  Sensitive measurement of electrical signals is at the heart of modern science
and technology. According to quantum mechanics, any detector or amplifier is
required to add a certain amount of noise to the signal, equaling at best the
energy of quantum fluctuations. The quantum limit of added noise has nearly
been reached with superconducting devices which take advantage of
nonlinearities in Josephson junctions. Here, we introduce a new paradigm of
amplification of microwave signals with the help of a mechanical oscillator. By
relying on the radiation pressure force on a nanomechanical resonator, we
provide an experimental demonstration and an analytical description of how the
injection of microwaves induces coherent stimulated emission and signal
amplification. This scheme, based on two linear oscillators, has the advantage
of being conceptually and practically simpler than the Josephson junction
devices, and, at the same time, has a high potential to reach quantum limited
operation. With a measured signal amplification of 25 decibels and the addition
of 20 quanta of noise, we anticipate near quantum-limited mechanical microwave
amplification is feasible in various applications involving integrated
electrical circuits.
