Efficient Qubit Measurement with a Nonreciprocal Microwave Amplifier.

The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here, we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier, we achieve a measurement efficiency of (72±4)%. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a test bed for the experimental study of ideal weak measurements, and it opens the way toward quantum feedback protocols based on weak measurement such as state stabilization or error correction.

Ultrastrong Parametric Coupling between a Superconducting Cavity and a Mechanical Resonator.

We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling not only exceeds the dissipation in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.

Reconfigurable re-entrant cavity for wireless coupling to an electro-optomechanical device.

An electro-optomechanical device capable of microwave-to-optics conversion has recently been demonstrated, with the vision of enabling optical networks of superconducting qubits. Here we present an improved converter design that uses a three-dimensional microwave cavity for coupling between the microwave transmission line and an integrated LC resonator on the converter chip. The new design simplifies the optical assembly and decouples it from the microwave part of the setup. Experimental demonstrations show that the modular device assembly allows us to flexibly tune the microwave coupling to the converter chip while maintaining small loss. We also find that electromechanical experiments are not impacted by the additional microwave cavity. Our design is compatible with a high-finesse optical cavity and will improve optical performance.

Nonreciprocal Microwave Signal Processing with a Field-Programmable Josephson Amplifier.

We report on the design and implementation of a field-programmable Josephson amplifier (FPJA)-a compact and lossless superconducting circuit that can be programmed in situ by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work, we demonstrate four modes of operation: frequency conversion (transmission of -0.5 dB, reflection of -30 dB), circulation (transmission of -0.5 dB, reflection of -30 dB, isolation of 30 dB), phase-preserving amplification (gain > 20 dB, one photon of added noise) and directional phase-preserving amplification (reflection of -10 dB, forward gain of 18 dB, reverse isolation of 8 dB, one photon of added noise). The system exhibits quantitative agreement with the theoretical prediction. Based on a gradiometric superconducting quantum-interference device with Nb/Al-AlOx/Nb Josephson junctions, the FPJA is first-order insensitive to flux noise and can be operated without magnetic shielding at low temperature. Owing to its flexible design and compatibility with existing superconducting fabrication techniques, the FPJA offers a straightforward route toward on-chip integration with superconducting quantum circuits such as qubits and microwave optomechanical systems.

Mechanically Mediated Microwave Frequency Conversion in the Quantum Regime.

We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than 10^{12} photons/s with a 95% efficiency and a 14 kHz bandwidth. With less than 10^{-1} photons·s^{-1}·Hz^{-1} of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.

Overwhelming Thermomechanical Motion with Microwave Radiation Pressure Shot Noise.

We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noise that enforce the standard quantum limit: the measurement imprecision and radiation pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for cavity optomechanical systems.

Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object.

By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.

Tunable resonant and nonresonant interactions between a phase qubit and LC resonator.

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

Entangling mechanical motion with microwave fields.

When two physical systems share the quantum property of entanglement, measurements of one system appear to determine the state of the other. This peculiar property is used in optical, atomic, and electrical systems in an effort to exceed classical bounds when processing information. We extended the domain of this quantum resource by entangling the motion of a macroscopic mechanical oscillator with a propagating electrical signal and by storing one half of the entangled state in the mechanical oscillator. This result demonstrates an essential requirement for using compact and low-loss micromechanical oscillators in a quantum processor, can be extended to sense forces beyond the standard quantum limit, and may enable tests of quantum theory.

Coherent state transfer between itinerant microwave fields and a mechanical oscillator.

Macroscopic mechanical oscillators have been coaxed into a regime of quantum behaviour by direct refrigeration or a combination of refrigeration and laser-like cooling. This result supports the idea that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits, either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems. As yet, the transfer of an itinerant state or a propagating mode of a microwave field to and from a storage medium has not been demonstrated, owing to the inability to turn on and off the interaction between the microwave field and the medium sufficiently quickly. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mechanical oscillator with amplitudes at the single-quantum level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store quantum information and enable its transfer between otherwise incompatible systems.

Sideband cooling of micromechanical motion to the quantum ground state.

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems, fuelling progress towards quantum computing with trapped ions and generating new states of matter with Bose-Einstein condensates. Analogous cooling techniques can provide a general and flexible method of preparing macroscopic objects in their motional ground state. Cavity optomechanical or electromechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime--in which a system has less than a single quantum of motion--has been difficult because sideband cooling has not sufficiently overwhelmed the coupling of low-frequency mechanical systems to their hot environments. Here we demonstrate sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state. This achievement required a large electromechanical interaction, which was obtained by embedding a micromechanical membrane into a superconducting microwave resonant circuit. To verify the cooling of the membrane motion to a phonon occupation of 0.34 ± 0.05 phonons, we perform a near-Heisenberg-limited position measurement within (5.1 ± 0.4)h/2π, where h is Planck's constant. Furthermore, our device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass. Because mechanical oscillators can couple to light of any frequency, they could also serve as a unique intermediary for transferring quantum information between microwave and optical domains.

Circuit cavity electromechanics in the strong-coupling regime.

Demonstrating and exploiting the quantum nature of macroscopic mechanical objects would help us to investigate directly the limitations of quantum-based measurements and quantum information protocols, as well as to test long-standing questions about macroscopic quantum coherence. Central to this effort is the necessity of long-lived mechanical states. Previous efforts have witnessed quantum behaviour, but for a low-quality-factor mechanical system. The field of cavity optomechanics and electromechanics, in which a high-quality-factor mechanical oscillator is parametrically coupled to an electromagnetic cavity resonance, provides a practical architecture for cooling, manipulation and detection of motion at the quantum level. One requirement is strong coupling, in which the interaction between the two systems is faster than the dissipation of energy from either system. Here, by incorporating a free-standing, flexible aluminium membrane into a lumped-element superconducting resonant cavity, we have increased the single-photon coupling strength between these two systems by more than two orders of magnitude, compared to previously obtained coupling strengths. A parametric drive tone at the difference frequency between the mechanical oscillator and the cavity resonance dramatically increases the overall coupling strength, allowing us to completely enter the quantum-enabled, strong-coupling regime. This is evidenced by a maximum normal-mode splitting of nearly six bare cavity linewidths. Spectroscopic measurements of these 'dressed states' are in excellent quantitative agreement with recent theoretical predictions. The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion.

rf-SQUID-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator.

We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.

Josephson junction microscope for low-frequency fluctuators.

The high-Q harmonic oscillator mode of a Josephson junction can be used as a novel probe of spurious two-level systems (TLSs) inside the amorphous oxide tunnel barrier of the junction. In particular, we show that spectroscopic transmission measurements of the junction resonator mode can reveal how the coupling magnitude between the junction and the TLSs varies with an external magnetic field applied in the plane of the tunnel barrier. The proposed experiments offer the possibility of clearly resolving the underlying coupling mechanism for these spurious TLSs, an important decoherence source limiting the quality of superconducting quantum devices.

Decoherence in Josephson qubits from dielectric loss.

Dielectric loss from two-level states is shown to be a dominant decoherence source in superconducting quantum bits. Depending on the qubit design, dielectric loss from insulating materials or the tunnel junction can lead to short coherence times. We show that a variety of microwave and qubit measurements are well modeled by loss from resonant absorption of two-level defects. Our results demonstrate that this loss can be significantly reduced by using better dielectrics and fabricating junctions of small area . With a redesigned phase qubit employing low-loss dielectrics, the energy relaxation rate has been improved by a factor of 20, opening up the possibility of multiqubit gates and algorithms.

Simultaneous state measurement of coupled Josephson phase qubits.

One of the many challenges of building a scalable quantum computer is single-shot measurement of all the quantum bits (qubits). We have used simultaneous single-shot measurement of coupled Josephson phase qubits to directly probe interaction of the qubits in the time domain. The concept of measurement crosstalk is introduced, and we show that its effects are minimized by careful adjustment of the timing of the measurements. We observe the antiphase oscillation of the two-qubit 01 and 10 states, consistent with quantum mechanical entanglement of these states, thereby opening the possibility for full characterization of multiqubit gates and elementary quantum algorithms.

Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout.

We have detected coherent quantum oscillations between Josephson phase qubits and critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. These results reveal a new aspect of the quantum behavior of Josephson junctions, and they demonstrate the means to measure two-qubit interactions in the time domain. The junction-fluctuator interaction also points to a possible mechanism for decoherence and reduced fidelity in superconducting qubits.

Decoherence in josephson phase qubits from junction resonators.

Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.

Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+delta.

The electronic structure of simple crystalline solids can be completely described in terms either of local quantum states in real space (r-space), or of wave-like states defined in momentum-space (k-space). However, in the copper oxide superconductors, neither of these descriptions alone may be sufficient. Indeed, comparisons between r-space and k-space studies of Bi2Sr2CaCu2O8+delta (Bi-2212) reveal numerous unexplained phenomena and apparent contradictions. Here, to explore these issues, we report Fourier transform studies of atomic-scale spatial modulations in the Bi-2212 density of states. When analysed as arising from quasiparticle interference, the modulations yield elements of the Fermi-surface and energy gap in agreement with photoemission experiments. The consistency of numerous sets of dispersing modulations with the quasiparticle interference model shows that no additional order parameter is required. We also explore the momentum-space structure of the unoccupied states that are inaccessible to photoemission, and find strong similarities to the structure of the occupied states. The copper oxide quasiparticles therefore apparently exhibit particle-hole mixing similar to that of conventional superconductors. Near the energy gap maximum, the modulations become intense, commensurate with the crystal, and bounded by nanometre-scale domains. Scattering of the antinodal quasiparticles is therefore strongly influenced by nanometre-scale disorder.

Quantum interference of superfluid 3He.

Celebrated interference experiments have demonstrated the wave nature of light and electrons, quantum interference being the manifestation of wave-particle duality. More recently, double-path interference experiments have also demonstrated the quantum-wave nature of beams of neutrons, atoms and Bose-Einstein condensates. In condensed matter systems, double-path quantum interference is observed in the d.c. superconducting quantum interference device (d.c. SQUID). Here we report a double-path quantum interference experiment involving a liquid: superfluid 3He. Using a geometry analogous to the superconducting d.c. SQUID, we control a quantum phase shift by using the rotation of the Earth, and find the classic interference pattern with periodicity determined by the 3He quantum of circulation.