Abstract We explore the energy content of superpositions of single-excitation current states. Specifically, we focus on the maximum energy that can be extracted from them through local unitary transformations. The figure of merit we employ is the local ergotropy. We consider an XY spin-chain model and perform a complete analysis in the whole range of the system parameters. This way, we prove that superpositions of two current states in spatially closed spin networks are characterized by specific peaks in extractable energy, generally overcoming the ergotropy of each of the two separate current states characterized by a single winding number. The many-body state dynamics entails to ergotropy evolving in a controlled fashion. The implementation we suggest is based on a Rydberg-atom platform. Optimal transformations able to extract locally the maximum possible amount of energy are sorted out.
Abstract We explore the energy content of superpositions of single-excitation current states. Specifically, we focus on the maximum energy that can be extracted from them through local unitary transformations. The figure of merit we employ is the local ergotropy. We consider an XY spin-chain model and perform a complete analysis in the whole range of the system parameters. This way, we prove that superpositions of two current states in spatially closed spin networks are characterized by specific peaks in extractable energy, generally overcoming the ergotropy of each of the two separate current states characterized by a single winding number. The many-body state dynamics entails to ergotropy evolving in a controlled fashion. The implementation we suggest is based on a Rydberg-atom platform. Optimal transformations able to extract locally the maximum possible amount of energy are sorted out.
Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting subsystems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Second, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide recipes to obtain numerical upper bounds via semidefinite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.
We investigate the problem of finding the local analog of the ergotropy, which is the maximum work that can be extracted from a system if we can only apply local unitary transformation acting on a given subsystem. In particular, we provide a closed formula for the local ergotropy in the special case in which the local system has only two levels, and we give analytic lower bounds and semidefinite programming upper bounds for the general case. As nontrivial examples of application, we compute the local ergotropy for an atom in an electromagnetic cavity with Jaynes-Cummings coupling and the local ergotropy for a spin site in an XXZ Heisenberg chain, showing that the amount of work that can be extracted with a unitary operation on the coupled system can be greater than the work obtainable by quenching off the coupling with the environment before the unitary transformation.
Abstract In this mini-review, we discuss work extraction under restricted control, where only the system is accessible while other degrees of freedom remain uncontrolled. In this setting, local ergotropy is the maximum work extractable by cyclic unitaries on the system, and it can differ strongly from “switch-off” extraction after quenching the system-environment coupling. We review two settings where correlations and many-body effects shape local work. First, in a two-qubit quantum Rabi model, dissipation induces a Berezinskii–Kosterlitz–Thouless quantum phase transition. A gate-based charge-store-extract protocol uses a decoherence-free state to stabilize storage and makes strong system-bath coupling a resource, yielding local ergotropy above switch-off extraction and making its dynamics transition-dependent, also in relative fluctuations. Second, in a disordered XXZ chain where the first two spins form a battery coupled to an interacting spin bath, local ergotropy shows distinct long-time behavior across Anderson, many-body localized, and ergodic regimes, linking extractable work to localization transitions. Overall, the examples reviewed here show that local ergotropic observables quantify quantum-battery performance under local control and probe collective phenomena.
A subsystem of an entangled ground state (GS) is in a mixed state. Thus, if we isolate this subsystem from its surroundings, we may be able to extract work applying unitary transformations, up to a maximal amount which is called ergotropy. Once this work has been extracted, the subsystem will still contain some bound energy above its local GS, which can provide valuable information about the entanglement structure. We show that the bound energy for half a free fermionic chain decays as the square of the entanglement entropy divided by the chain length, thus approaching zero for large system sizes, and we conjecture that this relation holds for all one-dimensional critical states.
The energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries (QB). In this context, one of the main figures of merit is the ergotropy, which measures the maximal amount of energy (as work) that can be extracted from the quantum source by means of unitary operations. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. This assumption, in general, fails in practice since the operations that can be done are limited and depend on the quantum hardware (experimental platform) one has available. In this work, we propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm. In this approach, we explicitly take into account a limited set of unitaries by using the hardware efficient ansatz (HEA) class of parameterized quantum circuits. As a QB we use an one-dimensional spin chain described by a family of paradigmatic first neighbor hamiltonians such as the XXX, XXZ, XYZ, XX, XY, and transverse Ising models. By building our parameterized quantum circuits assuming that different types of connectivity may be available depending on the quantum hardware, we numerically compare the efficiency of work extraction for each model. Our results show that the best efficiency is generally obtained with quantum circuits that have connectivity between first neighbor spins.
Quantum many-body scars break ergodicity and evade thermalization, resulting in sub-volume law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy in the thermodynamic limit. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occupy, can be efficiently exploited for storing extractable energy, and "scarring" a many-body system as a promising route for engineering quantum many-body battery.