  We introduce a simple experiment involving a double-slit interferometer by
which one can learn basic concepts of quantum interference such as which-path
marking, quantum erasers, and geometric phases. Each of them exhibits seemingly
mysterious phenomena in quantum physics. In our experiment, we use the
double-slit interference of visible light with the polarization as an internal
state to demonstrate the disappearance of fringes by which-path marking,
recovery of interference using quantum erasers, and the rapid shifting of the
fringe pattern induced by the geometric phase. We also present a simple
theoretical analysis of an interferometer with an internal state.
