Connecting a Dell XPS running Windows 8.1 to a Thunderbolt Display
I don't believe your "Thunderbolt" port on your Dell XPS is a Thunderbolt port, it's more likely to be a DisplayPort connector. I'm not aware of Dell making any equipment that has a Thunderbolt port. Thunderbolt and DisplayPort do use an identical form factor, so it's easy to get them confused.

You cannot use a Thunderbolt display in a DisplayPort connector.



Since this answer was originally written, Dell has indeed added Thunderbolt 2 or 3 ports to their XPS line of laptops. Double check it is a thunderbolt port in the specs of your exact model and year, but a Dell XPS works well with my Thunderbolt display since the addition of a Thunderbolt port.