I am trying to find out which Prog. language or Technology goes into the working of Google Flights or the ITA matrix solutions like QPX.
Have you thought about reading Wikipedia ?
ITA is also one of the highest-profile companies to base their software on Common Lisp
Once you know the magic word "lisp" and you know "qpx", the world (or rather Google) is your oyster. Here's a couple things I found for you:
Another source claims
ITA Software, one of the largest employers of lispers
The vast majority of our "thinking" code is in Common Lisp. We run both CMUCL and Franz
we use C++ code to memory-map huge files containing pointerless C structs (of flights, fares, etc), and then access these from Common Lisp using foreign data accesses
Later a semi official Common Lisp Survey mentions that QPX uses Steel Bank CL (SBCL) which was forked from CMU CL in December, 1999 so at one point they switched from CMUCL to SBCL. It's not clear whether they still run Allegro. At least in 2013 we can find mentions about how ITA QPX now at Google wants to speed up SBCL so they are certainly were using it at that point.
According to this post when they started working on Polaris (which Air Canada picked up and then dropped so I am not sure what came out of it) they also used a Lisp, albeit a different one.