We analyze work extraction from a qubit into a waveguide (WG) acting as a battery, where work is the coherent component of the energy radiated by the qubit. The process is stimulated by a wave packet whose mean photon number (the battery's charge) can be adjusted. We show that the extracted work is bounded by the qubit's ergotropy, and that the bound is saturated for a large enough battery's charge. If this charge is small, work can still be extracted. Its amount is controlled by the quantum coherence initially injected in the qubit's state, that appears as a key parameter when energetic resources are limited. This new and autonomous scenario for the study of quantum batteries can be implemented with state-of-the-art artificial qubits coupled to WGs.

The nearest-neighbor superexchange-mediated mechanism for d x 2 −y 2 superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion U = 9t and nearest-neighbor repulsion V = 0, 2t, 4t. In the underdoped regime, V increases the CDMFT superconducting transition temperature T d c even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime V decreases T d c . We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though V has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through J = 4t 2 /(U − V ). Retardation is thus crucial to understand pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large V and on the persistence of d-wave superconductivity over extended-s or s + d-wave.