Stealth aircraft have been so far unable to prevent contrails from forming behind them for the same reason that you’d be unable to stop your breath from becoming visible in the cold winter air. According to Scientific American, the exhaust expelled by jet engines is hot and humid — much like your breath — and in the cold, low-pressure upper atmosphere, the water vapor in the exhaust freezes in a similar process to natural cloud formation.
As reported by Popular Mechanics, the U.S. military has experimented with everything from turbulence-inducing jet nozzles to dosing the exhaust with acid in their quest to permanently eliminate contrails, but all to no avail. Instead, the next best solution was to try and predict what conditions would lead to contrails and then avoid flying in that airspace, opting instead to go above or around. Other technologies, ranging from laser beams to rearview mirrors (yes, really) have been employed to help aircrew quickly detect contrail formation so they can make adjustments on the fly.
Of course, the furthest limits of technological achievement — particularly where national defense is concerned — aren’t likely to be made immediately public. Advanced stealth aircraft such as the B-21 Raider might be equipped with secret contrail prevention technology years ahead of anything else. But, because contrail formation contributes more to climate change than the actual burning of jet fuel itself, we hope that such a breakthrough would quickly make its way to the private sector to clear away those cloudy skies.