The quantum nature of an oscillating mechanical object is anything but apparent. The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures the mechanical energy with a precision greater than the energy of a single phonon, ω m . One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish different phonon number states by resolvable differences in the atom's transition frequency. For photons, such dispersive measurements have been studied in cavity [1,2] and circuit quantum electrodynamics [3] where experiments using real and artificial atoms have resolved the photon number states of cavities. Here, we report an experiment where an artificial atom senses the motional energy of a driven nanomechanical oscillator with sufficient sensitivity to resolve the quantization of its energy. To realize this, we build a hybrid platform that integrates nanomechanical piezoelectric resonators with a microwave superconducting qubit on the same chip. We excite phonons with resonant pulses of varying amplitude and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts ≈ 5 times larger than the qubit linewidth. Our result demonstrates a fully integrated platform for quantum acoustics that combines large couplings, considerable coherence times, and excellent control over the mechanical mode structure. With modest experimental improvements, we expect our approach will make quantum nondemolition measurements of phonons [4] an experimental reality, leading the way to new quantum sensors and information processing approaches [5] that use chip-scale nanomechanical devices.In the last decade, mechanical devices have been brought squarely into the domain of quantum science through a series of remarkable experiments exploring * These authors contributed equally to this workPhonon number splitting outline. The state of a mechanical oscillator is described in quantum mechanics by a linear superposition of equally-spaced energy eigenstates |n , each representing a state of n phonons in the system. This quantized structure is normally not resolvable since the transitions between the energy levels all occur at the same frequency ωm. By coupling the resonator to a qubit of transition frequency ωge with a rate g, we cause a splitting in the qubit spectrum parameterized by a dispersive coupling rate χ. This allows us to distinguish between the different phonon number states that are present in the oscillator.the physics of measurement, transduction, and sensing [6][7][8][9][10][11][12][13]. Two paradigms for obtaining quantum control over these systems are those of cavity optomechanics (COM), where the positionx parametrically couple...

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Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined phase of either 0 or π. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevents the environment from learning the randomly chosen phase of the oscillator. This allows the system to oscillate briefly in a quantum superposition of both phases at onceeffectively generating a nonclassical Schrödinger's cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime. * These two authors contributed equally † safavi@stanford.edu 2⠆⠆ââ , whereâ is the annihilation operator of the resonator and χ/2π = 17.3 MHz is the resonator frequency shift per photon ( Fig. 2A). The linewidth of the resonator is κ/2π ≈ 1.1 MHz, which means that we are well within the single-photon Kerr regime [19] with χ/κ ≈ 17. The resonator frequency ω c /2π can be tuned arXiv:1901.09171v1 [quant-ph]

Experimental trace element partitioning values are often used to model the chemical evolution of metallic phases in meteorites, but limited experimental data were previously available to constrain the partitioning behavior in the basic Fe-Ni system. In this study, we conducted experiments that produced equilibrium solid metal and liquid metal phases in the Fe-Ni system and measured the partition coefficients of 25 elements. The results are in good agreement with values modeled from IVB iron meteorites and with the limited previous experimental data. Additional experiments with low levels of S and P were also conducted, to help constrain the partitioning behaviors of elements as a function of these light elements. The new experimental results were used to derive a set of parameterization values for element solid metal-liquid metal partitioning behavior in the Fe-Ni-S, Fe-Ni-P, and Fe-Ni-C ternary systems at 0.1 MPa. The new parameterizations require that the partitioning behaviors in the light-element-free Fe-Ni system are those determined experimentally by this study, in contrast to previous parameterizations that allowed this value to be determined as a best-fit parameter. These new parameterizations, with self-consistent values for partitioning in the end-member Fe-Ni system, provide a valuable resource for future studies that model the chemical evolution of metallic phases in meteorites.

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6-GHz acoustic resonance to a wavelength-scale volume of less than 1 cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate g=2π ≈ 1.6 MHz and a mechanical quality factor Q m ≈ 3 × 10 4 , leading to a cooperativity C ∼ 4 when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.