Mechanically Detecting and Avoiding the Quantum Fluctuations of a Microwave Field

During the theoretical investigation of the ultimate sensitivity of gravitational wave detectors through the 1970's and '80's, it was debated whether quantum fluctuations of the light field used for detection, also known as photon shot noise, would ultimately produce a force noise which would disturb the detector and limit the sensitivity. Carlton Caves famously answered this question with "They do." With this understanding came ideas how to avoid this limitation by giving up complete knowledge of the detector's motion. In these back-action evading (BAE) or quantum non-demolition (QND) schemes, one manipulates the required quantum measurement back-action by placing it into a component of the motion which is unobserved and dynamically isolated. Using a superconducting, electro-mechanical device, we realize a sensitive measurement of a single motional quadrature with imprecision below the zero-point fluctuations of motion, detect both the classical and quantum measurement back-action, and demonstrate BAE avoiding the quantum back-action from the microwave photons by 9 dB. Further improvements of these techniques are expected to provide a practical route to manipulate and prepare a squeezed state of motion with mechanical fluctuations below the quantum zero-point level, which is of interest both fundamentally and for the detection of very weak forces

Observation and interpretation of motional sideband asymmetry in a quantum electro-mechanical device

Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up and down frequency-conversion of microwave photons. Due to quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radio-frequency mechanical mode, cooled near the ground state of motion. We also discuss the subtle origin of this imbalance: depending on the measurement scheme, the imbalance is most naturally attributed to the quantum fluctuations of either the mechanical mode or of the electromagnetic field

Quantum squeezing of motion in a mechanical resonator

As a result of the quantum, wave-like nature of the physical world, a harmonic oscillator can never be completely at rest. Even in the quantum ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. In this work, using microwave frequency radiation pressure, we both prepare a micron-scale mechanical system in a state near the quantum ground state and then manipulate its thermal fluctuations to produce a stationary, quadrature-squeezed state. We deduce that the variance of one motional quadrature is 0.80 times the zero-point level, or 1 dB of sub-zero-point squeezing. This work is 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 ultra-sensitive sensing of force and motion

Continuous-time Analysis of Anchor Acceleration

Recently, the anchor acceleration, an acceleration mechanism distinct from Nesterov's, has been discovered for minimax optimization and fixed-point problems, but its mechanism is not understood well, much less so than Nesterov acceleration. In this work, we analyze continuous-time models of anchor acceleration. We provide tight, unified analyses for characterizing the convergence rate as a function of the anchor coefficient $\beta(t)$, thereby providing insight into the anchor acceleration mechanism and its accelerated $\mathcal{O}(1/k^2)$-convergence rate. Finally, we present an adaptive method inspired by the continuous-time analyses and establish its effectiveness through theoretical analyses and experiments

Speckle-visibility spectroscopy: A tool to study time-varying dynamics

We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern formed by the scattered light as detected by a single exposure of a digital camera. Whereas previous multispeckle methods rely on correlations between images, here the connection with scattering site dynamics is made more simply in terms of the variance of intensity among the pixels of the camera for the specified exposure duration. The essence is that the speckle pattern is more visible, i.e. the variance of detected intensity levels is greater, when the dynamics of the scattering site motion is slow compared to the exposure time of the camera. The theory for analyzing the moments of the spatial intensity distribution in terms of the electric field autocorrelation is presented. It is demonstrated for two well-understood samples, a colloidal suspension of Brownian particles and a coarsening foam, where the dynamics can be treated as stationary. However, the method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue.Comment: review - theory and experimen

Electronic structures of Zn1−x_{1-x}Cox_xO using photoemission and x-ray absorption spectroscopy

Electronic structures of Zn$_{1-x}$Co$_x$O have been investigated using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). The Co 3d states are found to lie near the top of the O $2p$ valence band, with a peak around $\sim 3$ eV binding energy. The Co $2p$ XAS spectrum provides evidence that the Co ions in Zn$_{1-x}$Co$_{x}$O are in the divalent Co$^{2+}$ ($d^7$) states under the tetrahedral symmetry. Our finding indicates that the properly substituted Co ions for Zn sites will not produce the diluted ferromagnetic semiconductor property.Comment: 3 pages, 2 figure

Stripe structure, spectral feature and soliton gap in high Tc cuprates

We show that the lightly doped La_{2-x}Sr_{x}CuO_{4} can be described in terms of a stripe magnetic structure or soliton picture. The internal relationship between the recent neutron observation of the diagonal (x=0.05) to vertical (x >= 0.06) stripe transition, which was predicted, and the concomitant metal-insulator transition is clarified by this solitonic physics. The phase diagram with the unidentified transition lines between antiferromagnetic to stripe phases, the doping dependence of the modulation period, the origin of the mid-infrared optical absorption are investigated comparatively with other single layer systems: La_{2-x}Sr_{x}NiO_{4} and (La,Nd)_{2-x}Sr_{x}CuO_{4}. The novel type of quasi-particles and holes is fully responsible for metallic conduction and ultimately superconductivity.Comment: 4 pages RevTex, 5 figure