Security Of Mssql Database?

Hello, another question from a newbie to mssql.

Is there a way of allowing access to database only by providing username and
password (disabling trusted connection and preventing administrator to
access database through enterprise manager or otherwise without supplying
username and password)?

What I would like is that my application upon instalation creates database
with appropriate tables (already done this) and somehow solely creates and
manages user list and passwords so that there is no access to database other
through application. (Application would create a backdoor account should
something go wrong)