Fast protocols for charging a three-spin-chain quantum battery

We derive fast protocols for charging a three-qubit Ising spin-chain quantum battery, using amplitude and phase control of the global transverse field. For weak coupling between the qubits in the chain, where the initial ground state of the system is the spin-down state, we find that the optimal strategy is to fix the control amplitude at its maximum value while properly varying the phase with time. For the strong coupling case, where the initial ground state is the one-excitation Dicke state Formula: see text, we apply two related charging protocols. In the first approach we use a pulse-sequence derived numerically in the recent work (Stojanović and Nauth in Phys Rev A 108:012608, 2023. https://doi.org/10.1103/PhysRevA.108.012608), composed of delta Bang pulses and intervals where the control is switched off. We call this method fast charging via subspace decomposition, since it involves identifying and manipulating effective two-level subsystems. Here we find analytically the characteristics of the pulses composing the sequence, which were calculated numerically in the above reference. In the second approach, we apply a similar pulse-sequence with delta Bang pulses and Off intervals, but with a carrier frequency which brings on resonance the initial Formula: see text state and the target spin-up state of maximum energy. We call this method charging via resonant excitation. We calculate numerically the characteristics of the pulses in the sequence and find a shorter charging time compared to the non-resonant method inspired by the above reference. We also use numerical optimal control to solve the problem of full charging the quantum battery but for finite values of the control amplitude and find that, for some relatively large values of this bound, the optimal solution has similar structure with the sequence incorporating delta Bang pulses but longer duration, as expected. Although this study focuses on a three-spin chain, the proposed methodology can be also extended to larger spin-chains. The lowest and highest energy eigenstates need to be identified first, serving as the initial and target states. Then, optimal control can be exploited to find the amplitude and phase modulation of a field resonant to this transition, which maximize the stored energy in the battery for a given duration.