  We demonstrate that it is possible, in principle, to perform a Ramsey-type
interference experiment to exhibit a coherent superposition of a single atom
and a diatomic molecule. This gedanken experiment, based on the techniques of
Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the
commonly-accepted superselection rule that forbids coherent superpositions of
eigenstates of differing atom number. This interference experiment makes use of
a Bose-Einstein condensate as a reference frame with which to perform the
coherent operations analogous to Ramsey pulses. We also investigate an
analogous gedanken experiment to exhibit a coherent superposition of a single
boson and a fermion, violating the commonly-accepted superselection rule
forbidding coherent superpositions of states of differing particle statistics;
in this case, the reference frame is realized by a multi-mode state of many
fermions. This latter case reproduces all of the relevant features of Ramsey
interferometry, including Ramsey fringes over many repetitions of the
experiment. However, the apparent inability of this proposed experiment to
produce well-defined relative phases between two distinct systems each
described by a coherent superposition of a boson and a fermion demonstrates
that there are additional, outstanding requirements to fully ``lift'' the
univalence superselection rule.
