We investigate the quantum noise properties of a weakly nonlinear Duffingresonator in the deep quantum regime, where only few quanta are excited. Thisregime is dominated by the appearance of coherent multiphoton resonances in thenonlinear response of the resonator to the modulation. We determine simpleexpressions for the photon noise spectrum and find that the multiphotonresonances also induces a multiple peak structure in that noise. When thecorresponding multiphoton Rabi oscillations are underdamped, zero temperaturequantum fluctuations determine comparable populations of all quasienergy stateswhich belong to a resonant multiphoton doublet. Most interestingly, the quantumfluctuations probe the multiphoton transitions by inducing several peaks in thenoise spectrum of the resonator observables. In particular, the noise of thephoton number contains complete information about the multiphoton states andtheir stationary populations via pairs of nearly symmetric peaks at oppositefrequencies. Their widths are determined by the damping of the Rabioscillations and their heights are proportional to the stationary nonequilbriumpopulations. A finite detuning from a multiphoton resonance generates aquasielastic noise peak at zero frequency. In addition, we relate thestationary populations of the quasienergy states with an effective quantumtemperature and discuss the role of a finite temperature.
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