Call it the little chill. A group of theoretical physicists has mapped out the physics framework for what may be the smallest refrigerators imaginable. Each device would target just one quantum bit, or qubit, for cooling, and would require just one or two additional quantum particles to do the job.



Theoretical physicists Noah Linden and Sandu Popescu, along with graduate student Paul Skrzypczyk, all of the University of Bristol in England, describe their concept in a paper to be published in Physical Review Letters. If it can be implemented, the work could find use in preparing qubits, which are often single atoms, for use in quantum-information systems by initializing them to a known state.



The model is in some sense simply a scaled-down version of the refrigerators humming away in kitchens around the world—it has an engine qubit to drive the cooling process and a heat-coil qubit to vent the heat drawn away from the refrigerator's contents (the qubit to be chilled) to the outside world.



Just as with classical bits in everyday electronic devices, each qubit can be 0 or 1, as represented by the individual qubit's energy level. (Thanks to the fundamental quirks of quantum mechanics, a qubit can also be in a superposition, existing simultaneously as 0 and 1.) Each qubit requires a certain amount of energy to move from 0 to 1, known as its energy level spacing. (An even smaller concept for the fridge condenses the engine and the coil into a single particle with three energy levels, known as a qutrit.)



In the Bristol group's theoretical depiction, crucially, the energy level spacing of the qubit to be cooled and that of the refrigerator's "engine" together add up to exactly the energy level spacing of the refrigerator's "heat coil." In other words, exciting (heating) both the engine and the fridge contents takes just as much energy as exciting the coil alone. Because of that condition, the two states—excited coil or excited engine and contents—can alternate at ease, making each scenario just as likely as the other, all things being equal.



But what if all things aren't equal? Setting each of the qubits in its own heat bath, each at a different temperature, throws the system out of equilibrium. "They can make a transition back and forth, but we can bias the transition by putting them at different temperatures," Popescu says. Placing the engine qubit in a hot environment raises the probability of that qubit residing in its excited state, which in turn makes it more likely that the entire system will reach the state with both engine and contents excited than with only the coil excited.



That shift in starting conditions means that when the system transitions between equal-energy states, it is more likely to take the refrigerated qubit from its excited state to its ground (cool) state than vice versa. That same transition takes the heat-coil qubit from its ground state to its excited state; effectively, the system transfers excitations from the refrigerated qubit to the coil qubit, which dissipates energy into the coil's own tepid heat bath.



Although the proposal is couched in ground states and excitations, the language of quantum physics, the researchers say it is perfectly appropriate to think of the outcome in the more classical hot-and-cold terms of thermodynamics. "Being colder means to have lower energy," Popescu says; because the fridge lowers the energy of the refrigerated qubit, the qubit's temperature decreases as well. Once the chilling qubit has a temperature lower than its environment, it will draw heat away from its surroundings, Linden notes. "How do we know this works as a fridge in the normal sense? The refrigerator does indeed draw heat away from its cold bath," he says.



As long as the engine's heat bath stays warmer than the coil's tepid bath the process will repeat itself, drawing the refrigerated qubit to ever lower temperatures. "The point is when you have to choose between those two energy states, you bias the system toward one of them, and that is what gradually cools the qubit," Popescu says. In principle, the refrigerator can chill arbitrarily close to absolute zero.



Others have devised and even built such small-scale cooling systems, says Leonard Schulman, a professor of computer science at the California Institute of Technology, but the distinction in the new work is that it is self-contained—the qubits do not need to receive instructions from outside the system. "All the external environment needs to maintain is suitable heat baths at two different temperatures," Schulman says, "and it will just sit there and 'cook,' or rather 'cool,' endlessly."



Two physicists who have experimentally implemented a three-qubit chiller that used external radio-frequency pulses to drive the cooling process say the new approach has promise. "It's a neat theoretical idea," says Osama Moussa, a postdoctoral fellow at the University of Waterloo's Institute for Quantum Computing (IQC). "The system has a number of parameters, and if you set them just so, then the system evolves on its own."



Technically speaking, it might be difficult to find a system—or to engineer one—with those exact parameters, such as the energy level spacings that perfectly balance one another and an interaction between the three qubits that links their energy levels. Adds Raymond Laflamme, a Waterloo physicist who directs the IQC, "It's only a very, very rare system where you can get this three-body interaction." But that is not to say that experimentalists will be deterred by the challenge put forth in the new theoretical study. "Once you know that something is possible, then it's a lot easier to go and find it," Laflamme says.