Microwave-to-optical transduction with erbium ions coupled to planar photonic and superconducting resonators.

Optical quantum networks can connect distant quantum processors to enable secure quantum communication and distributed quantum computing. Superconducting qubits are a leading technology for quantum information processing but cannot couple to long-distance optical networks without an efficient, coherent, and low noise interface between microwave and optical photons. Here, we demonstrate a microwave-to-optical transducer using an ensemble of erbium ions that is simultaneously coupled to a superconducting microwave resonator and a nanophotonic optical resonator. The coherent atomic transitions of the ions mediate the frequency conversion from microwave photons to optical photons and using photon counting we observed device conversion efficiency approaching 10-7. With pulsed operation at a low duty cycle, the device maintained a spin temperature below 100 mK and microwave resonator heating of less than 0.15 quanta.

Resonant thermoelectric nanophotonics.

Photodetectors are typically based either on photocurrent generation from electron-hole pairs in semiconductor structures or on bolometry for wavelengths that are below bandgap absorption. In both cases, resonant plasmonic and nanophotonic structures have been successfully used to enhance performance. Here, we show subwavelength thermoelectric nanostructures designed for resonant spectrally selective absorption, which creates large localized temperature gradients even with unfocused, spatially uniform illumination to generate a thermoelectric voltage. We show that such structures are tunable and are capable of wavelength-specific detection, with an input power responsivity of up to 38 V W-1, referenced to incident illumination, and bandwidth of nearly 3 kHz. This is obtained by combining resonant absorption and thermoelectric junctions within a single suspended membrane nanostructure, yielding a bandgap-independent photodetection mechanism. We report results for both bismuth telluride/antimony telluride and chromel/alumel structures as examples of a potentially broader class of resonant nanophotonic thermoelectric materials for optoelectronic applications such as non-bandgap-limited hyperspectral and broadband photodetectors.

Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit.

We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe 4.7±0.9 dB of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.

QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.

Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.

Thermally induced parametric instability in a back-action evading measurement of a micromechanical quadrature near the zero-point level.

We report the results of back-action evading experiments utilizing a tightly coupled electro-mechanical system formed by a radio frequency micromechanical resonator parametrically coupled to a NbTiN superconducting microwave resonator. Due to excess dissipation in the microwave resonator, we observe a parametric instability induced by a thermal shift of the mechanical resonance frequency. In light of these measurements, we discuss the constraints on microwave dissipation needed to perform BAE measurements far below the zero-point level.

Preparation and detection of a mechanical resonator near the ground state of motion.

Cold, macroscopic mechanical systems are expected to behave contrary to our usual classical understanding of reality; the most striking and counterintuitive predictions involve the existence of states in which the mechanical system is located in two places simultaneously. Various schemes have been proposed to generate and detect such states, and all require starting from mechanical states that are close to the lowest energy eigenstate, the mechanical ground state. Here we report the cooling of the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven, microwave-frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as 3.8 +/- 1.3 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Further cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath. This level of cooling is expected to make possible a series of fundamental quantum mechanical observations including direct measurement of the Heisenberg uncertainty principle and quantum entanglement with qubits.

Nanomechanical measurements of a superconducting qubit.

The observation of the quantum states of motion of a macroscopic mechanical structure remains an open challenge in quantum-state preparation and measurement. One approach that has received extensive theoretical attention is the integration of superconducting qubits as control and detection elements in nanoelectromechanical systems (NEMS). Here we report measurements of a NEMS resonator coupled to a superconducting qubit, a Cooper-pair box. We demonstrate that the coupling results in a dispersive shift of the nanomechanical frequency that is the mechanical analogue of the 'single-atom index effect' experienced by electromagnetic resonators in cavity quantum electrodynamics. The large magnitude of the dispersive interaction allows us to perform NEMS-based spectroscopy of the superconducting qubit, and enables observation of Landau-Zener interference effects-a demonstration of nanomechanical read-out of quantum interference.

Radio-frequency scanning tunnelling microscopy.

The scanning tunnelling microscope (STM) relies on localized electron tunnelling between a sharp probe tip and a conducting sample to attain atomic-scale spatial resolution. In the 25-year period since its invention, the STM has helped uncover a wealth of phenomena in diverse physical systems--ranging from semiconductors to superconductors to atomic and molecular nanosystems. A severe limitation in scanning tunnelling microscopy is the low temporal resolution, originating from the diminished high-frequency response of the tunnel current readout circuitry. Here we overcome this limitation by measuring the reflection from a resonant inductor-capacitor circuit in which the tunnel junction is embedded, and demonstrate electronic bandwidths as high as 10 MHz. This approximately 100-fold bandwidth improvement on the state of the art translates into fast surface topography as well as delicate measurements in mesoscopic electronics and mechanics. Broadband noise measurements across the tunnel junction using this radio-frequency STM have allowed us to perform thermometry at the nanometre scale. Furthermore, we have detected high-frequency mechanical motion with a sensitivity approaching approximately 15 fm Hz(-1/2). This sensitivity is on par with the highest available from nanoscale optical and electrical displacement detection techniques, and the radio-frequency STM is expected to be capable of quantum-limited position measurements.

Self-cooling of a micromirror by radiation pressure.

Cooling of mechanical resonators is currently a popular topic in many fields of physics including ultra-high precision measurements, detection of gravitational waves and the study of the transition between classical and quantum behaviour of a mechanical system. Here we report the observation of self-cooling of a micromirror by radiation pressure inside a high-finesse optical cavity. In essence, changes in intensity in a detuned cavity, as caused by the thermal vibration of the mirror, provide the mechanism for entropy flow from the mirror's oscillatory motion to the low-entropy cavity field. The crucial coupling between radiation and mechanical motion was made possible by producing free-standing micromirrors of low mass (m approximately 400 ng), high reflectance (more than 99.6%) and high mechanical quality (Q approximately 10,000). We observe cooling of the mechanical oscillator by a factor of more than 30; that is, from room temperature to below 10 K. In addition to purely photothermal effects we identify radiation pressure as a relevant mechanism responsible for the cooling. In contrast with earlier experiments, our technique does not need any active feedback. We expect that improvements of our method will permit cooling ratios beyond 1,000 and will thus possibly enable cooling all the way down to the quantum mechanical ground state of the micromirror.

Cooling a nanomechanical resonator with quantum back-action.

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK--an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

Approaching the quantum limit of a nanomechanical resonator.

By coupling a single-electron transistor to a high-quality factor, 19.7-megahertz nanomechanical resonator, we demonstrate position detection approaching that set by the Heisenberg uncertainty principle limit. At millikelvin temperatures, position resolution a factor of 4.3 above the quantum limit is achieved and demonstrates the near-ideal performance of the single-electron transistor as a linear amplifier. We have observed the resonator's thermal motion at temperatures as low as 56 millikelvin, with quantum occupation factors of NTH = 58. The implications of this experiment reach from the ultimate limits of force microscopy to qubit readout for quantum information devices.

Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box.

We analyze the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper-pair box. With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states. The Cooper box can also be used to probe the decay of the resonator superposition state due to environmental decoherence.