Can rebuilding indexes cause worse performance after the rebuild is finished?
Yes, rebuilding indexes (especially on SSD) can cause worse performance. Most high speed SSD prefer many, smaller block requests instead of fewer, larger requests. This is exactly the opposite pattern preferred by traditional, spinning rust.

Assume you have a highly fragmented B-tree. Because nothing is ordered on the disk, you will typically issue a lot of 8KB I/O requests to scan the tree. If you were to defragment the tree, then you can get up to 512KB in a single request. Those large requests will have higher latency on the SSD, because the SSD internally breaks it down to 8KB chunks (unlike a hard drive, which will issue a sequential I/O). For a great many cases: Higher disk latency = slower queries

All that being said, please do make sure you check that you are actually getting the same query plans that you were getting before the rebuild.

An finally: Unless you are low on space, why are you wasting your precious DBA time with index rebuilds when you run on SSD?