Energy Storage and Fluctuations in a Central-Spin Quantum Battery with Nearest-Neighbour Interactions

Abstract

In this thesis the stored energy and its fluctuations of a central spin battery with nearest-
neighbour interactions between the battery spins are investigated. Using analytical ex-
pressions, it is shown that for 2 battery spins and equal strength in the flip-flop interaction
g and nearest-neighbour interaction J, the fluctuations are minimal whenever the bat-
tery is maximally charged when taking at least four charge spins. Similarly, whenever
the formed envelopes of the energy have a zero, the fluctuations have a global maximum.
In the same limit, it could also be seen that an increase of the charge spins Nc and
spin-ups m, resulted in a higher global maximum of the stored energy. Furthermore for
2 battery spins, taking the limit J ≫ g results in a situation where the battery cannot
be charged at all, whereas taking the limit g ≫ J results in a central spin battery where
no nearest-neighbour interactions are present; its stored energy as a function of time is
a single cosine function, that is always able to reach its theoretical maximum.
Similar results were found for systems with more than 2 battery spins. Increasing J with
constant g resulted in a decrease of the global maximum of the energy, dropping from its
theoretical maximum to its minimum. Opposite behaviour could be seen when increasing
g with constant J. Whenever the global maximum of the energy crossed the line E = 0,
the fluctuations at the same moment in time formed a peak.