  The building blocks of Nature, namely atoms and elementary particles, are
described by quantum mechanics. This fundamental theory is the ground on which
physicists have built their major mathematical models [1]. Today, the unique
features of quantum objects have led to the advent of promising quantum
technologies [2, 3]. However, the macroscopic world is manifestly classical,
and the nature of the quantum-to-classical crossover remains one of the most
challenging open question of Science to date. In this respect, moving objects
play a specific role [4, 5]. Pioneering experiments over the last few years
have begun exploring quantum behaviour of micron-sized mechanical
systems,either by passively cooling single GHz modes, or by adapting laser
cooling techniques developed in atomic physics to cool specific modes far below
the temperature of their surroundings [6-11]. Here instead we describe a very
different approach, passive cooling of a micromechanical system down to 500
microK, reducing the average number of quanta in the fundamental vibrational
mode at 15 MHz to just 0.3 (with even lower values expected for higher
harmonics); the challenge being to be still able to detect the motion without
disturbing the system noticeably. With such an approach higher harmonics and
the surrounding environment are also cooled, leading to potentially much longer
mechanical coherence times, and enabling experiments questioning mechanical
wave-function collapse [12], potentially from the gravitational background [13,
14], and quantum thermodynamics [15]. Beyond the average behaviour, here we
also report on the fluctuations of the fundamental vibrational mode of the
device in-equilibrium with the cryostat. These reveal a surprisingly complex
interplay with the local environment and allow characteristics of two distinct
thermodynamic baths to be probed.
