to a very long coherence length.
Here, we present an experiment where we have determined Lphi in the quantum Hall regime, by measuring the visibility of quantum interferences in an electronic Mach-Zhender Interferometer. Lphi presents a 1/T dependence which is shown to result from the coupling between the two neighboring edge states and thermal noise: the thermal charge noise in one edge state blur the phase on the other edge state, and hence leads to a finite coherence length proportional to 1/T.
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La mise au point d’une architecture capable d’implémenter un processeur quantique d’information requiert des qubits avec des temps de cohérence suffisamment longs pour enchaîner des portes quantiques, d’effectuer ces dernières avec précision, et de lire l’état du registre de qubits en effectuant une mesure projective avec une grande fidélité. Des progrès appréciables sur le front de la cohérence quantique ont été récemment obtenus dans le domaine des qubits Josephson en plaçant une version modifiée de la boîte à paires de Cooper, appelée transmon, dans une cavité microonde résonnante. Ce circuit conceptuellement très proche de l’électrodynamique quantique en cavité manquait toutefois d’une méthode de lecture assez performante pour tester réellement un algorithme quantique même élémentaire ou les inégalités de Bell sur une paire de qubits intriqués. La méthode de lecture par la transmission de la cavité ne permet en effet pas la discrimination fidèle et rapide des états du qubit en raison du bruit encore trop important de l’électronique de mesure. Pour surmonter cette difficulté, nous avons utilisé une cavité non-linéaire dont la transition de bifurcation entre deux états dynamiques peut discriminer rapidement les deux états d’un qubit comme déjà démontré pour d’autres qubits Josephson. Le transmon offre de plus à cette méthode des avantages intrinsèques qui laissent espérer des performances supérieures. L’observation d’oscillations de Rabi avec un contraste atteignant 94% confirme la très bonne fidélité de la lecture réalisée. En effectuant des mesures répétées, nous testons par ailleurs la fidélité de projection de la mesure, et montrons qu’elle n’induit pas de relaxation supplémentaire. Nous discuterons les perspectives ouvertes par ces résultats pour les circuits à plusieurs qubits.
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La jonction Josephson est un système électronique régit par la mécanique quantique. Ses propriétés sont directement issues de la cohérence de phase macroscopique des supraconducteurs. Au-delà de ses fascinantes propriétés physiques, elle est aussi la brique de base élémentaire de l’électronique supraconductrice, essentiellement développée autour des matériaux à basse température critique opérant à 4K.
La découverte de supraconducteurs dont la température critique est supérieure à celle de l’azote liquide (77K) a fait naître l’espoir qu’une électronique cryogénique commercialisable était à portée de main, dont les performances en terme de rapidité et de consommation énergétique seraient en principe plusieurs ordres de grandeur supérieures à celles des systèmes basés sur la technologie silicium C-MOS. Malheureusement, des difficultés inhérentes aux matériaux eux-même, mais aussi à leur supraconductivité non conventionnelle ont considérablement freiné le développement de dispositifs à grande échelle.
Au cours de ce séminaire, nous présenterons d’abord brièvement les applications des jonctions Josephson dans le domaine de l’électronique, et les bénéfices que l’on peut tirer de leur utilisation. Ensuite, nous montrerons comment la compréhension de la physique de base des supraconducteur à haute température critique, et en particulier la symétrie “onde-d” de leur paramètre d’ordre, nous a conduit à développer des nanojonctions Josephson qui suscitent un réel intérêt pour les applications. Enfin, nous détaillerons les performances de ces jonctions, et nous expliquerons comment le souci de les améliorer nous a conduit à retourner vers la physique fondamentale, et à étudier la propagation de corrélations supraconductrices dans ces systèmes, dans ce qu’on appelle le régime de proximité.

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