A tall glass of diet soda on a table. The Atkins diet is a low-carbohydrate diet, and although diet sodas generally do not contain any carbohydrates, not all of them are allowed on the Atkins diet. Learning which diet sodas are allowed on the Atkins diet is essential if you are on the diet or considering starting it and plan to drink diet soda. Consult your physician prior to starting the Atkins diet or any other weight loss program.