Keith gets it right. The answer is the fuel turbopump for the space shuttle main engine.
And there’s a bit of a story there…
There are a variety of different ways to make liquid fuel rockets work. In simple rockets, you use pressure in the tanks to force propellant into the combusion chamber. But you can’t run the pressure that high (tanks can’t take it), so you don’t get much efficiency. But it’s simple.
To do better, you need to use some sort of pump. The simplest thing to do is to run the fuel and oxidizer through tubing in the nozzle to heat it up. This gives you high pressure which use you use drive a turbine which pump more fuel and oxidizer in. This gives you more power, but is also limited in how much propellant and oxidizer you can get into the rocket engine.
If that’s not enough power – and a vehicle like shuttle needed a really high-power design – you burn the some of the hydrogen and oxygen, and use that to drive a turbine (which drives a pump), and then send the exhaust into the combustion chamber to add to your thrust.
Well, there are a lot more details, but that’s the basic idea.
The oxygen turbopump is the baby one. It burns hydrogen and oxygen at about 1500 degrees, spins at 23,700 RPM, and generates 26,800 hp.
The hydrogen turbopump is bigger (remember your chemistry if you wonder why). It burns at about 2000 degrees, spins at 36,200 RPM, and generates a cool 76,000 hp. All in a 3 foot long tubine that weighs 775 lbs.
Not surprisingly, that puts the pumps right at the edge of materials design. The original intention was that the engines would fly lots of missions with minimal service, but like lots of things on shuttle, the full engine is pulled and refurbished after flight.
Because of their advanced design, the main engines were thought to be a big risk factor, but there’s only been one main engine early shutdown in the history of the program and 5 pad aborts before launch. Counting all the static tests, rocketdyne has an accumulated run time of a million seconds on these engines now.
Somewhat interestingly, the turbopumps in the block II engine are produced by Pratt & Whitney (I think the originals were done by Rocketdyne), which are better than the original ones. Interestingly, improvements to the engines over the years (such as better turbopumps) have yielded engines that now can produce up to 109% of their original design thrust.
I do find some of the other answers intriguing, and I wouldn’t be surprised if you could build (or somebody has built) a small turbine that would exceed the that power/weight ratio, small normally being easier than large.
With jet engintes, there’s no easy conversion between thrust and hp, but if you look at typical commercial jet engines, you might see 12 hp/lb or so. Most of the high power ones couldn’t be used to power a pump.
I looked a bit at the nano-motors, but didn’t find enough data to really be able to tell one way or another.