Quantum fluctuations in the chirped pendulum

Abstract

Anharmonic oscillators, such as the pendulum, are widely used for precision measurement¹ and to model nonlinear phenomena². 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 value³. This phenomenon, known as autoresonance, is significant in planetary dynamics⁴ and plasmas⁵, enables the excitation of particles in cyclotron accelerators⁶ and may even be used to detect the state of a quantum two-level system⁷. 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.