Quantum noise properties of multiphoton transitions in driven nonlinear resonators

We investigate the quantum noise properties of a weakly nonlinear Duffing resonator in the deep quantum regime, where only a few quanta are excited. This regime is dominated by the appearance of coherent multiphoton resonances in the nonlinear response of the resonator to the modulation. We determine simple expressions for the photon noise spectrum and find that the multiphoton resonances also induce a multiple peak structure in that spectrum. When the corresponding multiphoton Rabi oscillations are underdamped, zero-temperature quantum fluctuations determine comparable populations of all quasienergy states which belong to a resonant multiphoton doublet. Most interestingly, the quantum fluctuations probe the multiphoton transitions by inducing several peaks in the noise spectrum of the resonator observables. In particular, the noise of the photon number contains complete information about the multiphoton states and their stationary populations via pairs of nearly symmetric peaks at opposite frequencies. Their widths are determined by the damping of the Rabi oscillations and their heights are proportional to the stationary nonequilibrium populations. A finite detuning from a multiphoton resonance generates a quasielastic noise peak at zero frequency. In addition, we relate the stationary populations of the quasienergy states with an effective quantum temperature and discuss the role of a finite temperature.