A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass m_P (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

This paper presents the results of the observations of the detectors participating in the International Gravitational Event Collaboration (IGEC) from 1997 to 2000 and reviews the data analysis methods. The analysis is designed to search for coincident excitations in multiple detectors. The data set analyzed in this article covers a longer period and is more complete than that given in previous reports. The current analysis is more accurate for determining the false dismissal probability for a time coincidence search and it optimizes the search with respect to a target amplitude and direction of the signal. The statistics of the accidental coincidences agrees with the model used for drawing the results. The observations of this IGEC search are consistent with no detection of gravitational wave burst events. A new conservative upper limit has been set on the rate of gravitational wave bursts with a Fourier component $H>\mathrm{}2\mathrm{}\times {10}^{-21}{\mathrm{Hz}}^{-1},$ both for searches with and without a filter for the galactic center direction. This study confirms that the false alarm rate of the observation can be negligible when at least three detectors are operating simultaneously.

We report the initial results from a search for bursts of gravitational radiation by a network of five cryogenic resonant detectors during 1997 and 1998. This is the first significant search with more than two detectors observing simultaneously. No gravitational wave burst was detected. The false alarm rate was lower than 1 per ${10}^4$ yr when three or more detectors were operating simultaneously. The typical threshold was $H\simeq 4\times {10}^{-21\mathrm{}}{\mathrm{Hz}}^{-1\mathrm{}}$ on the Fourier component at $\sim {10}^3\mathrm{Hz}$ of the gravitational wave strain amplitude. New upper limits for amplitude and rate of gravitational wave bursts have been set.

We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the $-3\mathrm{dB}$ limit in the noise reduction, associated with parametric resonance, with a best experimental result of $-7.4\mathrm{dB}$. While the present experiment is in the classical regime, in a moderately cooled system our technique may allow squeezing of a macroscopic mechanical oscillator below the zero-point motion.

We apply a feedback cooling technique to simultaneously cool the three electromechanical normal modes of the ton-scale resonant-bar gravitational wave detector AURIGA. The measuring system is based on a dc superconducting quantum interference device (SQUID) amplifier, and the feedback cooling is applied electronically to the input circuit of the SQUID. Starting from a bath temperature of 4.2 K, we achieve a minimum temperature of 0.17 mK for the coolest normal mode. The same technique, implemented in a dedicated experiment at subkelvin bath temperature and with a quantum limited SQUID, could allow to approach the quantum ground state of a kilogram-scale mechanical resonator.