  We investigate the quantum noise properties of a weakly nonlinear Duffing
resonator in the deep quantum regime, where only 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 induces a multiple peak structure in that noise. 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 nonequilbrium
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.
