  We examine current fluctuations in tunnel junctions driven by a superposition
of a constant and a sinusoidal voltage source. In standard setups the external
voltage is applied to the tunneling element via an impedance providing an
electromagnetic environment of the junction. The modes of this environment are
excited by the time-dependent voltage and are the source of Johnson-Nyquist
noise. We determine the autocorrelation function of the current flowing in the
leads of the junction in the weak tunneling limit up to terms of second order
in the tunneling Hamiltonian. The driven modes of the electromagnetic
environment are treated exactly by means of a unitary transformation introduced
recently. Particular emphasis is placed on the spectral function of the current
fluctuations. The spectrum is found to comprise three contributions: a term
arising from the Johnson-Nyquist noise of the environmental impedance, a part
due to the shot noise of the tunneling element and a third contribution which
comes from the cross-correlation between fluctuations caused by the
electromagnetic environment and fluctuations of the tunneling current. All
three parts of the spectral function occur already for devices under dc bias.
The spectral function of ac driven tunneling elements can be determined from
the result for a dc bias by means of a photo-assisted tunneling relation of the
Tien-Gordon type. Specific results are given for an Ohmic environment and for a
junction driven through a resonator.
