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We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the **qubit**. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux **qubit**. In particular, when the number of Josephson junctions is increased, several low-energy modes can have **frequencies** lower than the **qubit** **frequency**. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of **oscillations** between the two counterpropagating current states at short times, followed by **oscillation**-like revivals at later times. We analyze how the system approaches such a dynamics as the ring's length is increased and discuss possible experimental implications of this non-adiabatic regime.

Data Types:

- Video

We explain how continuous-variable quantum error-correcting codes can be invoked to protect quantum gates in superconducting circuits against thermal and Hamiltonian noise. The gates are executed by turning on and off a tunable Josephson coupling between an LC **oscillator** and a **qubit** or pair of quits; assuming perfect **qubits**, we show that the gate errors are exponentially small when the **oscillator**'s impedance is large in natural units. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations.

Data Types:

- Video

circular **oscillations**

Data Types:

- Other

We present simulations and a theoretical treatment of vertically vibrated granular media. The systems considered are confined in narrow quasi-two-dimensional and quasi-one-dimensional (column) geometries, where the vertical extension of the container is much larger than both horizontal lengths. The additional geometric constraint present in the column setup frustrates the convection state that is normally observed in wider geometries. This makes it possible to study collective **oscillations** of the grains with a characteristic **frequency** that is much lower than the **frequency** of energy injection. The **frequency** and amplitude of these **oscillations** are studied as a function of the energy input parameters and the size of the container. We observe that, in the quasi-two-dimensional setup, low-**frequency** **oscillations** are present even in the convective regime. This suggests that they may play a significant role in the transition from a density inverted state to convection. Two models are also presented; the first one, based on Cauchy's equations, is able to predict with high accuracy the **frequency** of the particles' collective motion. This first principles model requires a single input parameter, i.e. the centre of mass of the system. The model shows that a sufficient condition for the existence of the low-**frequency** mode is an inverted density profile with distinct low and high density regions, a condition that may apply to other systems too. The second, simpler model just assumes an harmonic **oscillator** like behaviour and, using thermodynamic arguments, is also able to reproduce the observed **frequencies** with high accuracy.

Data Types:

- Video

A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-**qubit** interaction, a strong magnetic field gradient is required to couple the phonon-bus to the **qubit** states. The gate is performed using resonant microwave driving fields together with either a radio-**frequency** (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi **frequency** and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-**qubit** gates. The proposal can also be realized in laser-based set-ups.

Data Types:

- Video

We present band structure calculations and quantum **oscillation** measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum **oscillation** **frequencies** and masses yield zSi = 0.379 c in good agreement with numerical lattice relaxation.

Data Types:

- Video

The preparation stage of optical **qubits** is an essential task in all the experimental setups employed for the test and demonstration of quantum optics principles. We consider a deterministic protocol for the preparation of **qubits** as a superposition of vacuum and one photon number states, which has the advantage to reduce the amount of resources required via phase-sensitive measurements using a local **oscillator** ('dyne detection'). We investigate the performances of the protocol using different phase measurement schemes: homodyne, heterodyne, and adaptive dyne detection (involving a feedback loop). First, we define a suitable figure of merit for the prepared state and we obtain an analytical expression for that in terms of the phase measurement considered. Further, we study limitations that the phase measurement can exhibit, such as delay or limited resources in the feedback strategy. Finally, we evaluate the figure of merit of the protocol for different mode-shapes handily available in an experimental setup. We show that even in the presence of such limitations simple feedback algorithms can perform surprisingly well, outperforming the protocols when simple homodyne or heterodyne schemes are employed.

Data Types:

- Video

We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto–Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh **oscillators**. Such a regime extends the notion of splay state from a uniform distribution of phases to an **oscillating** one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the **frequency** of single units and that of the macroscopic field.

Data Types:

- Video

The acoustic emissions from single cavitation clouds at an early stage of development in 0.521 MHz focused ultrasound of varying intensity, are detected and directly correlated to high-speed microscopic observations, recorded at 1 × 106 frames per second. At lower intensities, a stable regime of cloud response is identified whereby bubble-ensembles exhibit **oscillations** at half the driving **frequency**, which is also detected in the acoustic emission spectra. Higher intensities generate clouds that develop more rapidly, with increased nonlinearity evidenced by a bifurcation in the **frequency** of ensemble response, and in the acoustic emissions. A single bubble **oscillation** model is subject to equivalent ultrasound conditions and fitted to features in the hydrophone and high-speed spectral data, allowing an effective quiescent radius to be inferred for the clouds that evolve at each intensity. The approach indicates that the acoustic emissions originate from the ensemble dynamics and that the cloud acts as a single bubble of equivalent radius in terms of the scattered field. Jetting from component cavities on the periphery of clouds is regularly observed at higher intensities. The results may be of relevance for monitoring and controlling cavitation in therapeutic applications of focused ultrasound, where the phenomenon has the potential to mediate drug delivery from vasculature.

Data Types:

- Video

We explore the fundamental limits on coherence preservation by dynamical decoupling methods in terms of control time scales and the spectrum/bandwidth of the environment. We focus on a decohering **qubit** controlled by arbitrary sequences of pi pulses. Using results from mathematical analysis, we establish a lower bound for coherence loss in terms of the minimum time between the pulses and the spectral cutoff **frequency** of the environment. We argue that similar bounds are applicable to a variety of open-loop unitary control methods while we find no explicit dependence of such lower bounds on the total control time. We use these findings to automatically generate "bandwidth adapted dynamical decoupling" sequences that can be used for preserving a **qubit** up to arbitrary times with the best fidelities theoretically possible given the available control capabilities. We also introduce "Walsh dynamical decoupling" schemes that are optimized for digital sequence generation. Our results imply that fact that, unlike in quantum fault-tolerant architecture, errors cannot be reduced indefinitely using reversible control methods yet a small error can be maintained for a long time.

Data Types:

- Video