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{{Short description|Quantum device proposed for storing and releasing energy}}

{{Quantum book backlink|Advanced and frontier topics}}

A '''quantum battery''' is a proposed quantum device that stores and releases energy using principles of [[Physics:Quantum mechanics|quantum mechanics]]. Unlike an ordinary electrochemical battery, a quantum battery is modeled in terms of quantum states, Hamiltonians, charging protocols, extractable work, and collective many-body effects.<ref name="Alicki2013">{{Cite journal |last1=Alicki |first1=Robert |last2=Fannes |first2=Mark |date=2013-04-25 |title=Entanglement boost for extractable work from ensembles of quantum batteries |url=https://journals.aps.org/pre/abstract/10.1103/PhysRevE.87.042123 |journal=Physical Review E |volume=87 |issue=4 |article-number=042123 |doi=10.1103/PhysRevE.87.042123 |pmid=23679388 |arxiv=1211.1209 |bibcode=2013PhRvE..87d2123A }}</ref>

Quantum batteries are studied as theoretical systems in which [[Physics:Quantum entanglement|entanglement]], collective interactions, coherence, and many-body dynamics may improve charging power or extractable work. They remain at an early stage of development, and no fully functional practical quantum battery is currently available.<ref name="Niroula">{{Cite news |last=Niroula |first=Pradeep |title=Quantum batteries harvest energy from light |work=Physics World |url=https://physicsworld.com/a/quantum-batteries-harvest-energy-from-light/}}</ref>

<div style="float:right; border:1px solid #e0d890; background:#fff8cc; padding:6px; margin:0 0 1em 1em; width:420px;">
[[File:Quantum_battery_yellow.png|400px]]
<div style="font-size:90%;">A quantum battery is modeled as a quantum system that can be charged, store energy, and release extractable work.</div>
</div>

=Overview=

The basic idea of a quantum battery is to treat energy storage as a problem in quantum thermodynamics. The battery is represented by a quantum system with an internal Hamiltonian. Charging corresponds to changing the state of the system so that it contains more usable energy, while discharging corresponds to extracting work from that state.

A central quantity in this field is '''ergotropy''', the maximum amount of work that can be extracted from a quantum state by unitary operations. The ergotropy depends not only on the average energy of the state, but also on how that energy is distributed among the quantum levels.<ref name="NewScientist2024">{{Cite journal |last=Padavic-Callaghan |first=Karmela |date=November 9, 2024 |title=Quantum batteries output more energy than they store |journal=New Scientist |page=19}}</ref>

Quantum batteries are of interest because quantum systems can be charged collectively. In some theoretical models, charging many quantum cells together may produce higher power than charging the same cells independently.<ref name="Alicki2013" /> This possibility is often called a '''quantum advantage''' in charging power.

=History=

The concept of quantum batteries was introduced in 2013 by Robert Alicki and Mark Fannes. They showed that entanglement could increase the extractable work from ensembles of quantum batteries.<ref name="Alicki2013" />

Later work investigated whether collective quantum effects could provide faster charging. One important proposal was the Dicke quantum battery, based on the Dicke model of collective light–matter coupling.<ref name="Ferraro2018">{{Cite journal |last1=Ferraro |first1=Dario |last2=Campisi |first2=Michele |last3=Andolina |first3=Gian Marcello |last4=Pellegrini |first4=Vittorio |last5=Polini |first5=Marco |date=2018-03-15 |title=High-Power Collective Charging of a Solid-State Quantum Battery |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.117702 |journal=Physical Review Letters |volume=120 |issue=11 |article-number=117702 |doi=10.1103/PhysRevLett.120.117702 |pmid=29601745 |arxiv=1707.04930 |bibcode=2018PhRvL.120k7702F }}</ref>

The original Dicke-battery proposal appeared to suggest a strong collective charging advantage. However, later analysis showed that the Hamiltonian must be scaled correctly in the thermodynamic limit. With this correction, the Dicke model does not provide the originally claimed quantum advantage.<ref name="JuliaFarre2020">{{Cite journal |last1=Julià-Farré |first1=Sergi |last2=Salamon |first2=Tymoteusz |last3=Riera |first3=Arnau |last4=Bera |first4=Manabendra N. |last5=Lewenstein |first5=Maciej |date=2020-05-01 |title=Bounds on the capacity and power of quantum batteries |url=https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.023113 |journal=Physical Review Research |volume=2 |issue=2 |article-number=023113 |doi=10.1103/PhysRevResearch.2.023113 |arxiv=1811.04005 |bibcode=2020PhRvR...2b3113J }}</ref>

In 2020, a many-body model based on the Sachdev–Ye–Kitaev model was proposed as a quantum battery. This SYK quantum battery showed a quantum advantage in the charging process within the studied model.<ref name="Rossini2020">{{Cite journal |last1=Rossini |first1=Davide |last2=Andolina |first2=Gian Marcello |last3=Rosa |first3=Dario |last4=Carrega |first4=Matteo |last5=Polini |first5=Marco |date=2020-12-02 |title=Quantum Advantage in the Charging Process of Sachdev-Ye-Kitaev Batteries |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.236402 |journal=Physical Review Letters |volume=125 |issue=23 |article-number=236402 |doi=10.1103/PhysRevLett.125.236402 |pmid=33337187 |arxiv=1912.07234 |bibcode=2020PhRvL.125w6402R }}</ref>

=Physical idea=

A quantum battery can be imagined as a set of quantum cells. Each cell may be a two-level system, qubit, spin, atom, or artificial quantum system. The battery is charged by applying an external interaction that raises the energy of the system.

The key question is not only how much energy is stored, but how much useful work can be extracted. In quantum thermodynamics, stored energy and extractable work are not always the same. A state may contain energy that cannot be fully converted into work by the allowed operations.

Quantum correlations can change this behavior. If the battery and the device being powered are treated as a single inseparable quantum system, the distinction between stored energy, usable work, and correlations becomes more subtle. This is why ergotropy, entanglement, and collective charging are central concepts in the theory of quantum batteries.<ref name="NewScientist2024" />

=Ergotropy=

The work that can be extracted from a quantum battery is called '''ergotropy'''. It measures the maximum useful work obtainable from a quantum state by unitary evolution.

A state with high average energy is not automatically a good battery state. If the state is passive, no work can be extracted from it by unitary operations. A charged quantum battery must therefore be prepared in a non-passive state.

Ergotropy is important because it separates stored energy from extractable energy. This distinction is one of the main differences between ordinary energy accounting and quantum energy storage.<ref name="NewScientist2024" />

=Collective charging=

In a classical battery pack, increasing the number of cells usually increases total stored energy in a roughly additive way. In a quantum battery, the cells may interact collectively. This raises the possibility that the charging power can scale faster than the number of cells.

For a battery made of <math>N</math> quantum cells, independent charging gives a power that scales approximately as <math>N</math>. Some quantum models predict faster scaling, for example

<math>\langle P \rangle_t \propto N^{3/2}</math>.

Such super-extensive scaling is interpreted as a possible quantum advantage. However, whether this advantage survives physical constraints depends on the model, the allowed interactions, and the correct thermodynamic scaling.<ref name="JuliaFarre2020" />

=Models=

==Dicke quantum battery==

The '''Dicke quantum battery''' uses the Dicke model to describe collective interaction between many two-level systems and a single electromagnetic mode. It was proposed because of its connection with collective light–matter coupling and superradiant behavior.<ref name="Ferraro2018" />

The Dicke model describes an ensemble of <math>N</math> two-level systems interacting with a cavity mode. A simplified Hamiltonian can be written as

<math>
H_{\text{Dicke}} =
\omega_c \hat{a}^{\dagger}\hat{a}
+
\omega_0 \sum_{i=1}^{N} \hat{\sigma}_i^z
+
g \sum_{i=1}^{N} \hat{\sigma}_i^x
\left(\hat{a}^{\dagger}+\hat{a}\right).
</math>

The first term represents the energy of the cavity photons. The second term represents the energy of the two-level systems. The third term represents the interaction between the photons and the two-level systems. The parameter <math>g</math> is the coupling strength.

In the original form, the model appeared to allow the mean charging power to scale as

<math>
\langle P \rangle_t \propto N^{3/2}.
</math>

However, this Hamiltonian is not well defined in the thermodynamic limit unless the coupling is scaled properly. The required replacement is

<math>
g \rightarrow g_{\text{TD}} = \frac{g}{\sqrt{N}}.
</math>

After this correction, the Dicke battery does not provide the originally expected quantum advantage.<ref name="JuliaFarre2020" />

==SYK quantum battery==

The '''SYK quantum battery''' uses the Sachdev–Ye–Kitaev model as a many-body charging model. It is important because it was proposed as a many-body quantum battery with a genuine advantage in charging power.<ref name="Rossini2020" />

A direct charging protocol can be written as

<math>
H_B(t) =
H_B^{(0)}
+
\lambda(t)
\left(
H_B^{(1)} - H_B^{(0)}
\right),
</math>

where

<math>
H_B^{(0)} =
\sum_{i=0}^{N}
\omega_0 \hat{\sigma}_i^y
</math>

is the initial battery Hamiltonian, and

<math>
H_B^{(1)} =
\sum_{i,j,k,l=1}^{N}
J_{i,j,k,l}
\hat{c}_i^\dagger
\hat{c}_j^\dagger
\hat{c}_k
\hat{c}_l
</math>

is the interacting many-body Hamiltonian.

In this model, the mean charging power can scale as

<math>
\langle P \rangle_t \propto N^{3/2}.
</math>

This makes the SYK quantum battery an important example in the theoretical study of collective quantum charging.<ref name="Rossini2020" />

=Experimental status=

Quantum batteries are still mainly theoretical. Experiments are beginning to explore the basic ingredients, including light harvesting, quantum coherence, collective charging, and controlled quantum energy transfer.<ref name="Niroula" />

The main challenge is that a useful quantum battery must do more than store energy in a microscopic quantum system. It must also preserve the stored energy long enough, allow controlled charging and discharging, avoid excessive decoherence, and deliver useful work to another system.

=Possible applications=

Quantum batteries are not expected to replace ordinary household batteries in the near future. Their possible applications are more likely to be in nanoscale or quantum technologies, where the device being powered is itself quantum mechanical.

Possible future applications include energy storage for quantum sensors, nanoscale machines, quantum communication components, and parts of [[Physics:Quantum information and computing|quantum information]] systems. Their main value at present is theoretical: they provide a testbed for understanding work, power, entropy, and energy flow in quantum systems.

=Limitations=

Several limitations remain unresolved. Quantum coherence is fragile, and interactions with the environment can destroy the correlations that make a quantum battery useful. Scaling a quantum battery to many cells may also introduce control problems and unwanted losses.

Another limitation is that a claimed quantum advantage depends strongly on the assumptions of the model. A model that appears to show faster charging may lose this advantage when physical constraints, locality, coupling strength, or thermodynamic consistency are imposed.<ref name="JuliaFarre2020" />

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Quantum battery|1}}

Physics:Quantum battery - Revision history

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