What can you use to stick down carpet tiles?

Carpet tiles are moderatly high tech flooring, the install instructions are available from the manufacturer & that will include the allowable & recommended adhesives.

Without any specifics, I can tell you that almost all recommend a "Pressure sensitive" adhesive, rolled on with a paint roller & allowed to dry to the touch before putting the tiles in place.

Look in the yellow pages for "carpet installation supply" store & ask them for a price & spread rate. Expect to pay 30-100 per gallon for this wonder goo. It isn't cheap but it goes on thin.