Superposition states at finite temperature

Abstract

We describe a method to create superposition states from a mixed state of a harmonic oscillator. If the initial state is described by a thermal state, then the resulting superposition state will be a "hot'' superposition state. Such a state can be distinguished from a statistical mixture by its coherence properties. Here we suggest how to demonstrate the coherence of the superposition state by observing interference fringes when the two parts of the wave packet are overlapped. In the case of the mixed superposition state, a partial overlap may not be sufficient to observe the presence of fringes. We introduce therefore the idea of a coherence length for the wave packet and demonstrate its relevance for interferometry of mixed states. We illustrate our ideas with the example of superposition states for the motion of a single trapped ion.