You said soil...I never would use garden soil in a container. A 4-6" minimum of sterile medium mixed with 1/3 good homemade compost would be a good base, then water with a fish/kelp fertilizer from time to time (about every 10 days). I presume this container will be under lights? "NE" for a location is pretty vague, but if you are gardening indoors, nowhere in the NE will you have sufficient light through a window throughout the winter. Those are sunloving, heat-loving herbs of the Mediterranean. Even if they survive, do not expect them to thrive & supply you with a daily, or even weekly, herbal harvest without enough light (i.e., 14-16 hours of artificial light daily).
Keep a close eye out for scale, aphids, whitefly, spider mites, etc.!

OK, thanks. What are the disadvantages of soil in a container? What's a good sterile medium? The plants are still in their containers, so it isn't too late to switch. The container is under lights, yes. I can leave the lights on all day if need be. I've been advised to keep a small fan running for air flow, and to not completely close off the lid. Is that correct? Thanks again.

If, by 'soil', you mean POTTING soil...that's what weedlady means by a good sterile medium. The terminology can get confusing. One should never use outdoor soil in containers. I don't even recommend the use of compost. It looks like you are using a bagged potting mix, right?

You plants would be much happier if your ingredients were mixed into an homogeneous medium, rather than the layering, which can confuse the root system. Adding a big portion of perlite can be a benefit to almost any store-bought potting medium.

I worry about your being able to water your plants properly in an aquarium. The water that collects in your gravel layer (which really isn't necessary, either) will be stagnant and you will have no way to get rid of it. You'll be forced into watering very conservatively and carefully. That will eliminate the introduction of large volumes of oxygenated water throughout the soil/root column. Oxygen is just as essential to plant health as anything else.

If you mix your solid ingredients together, I'd give your experiment a much greater chance of success, for a longer period of time. Be forewarned, as weedlady suggests, that it is going to be challenging to make these kinds of herbs happy in this kind of environment.

Thanks for the tips. It is bagged potting mix, yes. The white layer under it is actually perlite, and I was planning on putting another couple inches of soil in there. Maybe mix more perlite in with that? I'd read that a layer of gravel was needed for drainage. There's a layer of that, then charcoal, then sphagnum moss, then the perlite graduates up into the soil, followed by only the soil. Your comments about watering have me concerned, though. What if I devised some means to suck it out with a straw or something? I will think about it. Would you suggest a heat light in addition to the grow light? Thanks again!

First, I am suggesting that your plants will grow better if you dispense with all of the layering and mix those assorted ingredients together. Except for the gravel. Added perlite is always a good thing for any bagged potting soil.

If your completed medium is mixed (rather than layered), the water will travel more uniformly, and the roots will, too. Adding all of that extra perlite will increase the porosity within your planting mix, too. You'll really, really need that since you won't be able to introduce oxygen via drenching.

The gravel doesn't assist with drainage. That's something of a long lived myth. What it does is simply eliminate space for root development. I'm not overly worried about it with that large container, but you should know that it really doesn't provide the service you think. As a matter of fact, the fines (finest particles) from the sphagnum and potting mix will settle down there in the gravel, clogging it up nicely!

I wish I had a good solution for you regarding the watering issue. If you were planting a terrarium for cacti and succulents, it would be different.

I wouldn't use a heat lamp.

You know, I really should add that all of your preparations might be fine for a short term (one season) project. I tend to think of enduring situations and that needn't be the case, here. (Though I still think that you should mix all of those ingredients, rather than layer them.)

If all goes well, your plants will be so large come spring that you'll need to transplant them into bigger separate containers, or put them in the garden.

You should add some poison dart frogs... would look great :).

You can run a bit of rigid airline tubing down to the bottom and then attach some flexible airline to that, first blow the soil out of it, then suck and start a siphon, you can also hook that up to a small air pump and fill the whole under-root zone with fresh air.

Thanks again for all the great responses. I've been convinced to mix up the ingredients (even the moss and charcoal?) and let fly. Brendan, that sounds like great advice... could you maybe elaborate? Would the air pump need to operate continuously, or just every now and then?