Deterministic entanglement of superconducting qubits by parity measurement and feedback.

The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a classical state, destroying the coherence of an initial quantum superposition and the entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement, starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement, which projects the state of multiple qubits (quantum bits) to a state with an even or odd number of excited qubits. A parity meter must discern the two qubit-excitation parities with high fidelity while preserving coherence between same-parity states. Despite numerous proposals for atomic, semiconducting and superconducting qubits, realizing a parity meter that creates entanglement for both even and odd measurement results has remained an outstanding challenge. Here we perform a time-resolved, continuous parity measurement of two superconducting qubits using the cavity in a three-dimensional circuit quantum electrodynamics architecture and phase-sensitive parametric amplification. Using postselection, we produce entanglement by parity measurement reaching 88 per cent fidelity to the closest Bell state. Incorporating the parity meter in a feedback-control loop, we transform the entanglement generation from probabilistic to fully deterministic, achieving 66 per cent fidelity to a target Bell state on demand. These realizations of a parity meter and a feedback-enabled deterministic measurement protocol provide key ingredients for active quantum error correction in the solid state.

Tunable backaction of a DC SQUID on an integrated micromechanical resonator.

We have measured the backaction of a dc superconducting quantum interference device (SQUID) position detector on an integrated 1 MHz flexural resonator. The frequency and quality factor of the micromechanical resonator can be tuned with bias current and applied magnetic flux. The backaction is caused by the Lorentz force due to the change in circulating current when the resonator displaces. The experimental features are reproduced by numerical calculations using the resistively and capacitively shunted junction model.

Cavity electromechanics with parametric mechanical driving.

Microwave optomechanical circuits have been demonstrated to be powerful tools for both exploring fundamental physics of macroscopic mechanical oscillators, as well as being promising candidates for on-chip quantum-limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive element and its displacement is detected using the superconducting cavity, or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanics. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that this approach can realize a phase-sensitive parametric amplifier for intracavity microwave photons. Future perspectives of optomechanical systems with a parametrically driven mechanical oscillator include exotic bath engineering with negative effective photon temperatures, or systems with enhanced optomechanical nonlinearities.

Quantum interference in an interfacial superconductor.

The two-dimensional superconductor that forms at the interface between the complex oxides lanthanum aluminate (LAO) and strontium titanate (STO) has several intriguing properties that set it apart from conventional superconductors. Most notably, an electric field can be used to tune its critical temperature (Tc; ref. 7), revealing a dome-shaped phase diagram reminiscent of high-Tc superconductors. So far, experiments with oxide interfaces have measured quantities that probe only the magnitude of the superconducting order parameter and are not sensitive to its phase. Here, we perform phase-sensitive measurements by realizing the first superconducting quantum interference devices (SQUIDs) at the LAO/STO interface. Furthermore, we develop a new paradigm for the creation of superconducting circuit elements, where local gates enable the in situ creation and control of Josephson junctions. These gate-defined SQUIDs are unique in that the entire device is made from a single superconductor with purely electrostatic interfaces between the superconducting reservoir and the weak link. We complement our experiments with numerical simulations and show that the low superfluid density of this interfacial superconductor results in a large, gate-controllable kinetic inductance of the SQUID. Our observation of robust quantum interference opens up a new pathway to understanding the nature of superconductivity at oxide interfaces.

Self-sustained oscillations of a torsional SQUID resonator induced by Lorentz-force back-action.

For the study of nanomechanical resonators, ultra-sensitive measurement techniques are crucial. However, if the measurement sensitivity approaches quantum-mechanical limits, the back-action of the detector on the resonator cannot be neglected. If the back-action is strong enough, the corresponding instability can create self-sustained oscillators in the resonator. Here we demonstrate that a torsional mechanical resonator, which contains a direct current SQUID displacement detector, leads to this effect. We find that the Lorentz-force back-action can be so large that, in combination with complex nonlinear Josephson dynamics, it generates intrinsic self-sustained oscillations. The flux quantization limit of the maximum oscillation amplitude is exploited to calibrate the displacement resolution, which is shown to be below the standard quantum limit. The suspended torsional SQUID provides an interesting platform to study on-chip laser-like physics in an electromechanical system that can be controlled by both a flux and current bias.

Triplet Josephson effect with magnetic feedback in a superconductor-ferromagnet heterostructure.

We study the ac Josephson effect in a superconductor-ferromagnet heterostructure with a variable magnetic configuration. The system supports triplet proximity correlations whose dynamics is coupled to the magnetic dynamics. This feedback dramatically modifies the behavior of the junction. The current-phase relation becomes double periodic at both very low and high Josephson frequencies omegaJ. At intermediate frequencies, the periodicity in omegaJt may be lost.

Topological confinement in bilayer graphene.

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.

Tunneling in suspended carbon nanotubes assisted by longitudinal phonons.

Current-voltage characteristics of suspended single-wall carbon nanotube quantum dots show a series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Agreement is found with a Franck-Condon-based model in which the phonon-assisted tunneling process is modeled as a coupling of electronic levels to underdamped quantum harmonic oscillators. A comparison with this model indicates a rather strong electron-phonon coupling factor of order unity.

Single-electron tunneling with strong mechanical feedback.

A harmonic nanomechanical oscillator with a high quality factor weakly coupled to a single-electron tunneling device can provide a strong feedback for electron transport. Strong feedback occurs in a narrow voltage range just above the Coulomb blockade threshold. In this regime, current is strongly modified and current noise is drastically enhanced compared to the Schottky value.