Hi Udhayan,
There is no way to get modification date for non clustered index.
sys.all_objects does not show create or modify date for non clustered index.
sysobjects shows creation date for all indexes but not modification date.
You can do this by implementing trigger. Please check for help https://littlekendra.com/2016/12/13/index-create-and-last-modified-dates-in-sql-server/
Regards,
Zahid