  We demonstrate how an acoustic phonon bath when coupled to a quantum dot with
the help of a bichromatic laser field may effectively form a quantum squeezed
reservoir. This approach allows to achieve an arbitrary degree of squeezing of
the effective reservoir and it incorporates the properties of the reservoir
into two parameters, which can be controlled by varying the ratio of the Rabi
frequencies of the bichromatic field. It is found that for unequal Rabi
frequencies, the effective reservoir may appear as a quantum squeezed field of
ordinary or inverted harmonic oscillators. When the Rabi frequencies are equal
the effective reservoir appears as a perfectly squeezed field in which the
decay of one of the polarization quadratures of the quantum dot dipole moment
is inhibited. The decay of the quantum dot to a stationary state which depends
on the initial coherence is predicted. This unusual result is shown to be a
consequence of a quantum-nondemolition type coupling of the quantum dot to the
engineered squeezed reservoir. The effect of the initial coherence on the
steady-state dressed-state population distribution and the fluorescence
spectrum is discussed in details. The complete polarization of the dressed
state population and asymmetric spectra composed of only a single Rabi sideband
peak are obtained under strictly resonant excitation.
