Energy storage and coherence in closed and open quantum batteries

Francesco Caravelli1, Bin Yan1,2, Luis Pedro García-Pintos3, and Alioscia Hamma4

1Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
2Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
3Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
4Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA

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We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.

We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence.

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[1] Anna Delmonte, Alba Crescente, Matteo Carrega, Dario Ferraro, and Maura Sassetti, "Characterization of a Two-Photon Quantum Battery: Initial Conditions, Stability and Work Extraction", Entropy 23 5, 612 (2021).

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