> Engine manufacturers have spent a TON of R&D on fanjet engines and making them several orders of magnitude more efficient than the engines of 20 years ago even, but supersonic flight needs more than a fanjet - they need to look at turbojets, with afterburners etc. There is not much scope to play with with those unfortunately. What works at subsonic speeds at 30,000 feet won't at Mach 2+ at 80,000 feet.
Whether you fly subsonically or supersonically, thermodynamic efficiency will be driven by engine pressure ratio and turbine inlet temperature. The advanced turbofans flying today have very impressive gas generator cores (high-pressure compressor, low-emissions combustors, high-pressure turbines) that would be equally applicable to supersonic airframes. The low pressure part of the cycles will definitely optimize to a different point for subsonic vs. supersonic applications, with supersonic cruise preferring higher fan pressure ratios and lower bypass ratio. Like Concorde, you are going to want to size the engines such that you do not cruise in afterburner (assuming you are staying roughly below Mach 3; above 3 - 3.5, the ramjet cycle starts becoming more favorable). However, this is all within scope for what the aeropropulsion vendors know how to do. The big issue is that the specific engine configuration you are going to want for a supersonic cruiser is unique to that application. Originally, Aerion was going to use JT8Ds, which they later shifted away from.
My point here is it's not principally an R&D issue, it's that if you want to minimize supersonic fuel consumption, you are going to want a specific configuration for which there will not be a huge engine market. Contrast with the market for something like a CFM56 or V2500. Being able to leverage the ADVENT three-stream/variable cycle work (and GE YF120 before that) will also help, but the point still stands.