I think those are wireworms. I would check the Arbico website. I believe they have some natural products that work. I'm thinking maybe beneficial nematodes might work.

Are these "white worms" long and thin like a hair or a bit chubby like a grub? The most common carrot pest - depending on where you live (you don't indicate that) - is the larvae of the Carrot Fly. It looks like small white grub. See link and pic below.

Parasitic nematodes usually look like long, very thin hair-like worms.

Wire worms are long and skinny too but tend to be shades of beige and brown rather than white. Although there may very well be some white ones too.

Using beneficial nematodes as Tracy mentioned can help eliminate all three of the problems.

Dave

Here is a link that might be useful: Carrot pests and treatments