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| Fig. 1: An electron absorbs a photon (red), transitioning from its ground state to an excited state. After some time in an excited state, the electron decays and emits a new photon in a random direction but with the same energy as the original photon it absorbed. (Source: B. Kroul) |
Traditional batteries use chemical reactions to store and generate electrical energy. As electrochemical battery technology approaches its theoretical limits, physicists propose harnessing unique properties of quantum mechanics to create an entirely new type of battery: quantum batteries. [1]
A quantum battery (QB) is a quantum system capable of transferring and storing energy between light (electromagnetic radiation) and matter. Due to quantum coherence, the charging and discharging power (energy transfer per unit time) of a QB scales more than linearly to the number of its excitable molecules, providing a "quantum advantage" over the power of traditional batteries. [2-4] The concept of a quantum battery did not exist before 2004. [2] As such, the theoretical foundation of quantum batteries has only been explored within the past decade, and only within the last few years have advances in quantum technology made it possible to experimentally realize proof-of-concept devices. This report will summarize the current theory behind QBs, investigate experimental proof-of-concepts, and evaluate the role QBs could play in the future considering limitations of scalability, energy efficiency, energy density, and cost.
When light interacts with an electron in an atom, the electron absorbs a photon and transitions into an excited, high-energy state. This high-energy state is inherently less stable than the low-energy state it was in before, so the electron will eventually decay, spontaneously emitting its excited energy as a photon once more and transitioning back into its low-energy ground state (Fig. 1). [5] In this way, energy can be stored, temporarily, in a system of molecules that are easily excited in the presence of light, such as photosensitive molecules, superconducting atoms, trapped atoms, or quantum dots.
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| Fig. 2: Top: A QB absorbing energy from a coherent source of light. Bottom: A QB spontaneously releasing energy. (Source: B. Kroul) |
When the molecules in a QB are energized under the right conditions, their energetic transitions interfere constructively and couple to each other, all obeying a single coherent quantum state (Fig. 2). An ideally coupled quantum system has been known since 1954 to exhibit superradiance, where excited molecules collectively emit light with an intensity quadratically proportional to the number of excited molecules in the system, ∝N2. [3] The opposite process, superabsorption, was only theoretically shown in 2013. It is even more exciting: the rate of energy absorption (charging power) of a quantum system can also scale quadratically to the number of molecules, ∝N2. [4] The quantum advantage of a QB comes from the scaling of superabsorption and superradiance, which is dependent on the quantum coherence of the entire QB.
To maximize the coherence of the molecules within a QB, a coherent light source, uniform in wavelength and direction, must be transmitted globally, energizing every molecule at the same time. [6] This can be done using an ultra-short laser burst in a small cavity. [7] In an ideal QB where N molecules are coupled to every other molecule, charging power scales proportional to the square of the number of molecules (∝N2), but in the limit of large N, scales with N3/2. This is due to the time to reach maximal power scaling as N-1/2 and the absorbed energy scaling with N as coupling is reduced between every molecule. [8] So at the limit of large N, energy is absorbed almost instantaneously by the molecules!
The amount of energy that can be extracted from a quantum system (the work transferred to an output light source) is termed the ergotropy. [2] The efficiency η of a quantum battery is defined as the ergotropy ε over the work required to create the energized quantum state, η = ε/Wf. As the energy in a QB will spontaneously decay over time, maximal ergotropy is reached by interacting the quantum battery with the same uniform, global light source in order to cause collective stimulated emission, transferring as much work as possible back into the light source.
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| Fig. 3: Schematic of the QB in Quach et al. [7] An optical microcavity is engineered with an extremely high reflective index by using layered distributed Bragg reflectors (DBR)s, resonating the light back and forth in the cavity. An ultra-short duration laser pulse lasting 2 × 10-14 s is pulsed to resonate in the microcavity and excite varying concentrations of LFO molecules suspended in a matrix of polystyrene (PS). (Source: B. Kroul) |
In January 2022, researchers from the University of Adelaide and the Istituto di Fotonica e Nanotecnologia implemented the first QB to exhibit superabsorption with a macroscopic (large-scale) number of excited molecules. [7] They created a QB at room temperature by pulsing an ultra-short duration laser into an optical microcavity, exciting varying concentrations of the photosensitive dye Lumogen-F-Orange (LFO) (see Fig. 3). After an initial pulse of energy excites the dye molecules in the cavity, the same laser is used to measure the energy of the cavity over time. By varying the number of dye molecules N and the laser intensity r, the researchers experimentally found evidence of superabsorption. At low N, charging power and absorbed energy scales quadratically with N (∝N2), up to about N = 1.6 ×1010. At the limit of large N, charging power still scales at a rate ∝ N3/2, but absorbed energy scales linearly, and the energy contained in the battery decays quickly.
The reduction of scaling of power and energy at large N is due to an essential challenge facing any quantum process at large densities: intermolecular quenching. At large N, a high density of molecules prevents coupling between molecules to all other molecules in the system, lowering coherence and energy absorption. Energy is also able to decay quickly because of the presence of uncoupled, unenergized molecules which act as decay channels facilitating nearby excited molecules to transfer their energy.
To reduce intermolecular quenching, the researchers propose using different materials, such as a more transparent matrix to suspend the dye molecules, but there is no way to fully eliminate intermolecular quenching from a macroscopic quantum system.
The highest-performing QB setup that the researchers studied was the QB with a 1% LFO (710.9 g/mol) concentration by mass and a ratio of pump photons to LFO molecules of 2.4. It had a maximal energy of 0.184 eV per LFO and a maximal power of 1.008 eV/ps per LFO. Although higher concentrations of LFO had greater total values for energy and power, they had energy that decayed extremely quickly from the cavity. Lets compare this proof-of-concept quantum battery to a the low range of the parameters of a lithium-ion battery made in 2014, which has an energy density of up to 110 Wh/kg and a battery cost of $0.6 / Wh. [9]
First, we can calculate the specific energy of the PS-LFO material being energized within the optical microcavity, in watt-hours per kilogram:
| 0.184 eV LFO-1 ×
6.022 × 1023 LFO mole-1
× 1.6022 × 10-19 J eV-1
× 0.01
0.7109 kg mole-1 × 3600 J Wh-1 |
= | 0.0685 Wh kg-1 |
This is about 1,600 times less energy density than the lithium-ion battery.
Calculating the battery cost per unit energy, consider the price of LFO in 2023 from the chemical supplier Kremer Pigments, which Quach et al. cited as the source. [7] At $0.215 per gram of LFO, and assuming polystyrene is essentially free, the estimated cost per unit of energy of the PS-LFO material is:
| $0.215 g-1 × 1000 g
kg-1 0.0685 Wh kg-1 |
= | $3,139 Wh-1 |
This is about 5,200 times more expensive than the cost of lithium-ion, only considering the PS-LFO material itself!
The researchers estimate from the reflectivity of the microcavity that only 6-8% of the laser pump enters the cavity. This caps the battery efficiency at 6-8%, even before trying to transmit its stored energy into another form.
These numbers make it clear that even if QBs could be scaled up to form a real battery, they wouldn't even come close to matching the energy performance or cost of widely available batteries like lithium ion.
Quantum batteries face many challenges that make them hard to implement and hard to apply to real-world uses. Quantum systems rely on perfectly cohered light sources and decohere at the slightest introduction of environmental noise, allowing them to only store energy for extremely short periods of time. In the organic microcavity experiment, the coherence time was defined as 120 femtoseconds, which is 1.2 × 10-13 s. For low values of N, energy seems to be stored for a few hundred picoseconds before decaying, around 10-10 s. Organic solar cells, which also rely on excitations in photoluminescent dye in microcavities, have a maximal coherence time of 1.2 × 10-9 s. [10] This means the only systems QBs might be useful at storing energy for are other extremely fast quantum systems.
Another fundamental challenge of QBs is their ability to transfer usable work to an outside system, such as for driving an electrical current. Allahverdyan et al. propose adding conductive metal plates on either side of the organic microcavity in a way similar to the energy harvesting capability of organic solar cells to generate an electrical current, but a theoretical model has yet to be produced. [2] It also likely won't work well enough to be useful, as coupling the battery to more components would decrease the ergotropy of the battery and it is unclear how resonant light in the microcavity will create a to a potential difference on either side of the microcavity. Its unclear how to couple a quantum battery to directly or alternately drive an electromagnetic current in order to convert its work into electric work.
Many different types of quantum systems can be used to realize a quantum battery. In October 2022, a QB was implemented by coupling the nuclear spins of up to 38 charger molecules to a singular battery molecule. They found the spins interfere collectively just like in an electronic quantum battery, finding ∝ N3/2 dependence in ergotropy and energy scaling. Most surprisingly, they found their spin system had a coherence lifetime of around 200 seconds!
Quantum physics allows for processes that scale extremely well with the number of molecules, and yet these processes fall apart at a number of molecules too small to see any real-world usage. Quantum batteries are an exciting area of research that hold great potential for probing the smallest laws of thermodynamics and maximizing the fundamental performance of energy storage technology. Quantum batteries might have use in the future as a nanoscale energy storage unit to power other quantum technologies, where operations only occur at picosecond timescales. [2] Quantum batteries could also be useful as optical sensors in low-light conditions or for energy harvesting. [2,4] However, the development of practical quantum batteries is still in its infancy. The next step for implementing a working quantum battery is showing that a quantum system can transfer work into an electrical current or drive another laser that can then be used for energy.
© Ben Kroul. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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[8] D. Ferraro et al., "High-Power Collective Charging of a Solid-State Quantum Battery," Phys. Rev. Lett. 120, 117702 (2018).
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