State police say a 23-year-old Providence man is facing charges after he left his one-month old son alone at home while he went to a convenience store. The man was stopped shortly after midnight yesterday and was taken into custody on several outstanding warrants. Upon arrival at the Lincoln Barracks he told troopers his son was alone in his apartment. Police found the infant asleep and in good condition. The baby is in the custody of the state Department of Children, Youth and Families.