NMR Investigations and Feedback Estimation of Ergotropy : Applications in Quantum Battery and Entanglement Certification

Abstract

Quantum-level energy storage and usage is gaining significant interest among scientific communities with a newly introduced concept in quantum thermodynamics, namely ergotropy. Ergotropy quantifies the maximum amount of work that can be extracted unitarily from an energy-storing quantum device. Ergotropy is a core concept used in quantum batteries, and since it can help certify entanglement, it connects quantum thermodynamics with quantum information. With long coherence times, strong spin-spin interactions, and precise and intricate control over quantum dynamics, the nuclear spin qubits offer an excellent testbed for studying such quantum concepts. By manipulating qubit energy across different parts of star-topology spin systems, we experimentally realize quantum batteries, monitor their ergotropy, establish the quantum speedup, achieve asymptotic charging, and demonstrate a charger-battery-load circuit. We show that measuring specific variants of ergotropy can help certify bipartite entanglement in multiqubit systems without explicitly knowing their quantum states. In particular, the criteria depend on the difference in optimal global and local works extractable from an isolated quantum system under global and local interactions, respectively. As a proof of principle, we demonstrate entanglement certification on nuclear spin registers with up to 10 qubits. Finally, we propose and experimentally demonstrate a feedback-based algorithm (FQErgo) for estimating ergotropy. This method also transforms an arbitrary initial state to its passive state, which allows no further unitary work extraction, providing a practical way for unitary energy extraction and for preparing passive states. By numerically analyzing FQErgo on random initial states, we confirm the successful preparation of passive states and estimation of ergotropy, evenin the presence of drive errors. Finally, we implement FQErgo on two- and three-qubit NMR registers, prepare their passive states, and accurately estimate their ergotropy.