Quantum Physicists Dream Up Smallest Possible Refrigerator

by Adrian Cho 

Flipping brilliant! Skewing the rates of flipping between two equal-energy configurations of three quantum particles cause the second two to cool the first one.

You may have a $10,000 Sub-Zero fridge in your kitchen, but this is cooler. Theoretical physicists have dreamed up a scheme to make a refrigerator out of a pair of quantum particles such as ions or atoms, or even a single particle. The fridges may be the smallest ones possible. “It’s very elegant and innovative,” says Nicolas Gisin, a theorist at the University of Geneva in Switzerland. Theo Nieuwenhuizen, a theorist at the University of Amsterdam, says “I don’t see any error, so probably this would work.”

The challenge is to make a few quantum particles act like a so-called thermal machine, the theory of which was set out by French engineer Sadi Carnot in 1824. Carnot imagined a piston filled with gas that could be compressed or expanded. The piston could make contact with either of two large bodies (say, massive steel blocks) at different temperatures, which could serve as the “hot bath” and the “cold bath.”

Carnot put the imaginary piston through a cycle of motions, including one in which the gas expands while in contact with the hot bath and another in which it is compressed while in contact with the cold bath. During the cycle, the piston does work while absorbing heat from the hot bath and releasing heat into the cold one, making it a “heat engine.” Reverse the cycle and, in response to work done on it, the piston acts as a refrigerator, absorbing heat from the cold bath and releasing it into the hot one.

Now, Noah Linden, Sandu Popescu, and Paul Skrzypczyk of the University of Bristol in the United Kingdom report that, at least in principle, they can make a refrigerator out of a few quantum particles called “qubits.” Each qubit has only two possible quantum states: a zero-energy ground state and a fixed-energy excited state. The theorists have found a way to siphon energy out of one qubit by making it interact with just two others.

The theorists arrange things so that each qubit has a different excited-state energy but the trio of qubits has two configurations with the same total energy. One is the configuration in which only the first and third qubits are in their excited states—denoted (101). The other is the configuration in which only the second qubit is in its excited state—denoted (010). If all three qubits were at the same temperature, then the system would flip with equal probability back and forth between these two configurations.

But the researchers skew that flipping, as they explain in a paper in press at Physical Review Letters. The trick is to put the first two qubits in contact with a cold bath and the third one in contact with a hot bath. The higher temperature makes it more likely that the third qubit will be in its excited state—and thus that the trio will be in the (101) state instead of the (010) state. But that means the system is more likely to flip out of (101) and into (010) than the other way around. So on average the flipping takes the first qubit from its excited state to its ground state and draws energy out of the first qubit. After a flip, the qubits essentially reset by interacting with the baths, allowing the cycle to start again.

The theorists measure the fridge’s size in terms of the number of its quantum states, and the three qubits have a total of eight possible states. That number can be clipped to six, if they replace the second and third qubits with a single “qutrit,” a particle with a ground state and two excited states—although those two states have to be in contact with different baths. “We believe that’s probably the smallest number of states you can get away with,” Linden says.

In theory, such a fridge can get arbitrarily close to absolute zero, and Popescu says that it might be possible to make one using trapped ions for the qubits and streams of laser light as the baths. Some researchers hope to use such qubits as the guts for a quantum computer, and Popescu says the refrigerator scheme might allow researchers to cool some set of qubits with a few others. David Wineland, an experimental physicist with the U.S. National Institute of Standards and Technology in Boulder, Colorado, says he believes such schemes can indeed be implemented in trapped ions.

Others suggest that such tiny quantum refrigerators might already be humming along in nature. It’s possible that one part of a biomolecule might work to cool another in such a fashion, says Hans Briegel, a theorist at the University of Innsbruck in Austria. “I don’t expect that you will have a mechanism exactly like this,” Briegel says, “but it gives you a framework valuable for telling what to search for.”

No word yet on when physicists might unveil the smallest possible beer.