I'm looking for a pressurized pot where the pressure can be regulated in both directions, that is, higher and lower than atmospheric pressures (higher: high pressure cooker, lower: vacuum distillation).
Does something like this exist?
If so, what is its name?
I don't think that device exists, its hard to say something like that.
But I can tell you for sure that this kind of device wouldn't be very efficient or useful, let's assume you are using water for cooking, if you want to boil it and cook your food at higher temperatures you would use higher pressure, for lower temperature, lower pressure, but there is no need to control it with precision since the boiling temperature shows little variation with the pressure (at 2 atm you boil water around 120ºC, at 0,5 atm it is around 80ºC), so you basically have a pot that can be ajusted for high pressure or low pressure cooking, but without precision.
A second factor to consider is the packing, to go higher than 2 atm (where a normal pressured pot gets) you would have to get a more expensive packing system to prevent your pot from exploding, so now we have a regular pressured pot with the option for low pressure.
The low pressure system wold be quite complicated to develop, since when you boil the water it turns into vapor and will raise the pressure of your pot, so you need something that will keep put vapor out of your system, something like a pump would have to be constantly working fot that to happen, that's not very practical.
And at last, I can understand why you would want to cook with higher pressure, I do it quite often myself, but I can't see a good reason to do it with low pressure, there are many cooking techniques that use vacuum, sous-vide for exemple, but I have never seen one that uses it in a sealed pot like you are proposing. You could say you want to cook in low temperatures which is completely fine, but you can do it in a less complicated way, like using an electrical heater and thermostat.
So it may exis, but as i said it would be unpractical
