Ergotropy transport in a one-dimensional spin chain

We examine the transport of useful energy, i.e., extractable work as quantified by the ergotropy, along a spin chain with tunable exchange couplings between the sites. We focus on, and interpolate between, the two physically relevant limits of uniform interaction strengths and engineered couplings which achieve perfect state transfer (PST). By modeling the individual constituents as quantum batteries, we consider how the manner in which the extractable work appears in the initial state of the first site impacts the chain's ability to transport ergotropy to the final site. For non-PST couplings, we establish that there is a clear quantum advantage when the ergotropy is initially endowed in quantum coherences and demonstrate that this ergotropy is more efficiently transferred. For extractable work encoded in a population inverted state, we show that this considerably limits the length of chain over which any ergotropy can be faithfully transported. For PST couplings, we consider the robustness to disorder and again demonstrate a quantum advantage for coherently endowed ergotropy. Finally, we examine the work probability distribution associated with quenching on the interactions, which provides insight into the work cost in switching on the couplings. We show that PST couplings lead to smaller fluctuations in this work cost, indicating that they are more stable.