It is impossible. It's also unnecessary in order to reach negative temperatures (see below). But if you don't know
why it's impossible, then it can
seem like it's equivalent to reaching 0 pressure. But it's not equivalent, not at all.
One doesn't need zero atoms to achieve zero pressure. Practically speaking, it's probably
easier to achieve zero or even negative absolute pressure with LOTS of atoms - for example, water in a sealed piston. You can tune the pressure from positive to zero to negative by simply pushing or pulling on the piston.
This is actually a perfect example of not knowing the physics: when I tell you that negative temperatures are possible, you assume that this means a temperature BELOW 0 Kelvin. That's not an unreasonable assumption, but it's wrong. Negative temperatures exist
above infinite temperature, not
below 0 Kelvin. And the reason is that in thermodynamics, temperature is actually less fundamental than inverse temperature. As the energy of a system increases, the inverse temperature decreases. In most systems, the inverse temperature can never actually reach 0, but can only approach it asymptotically. But for some systems, the inverse temperature can pass through zero and go negative. That means there's a discontinuity in temperature: we go to infinite positive temperature, then infinite negative temperature, back to finite negative temperature. So negative temperatures are "hot", not "cold". Note also that even though there's a discontinuity in temperature, there is no discontinuity in inverse temperature, and that's actually the more fundamental property.
Negative temperatures violate most people's conception of what temperature is and what it means, but that's because most people don't really understand it in the first place. And why
would you, if you haven't studied it? I certainly didn't have a clue about what negative absolute temperatures were until I took a thermodynamics class, and I don't expect anyone else to.
Anyways, Wikipedia has a page on
negative temperatures if you're curious to learn more. They're fairly esoteric since only systems with a maximum possible energy can obtain negative temperatures, and if you place a system which can support negative temperatures in thermal contact with a system which cannot (and that's most systems), equilibrium will always be positive temperature.