Let me start off by saying that ancient economies are very difficult to study due to the scarcity of evidence, and there is a wide range of scholarly opinion on some of the most basic issues. Also, you asked about the empire, but I’m going to talk more about something which happened during the Republic, so sorry if this isn’t what you’re looking for.

I’d say that one major leap in agricultural efficiency during the Roman period was the introduction of large, slave-run estates during the middle to late Republic. From what we can tell about the early Republic, Rome in this period was a society of peasant farmers. But when the Romans started to expand overseas, they took lots of prisoners. Many of these slaves were brought back to Italy, where they were put to work on large estates. According to literary sources (the archaeological evidence shows a bit more variety, but this does not invalidate the texts), in the late Republic the Italian countryside was dominated by these latifundia owned by members of the elite and run by teams of slaves, at the expense of the old peasant small-holders.

It seems likely to me that this switch to a slave-based economy was a significant leap in agricultural efficiency. This is definitely not an uncontroversial statement, by the way. But there are texts from the last two centuries of the Republic which are basically agricultural handbooks, teaching the reader how to run a farm, and the sort of advice they give is based on the assumptions that the farmer a) owns slaves and b) wants to maximise the yield of their land. We get farms growing cash crops: vines were very popular, with wine produced on a huge scale and then exported to Gaul and elsewhere. A large estate worked by a well-organised slave labour force would surely be more efficient than that same area of land being farmed by multiple peasant small-holders.

Did this have the sort of impact you allude to? Measuring economic growth in antiquity is very haphazard, but those who have attempted to do so generally conclude that there was growth throughout much of the Roman period, but only a very miniscule amount when compared to the sort of economic growth we see in the modern world. But the switch to slave-run agriculture presumably increased food production, which may have been what enabled the significant population growth in this period, which saw Rome reach a population of a million. On the other hand, these slave-run estates were found primarily in Italy: other forms of economic organisation continued elsewhere in the empire, so it’s difficult to attribute population growth in Alexandria, for example, to Italian latifundia. And as mentioned, these large estates weren’t necessarily growing grain: they may have been producing wine or olive oil for export. So overall, even if we do see what happened in Italy as a major agricultural development, its overall impact wasn’t revolutionary.

Further reading: M. I. Finley, The Ancient Economy (2nd ed., 1985) – Finley’s answer to this question would have been very different from mine. I don’t think he would have seen slave labour as having had much of an impact on efficiency, as he argued that the ancients didn’t really have any concept of efficiency or maximising profits.

W. Scheidel et al. (eds), The Cambridge Economic History of the Greco-Roman World (2007) – see especially the chapters on Demography and Technlogy, and of course the chapters focusing on Rome.