Frequency-Tunable Josephson Junction Resonator for Quantum Computing

We have fabricated and measured a high-Q Josephson junction resonator with a tunable resonance frequency. A dc magnetic flux allows the resonance frequency to be changed by over 10 %. Weak coupling to the environment allows a quality factor of $\thicksim$7000 when on average less than one photon is stored in the resonator. At large photon numbers, the nonlinearity of the Josephson junction creates two stable oscillation states. This resonator can be used as a tool for investigating the quality of Josephson junctions in qubits below the single photon limit, and can be used as a microwave qubit readout at high photon numbers.Comment: 3 pages, 5 figure

Improving broadband displacement detection with quantum correlations

Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the tradeoff between the probe's shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as \textit{variational readout}, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And more generally our result is a salient example of how correlations can aid sensing in the presence of backaction.Comment: 17 pages, 5 figure

A phononic bandgap shield for high-Q membrane microresonators

A phononic crystal can control the acoustic coupling between a resonator and its support structure. We micromachine a phononic bandgap shield for high Q silicon nitride membranes and study the driven displacement spectra of the membranes and their support structures. We find that inside observed bandgaps the density and amplitude of non-membrane modes are greatly suppressed, and membrane modes are shielded from an external mechanical drive by up to 30 dB.Comment: 5 pages, 4 figure

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 microscopic critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. The period of the oscillations is consistent with the spectroscopic splittings observed in the qubit's resonant frequency. The results point to a possible mechanism for decoherence and reduced measurement fidelity in superconducting qubits and demonstrate the means to measure two-qubit interactions in the time domain

Demonstration of efficient nonreciprocity in a microwave optomechanical circuit

The ability to engineer nonreciprocal interactions is an essential tool in modern communication technology as well as a powerful resource for building quantum networks. Aside from large reverse isolation, a nonreciprocal device suitable for applications must also have high efficiency (low insertion loss) and low output noise. Recent theoretical and experimental studies have shown that nonreciprocal behavior can be achieved in optomechanical systems, but performance in these last two attributes has been limited. Here we demonstrate an efficient, frequency-converting microwave isolator based on the optomechanical interactions between electromagnetic fields and a mechanically compliant vacuum gap capacitor. We achieve simultaneous reverse isolation of more than 20 dB and insertion loss less than 1.5 dB over a bandwidth of 5 kHz. We characterize the nonreciprocal noise performance of the device, observing that the residual thermal noise from the mechanical environments is routed solely to the input of the isolator. Our measurements show quantitative agreement with a general coupled-mode theory. Unlike conventional isolators and circulators, these compact nonreciprocal devices do not require a static magnetic field, and they allow for dynamic control of the direction of isolation. With these advantages, similar devices could enable programmable, high-efficiency connections between disparate nodes of quantum networks, even efficiently bridging the microwave and optical domains.Comment: 9 pages, 6 figure

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte