Database

[{"_id":1,"cart":{"items":[{"_id":1,"productId":100,"quantity":5},{"_id":2,"productId":101,"quantity":10}]},"username":"abc","password":"xyz"}]

Query

db.collection.update({_id:1},{"$set":{"cart.items.1.quantity":2/**where 1 is index and 2=item.productId.stock*/}})

Result