We have theoratically and experimentally investigated the possibility of the phase mode operation of symmetrical four-junction Josephson interferometers (4J-loop), which are considered to play a key role as quantum logic devices for a Josephson switching system utilizing single-quanta as information bits, because of their excellent characters such as the kinetic momentum quantum effect and variety of the logic operations. The threshold characteristic, which is the most basic for Josephson interferometers to be operated in the phase mode and shows their fluxoid-quantum states, has experimentally been observed clearly for the first time for symmetrical 4J-loop\´s by using a novel radial-scanning, intensity-modulation technique, as predicted theoretically. It is characterized by a limited closed-shaped pattern. The number of the fluxoid-quantum states increases with LI
0for the loops. Two different basic types of switching behaviors, a vortex-to-vortex and a vortex-to-voltage transition, have been confirmed, which have clearly been separated on the threshold characteristic, for the loops with LI
0larger than

The optimum LI
0value for the phase mode operation of the loops has been found to be

. The desired performance of the phase mode operation of symmetrical 4J-loop has been confirmed by the shift motion of single fluxoids on the basis of the vortex-to-vortex transition of the loop. Finally, an application of such phase mode Josephson interferometers for pulse generators of Josephson sampling systems has been proposed.