In fact drug use begins very much earlier and the Romans probably took it over from others, most likely the Greeks. There is very much literature on the topic, and it seems that Opium was used mainly as a medical and sleeping drug.
The late Andrew Sherratt was an archaeologist who wrote several very good and interesting papers on the topic, covering everything from Neolithic to modern times - you might find some on the internet.
There is also a paper by Papadopoulos (2011) in the web, but written in Greek and mainly on ancient Greece.
Rather more popular is an article by H. Baykal in "Abenteuer Archäologie 4/2005), which can also be found on the internet
A well structured general treatmant of drug use all over the world and starting from the ancient Near East is the Spanish sociologist Antonio Escohotado's classic: Historia General de las Drogas (several editions since the nineteens). It is usefull in respect to the wide range of approaches taken and aspects treated, but to get the propper impression on its parts dealing with antiquity, one has to be aware of the fact that Escohotado is a sociologist and not an archaeologist or philologist of the so called classical languages Greek or Latin. Having this in mind, to me it seems even more impressing the enormous mass of material the author has worked through, proved by the large bibliography. As far as I can judge, the works used are well selected, but surely you may find more recent research elsewhere. Still I think the Historia General may be an adequate starting point for any research on your topic.
see G. COSTA, La sirena di Archimede, Alessandria 2008 (http://www.wuz.it/libro/9788862740852/costa-gabriele/sirena-archimede-etnolinguistica.html). It is a very questionable, but rich and intelligent book. I join here my review published in «L’indice» XXVI, 11, 2009, p. 23.