Highly entangled states of more than one quantum system are necessary
for tests of local hidden-variable theories and of quantum mechanics i
tself. We show how to produce field states, which are located in sever
al cavities and are highly entangled, by sending apropriately prepared
atoms through the cavities. We discuss both a two-cavity and a three-
cavity state in which either each cavity is in a one-photon number sta
te or each is in the vacuum state. Finally, a test of quantum mechanic
s using the two-cavity state is presented.