The process of removing an arrest and/or conviction from your criminal record is called an expungement. It is the the process of filing a motion with the court asking the court to order state agencies to remove the fact of the arrest and/or conviction from the record.
This is not an automatic process. A criminal record does not automatically clean itself. The expungement process must be proactively completed by the defendant or his/her attorney.
For more on expungements in Lousiana, click here.