On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories1, 2, 3, 4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.

Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light

An on-axis deflectometric microscope system (ODMS) is proposed for the microscopic surface measurement with high accuracy and a large slope dynamic range. To reduce the geometry sensitivity, a beam splitter is employed to build the coaxial configuration among the illumination screen, camera, and tested sample, which facilitates the calibration of system geometrical parameters. Due to the small working distance, the system model miscalibration in the model-ray-tracing-based "null" testing could cause obvious geometrical aberrations. In this paper, the geometrical aberrations due to the system model miscalibration are analyzed, and the corresponding calibration method based on computer-aided reverse optimization is applied to achieve accurate measurement. In addition, the systematic error introduced by the system components in the ODMS are also discussed. Both the simulation and experiment have been carried out to demonstrate the feasibility and high accuracy of the proposed measurement method. The proposed system is compact in structure, large in measurable slope range, and high in spatial resolution, providing a viable metrological tool for the microscopic testing of various freeform surfaces, microstructural elements, and micro-devices.

Design and error calibration of an on-axis deflectometric microscope system.

We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of 9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramer-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift phi while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling. 

Enhanced phase sensitivity in a Mach-Zehnder interferometer via photon recycling

The injection of squeezed vacuum state is an indispensable technology for the next generation gravitational wave observatory, which will open up a much larger window to the universe. After analyzing the absorption and dispersion properties of the reflected field of the dual-recycled Michelson interferometer (DRMI), we propose the phase-sensitive manipulation scheme of squeezed vacuum by utilizing the coupled-resonator-induced transparency in a dual-recycled Michelson interferometer (DRMI). In this way, the rotation frequency of squeezing ellipse can be finely tuned by the coupling strength, which overcome the limitation of the current solution (with a fixed rotation frequency) that employs a Fabry-Perot optical cavity as phase-sensitive manipulation element. This work will unleash the potential applications for quantum metrology beyond the shot noise limit.

Yaohua Peng

Papers

Phase-sensitive manipulation of squeezed vacuum via a dual-recycled Michelson interferometer