  Cavity opto-mechanical cooling via radiation pressure dynamical backaction
enables ground state cooling of mechanical oscillators, provided the laser
exhibits sufficiently low phase noise. Here, we investigate and measure the
excess phase noise of widely tunable external cavity diode lasers, which have
been used in a range of recent nano-optomechanical experiments, including
ground-state cooling. We report significant excess frequency noise, with peak
values on the order of 10^7 rad^2 Hz near 3.5 GHz, attributed to the diode
lasers' relaxation oscillations. The measurements reveal that even at GHz
frequencies diode lasers do not exhibit quantum limited performance. The
associated excess backaction can preclude ground-state cooling even in
state-of-the-art nano-optomechanical systems.
