Cooling with a Warm Glow

Michael Schirber

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Cooling with a Warm Glow

March 23, 2012• Physics 5, 36

Incoherent light from the sun or from an LED could cool a small object, according to two theory papers.

Figure caption — **Soaking up energy.** When an incoherent light beam with frequency $ω_{b}$ (coming from an LED or other source) strikes a mirror oscillating at frequency $ω_{c}$ , the interaction can remove heat from the mirror in the form of light at frequency $ω_{a}$ , the sum of the other two frequencies.

Lasers can cool atoms in part because their photons are “coherent,” meaning they are synchronized and orderly. Two theoretical papers in Physical Review Letters now show explicitly how to use disorderly, incoherent light to cool a small object. The papers employ different principles: in one, the heat is carried away by electrons, while in the other, the heat radiates away as light. But both refrigeration schemes use the energy levels of tailored quantum systems. This is part of a growing body of work showing that quantum machines should perform better than their classical analogs. The new schemes could be good news for researchers trying to cool down precision force meters or bits of a quantum computer.

Cooling with heat is not new. An absorption refrigerator uses heat from a small burner or other source to drive an evaporation-condensation cycle that is similar to the one in a normal refrigerator compressor. Light can be used as the heat source, but the cooling power is not very strong. Much better performance is obtained when laser light is used to cool clouds of atoms and other small objects to near absolute zero. Ideally, researchers would like to cool a small, solid object, such as the tip of an atomic force microscope, to its quantum ground state, the lowest possible temperature. These systems could be used to study quantum gravity or the quantum wave function of a macroscopic object.

A great deal of recent theoretical work has studied the application of thermodynamic principles such as heat and work at the quantum level [1]. It is now understood that quantum engines and refrigerators may have an advantage over classical ones because quantum particles can occur in well-defined energy states. A quantum system can therefore be optimized at a specific energy. But very few of these quantum machines have been built yet, so there is a strong push to come up with realizable designs [2–4].

Bart Cleuren and his colleagues at Hasselt University in Diepenbeek, Belgium, propose a cooling system that could conceivably work with sunlight. The solid object to be cooled—say a metal electrode—is electrically connected to a warmer object (another electrode). Current can flow between the electrodes through a pair of quantum dots, which could be tiny islands of semiconductor on a nonconducting surface. Each dot acts like an atom that can accept a single electron in one of two energy levels.

The team imagines adjusting the energy levels of the two dots so that cold electrons flow from the warm electrode to the cold one, while hot electrons flow in the opposite direction. To make this passage, a cold electron in the warm electrode hops into the lower energy level of the first dot, where it must absorb a photon in order to jump to the lower energy level of the second dot. Once there, the cold electron can hop into the cold electrode to help cool it. Hot electrons make a similar trip in the other direction, hopping across the dots’ upper energy levels and absorbing a photon along the way. A strong light source such as the sun is needed to drive the opposing currents.

Cleuren says that one can imagine the electrons are “evaporating” out of the cold object and “condensing” in the warm object, somewhat like an absorption refrigerator. The net heat flow would probably be quite small, but Cleuren imagines that an array of dots could be placed in between the hot and cold objects to increase the heat exchange.

Andrea Mari and Jens Eisert of the Free University in Berlin propose a different cooling mechanism. Previous experiments have shown that laser light can cool a small mirror that is part of a so-called optomechanical device. In these experiments, the mirror, which is allowed to vibrate, is opposite a second, fixed, semitransparent mirror. Laser light streams through the fixed mirror, and photons bouncing back and forth between them can build up a strong interaction with the first mirror. This interaction can cause most of the mirror’s vibrational energy to be converted to light, which is equivalent to cooling the mirror. But Mari and Eisert thought they could forego the laser. “To cool quantum systems, incoherent, cheap light sources such as LEDs could be used,” says Eisert.

They envision a three-mode interaction in which a mirror or similar object vibrates at one frequency, while also interacting with two separate frequencies of light. The optical frequencies would be chosen so that the difference between them is equal to the mirror’s vibration frequency. When the space between the two mirrors is filled with incoherent light of the lower optical frequency, the vibrating mirror absorbs some of that energy and heats up. But the calculations by Mari and Eisert show that this light also drives the conversion of mechanical energy into light at the higher optical frequency. They describe it as a transistor-like effect, in which light pumped in at one “connection” amplifies the light emitted at another “connection.” The team found that there is an optimal amount of higher-frequency light needed to get the maximum cooling, with which one could conceivably cool a room-temperature object down to around $70$ kelvin. This system might be useful for extremely sensitive force detectors that require very low thermal noise, Eisert says.

Günter Mahler from the University of Stuttgart, Germany, thinks a lot of theoretical groundwork was laid in previous studies looking at quantum thermodynamics. “What is new in [these latest papers] is the type of implementation, and this should not be underestimated,” Mahler says. He believes the designs are feasible, and some preliminary laboratory attempts may show up soon. But “anything about future technologies is much too early right now,” he says.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.

References

See references in A. Levy and R. Kosloff, “The quantum absorber refrigerator,” arXiv:1109.0728 (2011)
N. Linden, S. Popescu, and P. Skrzypczyk, “How Small Can Thermal Machines Be? The Smallest Possible Refrigerator,” Phys. Rev. Lett. 105, 130401 (2010)
Y.-X. Chen and S.-W. Li, “Quantum refrigerator driven by current noise,” Europhys. Lett. 97, 40003 (2012)
J. T. Peltonen, M. Helle, A. V. Timofeev, P. Solinas, F. W. Hekking, and J. P. Pekola, “Brownian refrigeration by hybrid tunnel junctions,” Phys. Rev. B 84, 144505 (2011)