Ajata is a Sanskrit word meaning no creation; that is, no origination.
Hui Neng, the Sixth Chinese Patriarch, summed up the point of view of ajata when he said, in the last two lines of his enlightenment poem:
Where there has been nothing from the start
how can dust alight?
Sunyata (also spelled Shunyata) is a Sanskrit word meaning emptiness.
Where there is nothing from the start, there is emptiness. Or, where there is emptiness, not anything can be originated—there is nothing from the start.
Ajata is a term associated with Advaita Vedanta. Sunyata is a term associated with Buddhism.
Both Advaita Vedanta and Buddhism have their roots in India. Buddha’s teachings on emptiness were the subject of a school of writers known largely as madhyamaka (also spelled madhyamika), who embraced the writings of the Indian monk Nagarjuna, from around 200 A.D.
The ajata of the Indian nonduality teacher Guadapada and the sunyata of the Indian monk Chandrakirti (or Candrakirti), around 600 A.D. were evidently an influence on each other.
The point of these teachings is that the basic condition, or “ultimate reality” is emptiness. Not any reality (or dharma) has ever had a beginning. Therefore anything which is supposed to exist, or be real, is in truth without substance. While things may appear to be real, all appearances are empty, and therefore have no true existence beyond their appearance. In other words, life as we think we know it, is purely an illusion.
Not anything has ever been created, or born. To the person who supposes that his life and death and the turmoil of his world are real, the realization of the truth of emptiness has little appeal.
But to those to whom an enlightened realization is the climax of life, emptiness is the final end to which nonduality points.
There is much written material on enlightenment, in both Vedanta and Buddhism, but—due likely to the difficulty of communicating such a difficult subject—the sources for material on emptiness are not abundant.
Yet as the teachings of nonduality become more prominent in the West, and the result is a greater number of the awakened, material on emptiness will be more widely sought.
What follows is some information that may be useful to you—several monographs, written by Robert Wolfe.