  An anharmonic oscillator when driven with a fast, frequency chirped voltage
pulse can oscillate with either small or large amplitude depending on whether
the drive voltage is below or above a critical value-a well studied classical
phenomenon known as autoresonance. Using a 6 GHz superconducting resonator
embedded with a Josephson tunnel junction, we have studied for the first time
the role of noise in this non-equilibrium system and find that the width of the
threshold for capture into autoresonance decreases as the square root of T, and
saturates below 150 mK due to zero point motion of the oscillator. This unique
scaling results from the non-equilibrium excitation where fluctuations, both
quantum and classical, only determine the initial oscillator motion and not its
subsequent dynamics. We have investigated this paradigm in an electrical
circuit but our findings are applicable to all out of equilibrium nonlinear
oscillators.
