Quantum fluctuations in the chirped pendulum

Anharmonic oscillators, such as the pendulum, are widely used for precision measurement and to model nonlinear phenomena. Fluctuations-such as thermal or quantum mechanical noise-can excite random motion in the oscillator, ultimately imposing a bound on measurement sensitivity. In systems where equilibrium is established with the environment, noise-induced broadening scales with the intensity of fluctuations. But how does noise affect an out-of-equilibrium oscillator where the motion is varied faster than energy is exchanged with the environment? We create such a scenario by applying fast, frequency-chirped voltage pulses to a nonlinear superconducting resonator where the ring-down time is longer than the pulse duration. Under these conditions, the circuit oscillates with either small or large amplitude depending on whether the drive voltage is below or above a critical value. This phenomenon, known as autoresonance, is significant in planetary dynamics and plasmas, enables the excitation of particles in cyclotron accelerators and may even be used to detect the state of a quantum two-level system. Our results show that the amplitude of fluctuations determines the initial conditions of such a non-equilibrium oscillator and does not affect its time evolution.