  We show that a cavity field can evolve from an initial displaced mixed
thermal state to a macroscopic superpositions of displaced thermal states via
resonant interaction with a two-level atom. As a macroscopic system (meter) is
really in a mixed state before coupling with the microscopic system at some
temperature, our result is important for studying the quantum measurement
problem and decoherence under real conditions. For the two-mode case,
entanglement of displaced thermal states between the modes can be obtained.
