Is jujube a good sleep aid and is it safe?

It sure is... At least for mice. I found only a mouse study looking at this effect of jujube. (http://www.Ncbi.Nlm.Nih.Gov/pubmed/17479419). It appears to have components that are sedative and without noticeable side effects.
Ziziphus jujuba. Semen ziziphi spinosae, the seed of ziziphus jujuba, is a herbal, alternative medicine used in traditional chinese medicine. Recently, its use in sleep/insomnia has been examined in the medical literature in china. As far as i know, presently, there are no definitive studies in humans, only studies in rats and mice. Seek the advise of your physician for sleep disturbances and insomnia.