The superposition of quantum states is one of the hallmarks of quantum physics, and clear demonstrations of superposition have been achieved in a number of quantum systems. However, mechanical systems have remained a challenge, with only indirect demonstrations of mechanical state superpositions, in spite of the intellectual appeal and technical utility such a capability would bring 1,2 . This is due in part to the highly linear response of most mechanical systems, making quantum operation difficult, as well as their characteristically low frequencies, making it difficult to reach the quantum ground state [3][4][5][6][7][8] . In this work, we demonstrate full quantum control of the mechanical state of a macroscopic mechanical resonator. We strongly couple a surface acoustic wave 9 resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. Most notably, we generate a quantum superposition of the zero and one phonon states and map this and other states using Wigner tomography 10-15 . This precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including using surface acoustic waves to couple disparate quantum systems 16,17 .Linear resonant systems are traditionally challenging to control at the level of single quanta, as they are always in the correspondence limit 18 . The recent advent of engineered quantum devices in the form of qubits has enabled full quantum control over some linear systems, in particular electromagnetic resonators 14,15 . A number of experiments have demonstrated that qubits may provide similar control over mechanical degrees of freedom, including qubits coupled to bulk acoustic modes 3,8 , surface acoustic waves 19,20 , and flexural modes in suspended beams [21][22][23][24] . Of particular note are experiments in which a superconducting qubit is coupled via a piezoelectric material to a microwave-frequency bulk acoustic mode 25 , where the ground state can be achieved at moderate cryogenic temperatures, and demonstrations include controlled vacuum Rabi swaps between the qubit and the mechanical mode 3,8 . However, the level of quantum control and measurement has been limited by the difficulty of engineer-ing a single mechanical mode with sufficient coupling and quantum state lifetime. More advanced operations, such as synthesizing arbitrary acoustic quantum states and measuring those states using Wigner tomography, remain a challenge. Here we report a significant advance in the level of quantum control of a mechanical device, where we couple a superconducting qubit to a microwave-frequency surface acoustic wave resonance, demonstrating groundstate operation, vacuum Rabi swaps between the qubit and the acoustic mode, and the synthesis of mechanical Fock states as well as a Fock state superposition. We map out the Wigner function for these mechanical states using qubit-based Wigner tomography. We note that a similar achievement has recently been reported with an ex...

1 arXiv:1507.06831v1 [quant-ph] Jul 2015The detection and characterization of paramagnetic species by electron-spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology, and materials science [1], from in-vivo imaging [2] to distance measurements in spinlabeled proteins [3]. ESR typically relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession -however, such signals can be very small, prohibiting the application of ESR at the nanoscale, for example, at the single-cell level or on individual nanoparticles. In this work, using a Josephson parametric microwave amplifier combined with high-quality factor superconducting micro-resonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly 4 orders of magnitude. We demonstrate the detection of 1700 bismuth donor spins in silicon within a single Hahn [4] echo with unit signal-to-noise (SNR) ratio, reduced to just 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence [5]. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance. The detection volume of our resonator is ∼0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new and versatile toolbox for ESR at the nanoscale.A wide variety of techniques are being actively explore to push the limits of sensitivity of ESR to the nanoscale, including approaches based on optical [6,7] or electrical [8,9] detection, as well as scanning probe methods [10,11]. Our focus in this work is to maximise the sensitivity of inductively detected pulsed ESR, in order to maintain the broad applicability to different spin species as well as fast high-bandwidth detection. Pulsed ESR spectroscopy proceeds by probing a sample coupled to a microwave resonator of frequency ω 0 and quality factor Q with sequences of microwave pulses that perform successive spin rotations, triggering the emission of a microwave signal called a spin-echo whose amplitude and shape contain the desired information about the number and properties of paramagnetic species. The spectrometer sensitivity is conveniently quantified by the minimal number of spins N min that can be detected within a single echo [4]. Conventional ESR spectrometers use 3D resonators with moderate quality factors in which the spins are only weakly coupled to the microwave photons and thus obtain a sensitivity of N min ∼ 10 13 spins at T = 300 K and X-band fre-2 quencies (ω 0 /2π ∼ 9 − 10 GHz). To increase the sensitivity, micro-fabricated metallic planar resonators with smaller mode volumes have been used, resulting in larger spin-microwave coupling [12,13]. Combined with operation at T = 4 K and the use of low-noise cryogenic amplifiers and superconducting high-Q thin-film resonators, sensitivities up to N min ∼ 10 7 spins have ...

We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20  μs range and a pure dephasing time comprised between 3 and 10  μs. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.