What does it actually mean for a battery to be fully charged? In the quantum world, the answer is less obvious than for an ordinary battery. Researchers from the University of Gdańsk have shown that in the smallest systems, it is not only the amount of usable energy that matters, but also the way it is internally organised.
The study, published in PRX Energy, suggests that two quantum batteries containing the same amount of usable energy can behave differently depending on how that energy is stored. The findings could help improve the design of future quantum computers, sensors, communication networks and other devices operating at the atomic scale.
Physicists and engineers are increasingly designing devices built from individual atoms, ions, photons or tiny superconducting circuits. At this scale, energy does not behave in the same way as it does in conventional batteries. Instead, it must be described using quantum mechanics.
Future quantum technologies will need not only to process information, but also to absorb, store and transfer energy, while inevitably losing some of it to the environment. Understanding what it means to charge such systems, how long they can retain energy and how much of that energy can later be recovered is therefore becoming increasingly important.
This is where the concept of a quantum battery comes in. A quantum battery is a microscopic system capable of storing energy and releasing it in a controlled way. It may consist of an atom, an ion, a system of light or a small superconducting circuit.
For physicists, however, a quantum battery is primarily a model for studying energy storage at the smallest scales. Such systems possess properties that ordinary batteries do not. Under certain conditions, they can charge more quickly, exploit the collective behaviour of many quantum components or store energy in the form of quantum coherence—a property that allows a system to exist in a combination of different states simultaneously.
These unique properties mean that energy storage in the quantum world has to be understood differently.
In everyday terms, a battery is considered charged if it contains a certain amount of energy. In quantum physics, that definition is not sufficient. A system may contain energy that cannot easily be converted into useful work. Since a battery is valuable only if its energy can be recovered in a controlled way, physicists instead use the concept of ergotropy—the fraction of a system's energy that can be extracted as useful work rather than lost as heat.
This distinction raises an important question. If ergotropy determines how much work can be extracted from a quantum battery, are two batteries with the same ergotropy effectively identical?
According to the Gdańsk researchers, they are not.
The team found that the same amount of usable energy can be stored in different ways. In the simplest two-level quantum system, some of the usable energy may come from the system occupying its higher-energy state more frequently. Another part may be associated with quantum coherence. Both approaches can produce the same ergotropy, even though they represent different physical states.
The researchers compare the situation to two backpacks of the same weight. One is neatly packed, with everything easy to reach. The other contains the same items arranged differently. Although both weigh the same, they are not equally practical. Likewise, knowing only the amount of usable energy stored in a quantum battery does not reveal how that energy is organised.
Physicists refer to such systems as isoergotropic states—states that contain the same amount of extractable work but differ in their internal structure.
The central question addressed in the paper is whether it is possible to transform one isoergotropic state into another without changing the amount of usable energy. The researchers show that it is. Rather than charging or discharging the battery, such operations reorganise how the energy is stored while preserving the same ergotropy.
The study (doi: 10.1103/2jtp-jpkn) examines two simple models of quantum batteries: a two-level system and a model based on light and quantum oscillators commonly used in quantum optics. In both cases, the researchers demonstrate that the same ergotropy can be distributed among different components and transformed between them.
Importantly, these transformations are not merely mathematical. According to the researchers, they can be linked to known physical interactions, including processes similar to those produced by optical beam splitters, which divide or mix light and can be used to control energy exchange between small quantum systems.
The work also highlights what happens when quantum batteries interact with their surroundings. In reality, no quantum system is perfectly isolated. Environmental interactions gradually cause it to lose useful energy.
The researchers found that two quantum batteries with the same initial ergotropy may discharge at different rates depending on how that energy is encoded. In one model, a greater contribution from quantum coherence allowed useful energy to be retained for longer. In another, a different internal arrangement proved more robust.
The findings suggest that in the quantum world, the amount of stored energy is only part of the story. The way that energy is stored can be just as important.
As quantum computers, sensors and communication networks continue to develop, a better understanding of quantum energy storage could help researchers build systems that are more stable and easier to control. The study also proposes a new way of thinking about quantum batteries: their charge can not only be increased or decreased, but also internally reorganised while keeping the same amount of usable energy—a difference that may ultimately determine how long a quantum battery remains effectively charged.
Krzysztof Petelczyc (PAP)
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