Abstract
This chapter is a survey of the published literature on quantum batteries – ensembles of non-degenerate quantum systems on which energy can be deposited, and from which work can be extracted. A pedagogical approach is used to familiarize the reader with the main results obtained in this field, starting from simple examples and proceeding with in-depth analysis. An outlook for the field and future developments are discussed at the end of the chapter.
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Notes
- 1.
In thermodynamics a closed system is only allowed to exchange either work or heat, in contrast with an isolated system which is not allowed to exchange either of them. Here, by closed, we mean isolated quantum system undergoing Schrödinger evolution, but whose initial state can be mixed.
- 2.
See Ref. [20] for an extended review on quantum speed limits and their applications.
- 3.
The unique distance on the space of pure states that is invariant under unitary operations is the Fubini-Study distance, given by the angle between the two considered states [21].
- 4.
The operator norm \(||\cdot ||_{\text {op}}\) of an operator H is equal to its largest singular value; if the operator H is Hermitian (and any Hamiltonian is) then the operator norm is equal to the largest eigenvalue.
- 5.
For example, in the case of 2-level systems such interactions have non-trivial components proportional to products of n Pauli operators \(\sigma _i^{(1)}\otimes \cdots \sigma _j^{(n)}\), with \(i=1,2,3\).
- 6.
More precisely, CPBs are referred to as charge qubits in the large charging energy regime; when the charging energy is small, they are referred to as flux qubits.
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Campaioli, F., Pollock, F.A., Vinjanampathy, S. (2018). Quantum Batteries. In: Binder, F., Correa, L., Gogolin, C., Anders, J., Adesso, G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-99046-0_8
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