  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,
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 to just 0.3; 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.
