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.
Abstract The reduced state of a small system strongly coupled to a charger in thermal equilibrium may be athermal and used as a small battery once disconnected. By harnessing the battery-charger correlations, the battery’s extractable energy can increase above the ergotropy. We introduce a protocol that uses a quantum system as a memory that measures the charger and leaves the battery intact in its charged state. Using the information gained from the measurement, the daemonic ergotropy of the battery is extracted. Then the battery is reconnected to the charger, thermalizing and charging it. However, the memory should return to its initial standard state to close the thermodynamic cycle. Thus, on the one hand, the work cost of the cycle is the sum of the disconnecting and reconnecting battery-charger work plus the measurement and erasure work. On the other hand, the extracted energy is the daemonic ergotropy of the battery plus the ergotropy of the memory. The ratio of these quantities defines the efficiency of the cycle. The protocol is exemplified by a modified transverse spin 1/2 Ising chain, one spin functioning as the battery and the others as the charger. The memory is another auxiliary spin 1/2. We found pairs of measurement schemes from which we extract the same daemonic ergotropy from the battery, they dissipate the same amount of energy, and one leaves the memory in an active state, the other in a passive state. We study the memory’s ergotropy and the daemonic ergotropy of the battery. We find that with measurements, the efficiency can surpass that of the unmeasured protocol, given conditions on temperature, coupling, and choice of the measurement operators.
We investigate the performance of a novel model based on a one-dimensional (1D) spin-
1/2 Heisenberg
XY−Γ(γ) quantum chain, also known as 1D Kitaev chain, as a working medium for a quantum battery (QB) in both closed and open system scenarios. We analyze the closed QB scenario by analytically evaluating ergotropy across different spin-spin couplings, anisotropies in spin interactions, Zeeman field strengths, charging field intensities,
Γ interactions, and temperature. Our results indicate that the ergotropy is highly dependent on spin-spin coupling and anisotropy. Under variable parameters, an increase in the spin-spin coupling strength displays quenches and exhibits non-equilibrium trends in ergotropy. After a quench, ergotropy may experience a sharp increase or drop, suggesting optimal operational conditions for QB performance. In the open QB scenario, we examine spin chains of sizes
2≤N≤8 under the influence of dephasing, focusing on the evolution of ergotropy. We study two charging schemes: parallel charging, where spins are non-interacting, and collective charging, involving spin-spin coupling. In the former, increased Zeeman field strength enhances both the peak ergotropy and charging rate, although without any quantum advantage or super-extensive scaling. In the latter, increasing spin-spin coupling might not achieve super-extensive scaling without introducing anisotropy in the spin-spin interaction. Our results suggest that optimal QB performance and a quantum advantage in scaling can be achieved by leveraging anisotropic spin-spin couplings and non-zero
Γ interactions, allowing for faster charging and higher ergotropy under super-extensive scaling conditions up to
α=1.24 for the given size of the spin chain.