The first is correct. The second is incorrect, or at least unusual.
However, there is a problem.
You would only put "experimental center" if you are describing the facility, rather than naming it... and "experimental center" is an unusual term. It is possible, but I think it is likely that you want a different term, such as "research center."
The best rule for the name of a facility, you would usually use the full official name, and since it is a proper name you would capitalize all the words in it. In other words, I would do a web search on the university's site and find the exact words the university itself uses.
These are example of real facility names:
"The Smithsonian Astrophysical Observatory (SAO) is a 'research institute' of the Smithsonian Institution. It is joined with the Harvard College Observatory (HCO) to form the Harvard-Smithsonian Center for Astrophysics (CfA)"
"The Center for Research in Security Prices is part of the University of Chicago Booth School of Business."