Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations

The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single, albeit probabilistic, outcome. The time-scale of this "instantaneous" process can be stretched using weak measurements so that it takes the form of a gradual random walk towards a final state. Remarkably, the interim measurement record is sufficient to continuously track and steer the quantum state using feedback. We monitor the dynamics of a resonantly driven quantum two-level system -- a superconducting quantum bit --using a near-noiseless parametric amplifier. The high-fidelity measurement output is used to actively stabilize the phase of Rabi oscillations, enabling them to persist indefinitely. This new functionality shows promise for fighting decoherence and defines a path for continuous quantum error correction.Comment: Manuscript: 5 Pages and 3 figures ; Supplementary Information: 9 pages and 3 figure

Current measurement by real-time counting of single electrons

The fact that electrical current is carried by individual charges has been known for over 100 years, yet this discreteness has not been directly observed so far. Almost all current measurements involve measuring the voltage drop across a resistor, using Ohm's law, in which the discrete nature of charge does not come into play. However, by sending a direct current through a microelectronic circuit with a chain of islands connected by small tunnel junctions, the individual electrons can be observed one by one. The quantum mechanical tunnelling of single charges in this one-dimensional array is time correlated, and consequently the detected signal has the average frequency f=I/e, where I is the current and e is the electron charge. Here we report a direct observation of these time-correlated single-electron tunnelling oscillations, and show electron counting in the range 5 fA-1 pA. This represents a fundamentally new way to measure extremely small currents, without offset or drift. Moreover, our current measurement, which is based on electron counting, is self-calibrated, as the measured frequency is related to the current only by a natural constant.Comment: 9 pages, 4 figures; v2: minor revisions, 2 refs added, words added to title, typos correcte

Synthetic Spectrum Constraints on a Model of the Cataclysmic Variable QU Carinae

Neither standard model SEDs nor truncated standard model SEDs fit observed spectra of QU Carinae with acceptable accuracy over the range 900\AA to 3000\AA. Non-standard model SEDs fit the observation set accurately. The non-standard accretion disk models have a hot region extending from the white dwarf to $R=1.36R_{\rm wd}$,a narrow intermediate temperature annulus, and an isothermal remainder to the tidal cutoff boundary. The models include a range of $\dot{M}$ values between $1.0{\times}10^{-7}M_{\odot} {\rm yr}^{-1}$ and $1.0{\times}10^{-6}M_{\odot} {\rm yr}^{-1}$ and limiting values of $M_{\rm wd}$ between $0.6M_{\odot}$ and $1.2M_{\odot}$. A solution with $M_{\rm wd}=1.2M_{\odot}$ is consistent with an empirical mass-period relation. The set of models agree on a limited range of possible isothermal region $T_{\rm eff}$ values between 14,000K and 18,000K. The model-to-model residuals are so similar that it is not possible to choose a best model. The Hipparcos distance, 610 pc, is representative of the model results. The orbital inclination is between 40\arcdeg and 60\arcdeg.Comment: 52 pages, 19 Figure

Experimental violation of a Bell's inequality in time with weak measurement

The violation of J. Bell's inequality with two entangled and spatially separated quantum two- level systems (TLS) is often considered as the most prominent demonstration that nature does not obey ?local realism?. Under different but related assumptions of "macrorealism", plausible for macroscopic systems, Leggett and Garg derived a similar inequality for a single degree of freedom undergoing coherent oscillations and being measured at successive times. Such a "Bell's inequality in time", which should be violated by a quantum TLS, is tested here. In this work, the TLS is a superconducting quantum circuit whose Rabi oscillations are continuously driven while it is continuously and weakly measured. The time correlations present at the detector output agree with quantum-mechanical predictions and violate the inequality by 5 standard deviations.Comment: 26 pages including 10 figures, preprint forma

Resonant Cooper-Pair Tunneling: Counting Statistics and Frequency-Dependent Current Noise

We discuss the counting statistics and current noise associated with the double Josephson quasiparticle resonance point in a superconducting single electron transistor. The counting statistics are in general phase-dependent, despite the fact that the average current has no dependence on phase. Focusing on parameter regimes where the counting statistics have no phase-dependence, we use a general relation first derived by MacDonald in 1948 to obtain the full frequency-dependent shot noise directly from the counting statistics, without any further approximations. We comment on problems posed by the phase-dependence of the counting statistics for the finite-frequency noise.Comment: 13 pages, 2 figures; to appear in the proceedings of the NATO ASI "New Directions in Mesoscopic Physics", Erice, 200

Conditional statistics of electron transport in interacting nanoscale conductors

Interactions between nanoscale semiconductor structures form the basis for charge detectors in the solid state. Recent experimental advances have demonstrated the on-chip detection of single electron transport through a quantum dot (QD). The discreteness of charge in units of e leads to intrinsic fluctuations in the electrical current, known as shot noise. To measure these single-electron fluctuations a nearby coherent conductor, called a quantum point contact (QPC), interacts with the QD and acts as a detector. An important property of the QPC charge detector is noninvasiveness: the system physically affects the detector, not visa-versa. Here we predict that even for ideal noninvasive detectors such as the QPC, when a particular detector result is observed, the system suffers an informational backaction, radically altering the statistics of transport through the QD as compared to the unconditional shot noise. We develop a theoretical model to make predictions about the joint current probability distributions and conditional transport statistics. The experimental findings reported here demonstrate the reality of informational backaction in nanoscale systems as well as a variety of new effects, such as conditional noise enhancement, which are in essentially perfect agreement with our model calculations. This type of switching telegraph process occurs abundantly in nature, indicating that these results are applicable to a wide variety of systems.Comment: 16 pages, 3 figures, to appear in Nature Physic

Mapping the optimal route between two quantum states

A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves in competition between continuous weak measurement and driven unitary evolution. By tracking individual trajectories that evolve between an arbitrary choice of initial and final states we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wave function collapse, and unitary evolution of the quantum state as described by the Schrodinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may enable new quantum control methods for state steering and information processing.Comment: 12 pages, 9 figure

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

The A - dependence of K0K^{0} and Λ\Lambda neutrinoproduction on nuclei

For the first time, the A- dependence of the production of $K^0$, $\Lambda$ and, for comparison, $\pi^-$ mesons is investigated in neutrinonuclear reactions, using the data obtained with SKAT bubble chamber. An exponential parametrization ($\sim A^{\beta}$) of the particle yields results in ${\beta}_{V^0} = 0.20 \pm 0.05$ for $V^0$ particles (combined $K^0$ and $\Lambda$), while for $\pi^-$ mesons the A- dependence is much weaker, ${\beta}_{\pi^-} = 0.068 \pm 0.007$. A nuclear enhancement of the ratio $K^0/\pi^-$ is found; this ratio increases from $0.055 \pm 0.013$ for $\nu N$- interactions up to $0.070 \pm 0.011$ at $A \approx 21$ and $0.099 \pm 0.011$ at $A \approx 45$. It is observed, that the multiplicity rise of $V^0$'s occures predominantely in the backward hemisphere of the hadronic c.m.s. It is shown, that the A- dependence of the nuclear enhancement of the ${\Lambda}^0$ and $\pi^-$ yields can be reproduced in the framework of a model, incorporating the secondary intranuclear interactions of pions originating from the primary $\nu N$- interactions, while only (29$\pm$9)% of that for $K^0$ at $A \approx 45$ can be attributed to intranuclear interactions.Comment: 18 pages, 8 figure