FAST Search for SharePoint allowed queries with the time portion in Sharepoint 2010 by using FQL, and fortunately you can do this in 2013 and Office 365 as well.
Doing FQL in 2013 in theory involves setting a parameter either on your REST queries or on the KeywordQuery object telling it your query is written in FQL and not KQL. The reality is a bit more complex involving a custom result source, and to tell you the truth. I have yet to be able to get FQL to work using REST this way.
How then? you might ask. Use use the RefinementFilters property instead! This property actually uses FQL which is what we need and is our “Get out of jail free card”. And all though KQL has more of the FQL operators in 2013, FQL still has some tricks up it's sleeve. Worth taking a look at for sure.
To limit on dates you will use the FQL range operator. The default behavior is to use “greater than” and “equal and less than” if not specified in the query.
The granularity of date/time queries are down to 7 decimals, as long as the crawler has been able to set this level of granularity during indexing.