We report the observation of a new room-temperature storage phenomenon based on quantum interference. Multiple, stable current-voltage curves extending continuously through zero bias have been observed in GaAs/AlAs double barrier quantum well diodes containing n--n+-n- spacer layers. Once placed on a particular branch, the devices retain memory of the branch they lie on, even when held at zero bias for extended periods of time. The devices can be repetitively switched between the different branches of the current-voltage characteristics. The experimental observations are consistent with the multiple self-consistent solutions to the coupled Schrodinger and Poisson equations found for diodes that combine heterostructure tunneling barriers with n--n+-n- spacer layers.