Quantum state preparation and tomography of entangled mechanical resonators.

Precisely engineered mechanical oscillators keep time, filter signals and sense motion, making them an indispensable part of the technological landscape of today. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors1-3. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout4,5, phonon number resolution6,7 and phonon-mediated qubit-qubit interactions8,9. At present, these acoustic platforms lack processors capable of controlling the quantum states of several mechanical oscillators with a single qubit and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the phonon number distributions of the resonators by means of Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step towards feedback-based operation of a quantum acoustic processor.

Resolving the energy levels of a nanomechanical oscillator.

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 a well defined energy, but are quantum superpositions of equally spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures energy with a precision greater than the energy of a single phonon. 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 energy eigenstates using resolvable differences in the atom's transition frequency. For photons, such dispersive measurements have been performed in cavity1,2 and circuit quantum electrodynamics3. Here we report an experiment in which 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 and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts that are about five 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 that our approach will enable quantum nondemolition measurements of phonons4 and will lead to quantum sensors and information-processing approaches5 that use chip-scale nanomechanical devices.

High-Q photonic resonators and electro-optic coupling using silicon-on-lithium-niobate.

Future quantum networks, in which superconducting quantum processors are connected via optical links, will require microwave-to-optical photon converters that preserve entanglement. A doubly-resonant electro-optic modulator (EOM) is a promising platform to realize this conversion. Here, we present our progress towards building such a modulator by demonstrating the optically-resonant half of the device. We demonstrate high quality (Q) factor ring, disk and photonic crystal resonators using a hybrid silicon-on-lithium-niobate material system. Optical Q factors up to 730,000 are achieved, corresponding to propagation loss of 0.8 dB/cm. We also use the electro-optic effect to modulate the resonance frequency of a photonic crystal cavity, achieving a electro-optic modulation coefficient between 1 and 2 pm/V. In addition to quantum technology, we expect that our results will be useful both in traditional silicon photonics applications and in high-sensitivity acousto-optic devices.