Tiny quantum engines reveal useful energy hiding in “waste heat”

Thermodynamics emerged in the 19th century largely to explain how large machines such as steam engines convert and transfer energy. Quantum physics, developed in the early 20th century, instead focuses on atoms and subatomic particles. Today, however, the two fields increasingly overlap. Tiny systems built from atoms and light particles (photons) can take in energy, transform it, and release it, allowing them to function as microscopic quantum machines.

A major challenge is finding a description that remains valid both when the entire system is treated quantum mechanically and in the semi-classical limit. The latter is the limiting case in which one part of the system is treated quantum mechanically, while classical physics is sufficient for the other part. Researchers in the group of Professor Patrick Potts at the University of Basel have now presented such an approach in Physical Review Letters.

A Tiny Quantum Light Engine

"Our calculations regard the concrete physical model of an atom that is placed in a cavity between two mirrors, where it can absorb and emit light particles," says postdoc Marcelo Janovitch. In this setup, a laser continuously supplies additional photons to the cavity, while some light escapes through the partially reflecting mirrors.

"This is a textbook example of a so-called driven-dissipative system that continuously receives energy and simultaneously loses it to the environment," says the researcher. The model gives physicists a way to investigate fundamental questions involving open quantum systems. In this case, the atom behaves much like a miniature heat engine, or more specifically, a "light engine."

Potts and his collaborators had previously shown that photons leaving the cavity should not automatically be treated as "waste heat" in a thermodynamic description. Some of the energy carried by that escaping light can still be used to perform useful work on another quantum system.

Their latest study examined what happens to this distinction between heat and useful energy when the system approaches the semi-classical limit.

Separating Useful Energy From Heat

In the semi-classical limit, the atom inside the cavity continues to be treated as a quantum system with discrete energy levels. The light, however, is treated as a classical electromagnetic wave, meaning its quantum effects can be ignored.

"Treating the light classically makes it much easier to define which part of the energy can be used to perform work and which part is disordered heat," says Janovitch. For the theory to be consistent, this classical limiting behavior should emerge naturally from the full quantum thermodynamic description.

Janovitch and his colleagues have now demonstrated mathematically that this is possible with their approach. When part of the emitted light is classified as useful work, the theory moves smoothly into the semi-classical limit.

The conventional approach produces a different result. If all energy leaving the cavity is counted as heat, the theory does not make the same consistent transition.

Quantum Fluctuations Become a Resource

The researchers also found that their calculations correctly describe how quantum effects can reduce fluctuations in the emitted light particles.

These reduced fluctuations could be especially valuable for quantum technologies. Heat often creates disturbances that make quantum systems harder to control, but under the right conditions, it could instead become a useful resource.

For example, the effect could help produce particular states of light that are useful for especially precise measurements in quantum metrology. The findings show how a better understanding of the boundary between heat and useful work could help researchers take advantage of energy that might otherwise appear to be lost.