The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat- and workflows of the machine, the average, the variance of the battery's energy, as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state, its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such, while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage, when the machine fails to extract heat from the cold bath, the influence of the measurements becomes less pronounced, leading to rather similar asymptotic states for the two measurement scenarios.
The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat- and workflows of the machine, the average, the variance of the battery's energy, as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state, its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such, while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage, when the machine fails to extract heat from the cold bath, the influence of the measurements becomes less pronounced, leading to rather similar asymptotic states for the two measurement scenarios.
Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., V^{†}=U (or V=U). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ν_{2}>ν_{1} is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.
In this paper, we consider fluctuations in a three-stroke cycle based on quantum measurement. In the first stroke, the engine is fueled by a nonselective quantum measurement; in the second stroke, an appropriate unitary operation is applied to extract work; and finally, the working medium is thermalized to complete the cycle. This protocol is analogous to charging, then discharging, and finally thermalizing a quantum battery. Using the Kirkwood-Dirac quasiprobability, we derive equations that provide insights into the fluctuations of heat and work, and thus into the charging and discharging processes. We then propose a quantum circuit to measure the cumulants of work and heat using a qubit ancilla. Afterward, we derive important upper and lower bounds on fluctuations in heat; this is thanks to the way we decompose heat fluctuations and the Kadison-Schwarz inequality. We also show, for the first time, that the imaginary part of the second cumulant of work equals the linear response of an average work (to be defined in the main text) or the quantum cross entropy. We further introduce an operator whose average defines the battery capacity and whose variance quantifies the corresponding fluctuations of the battery capacity. Our analytical results are illustrated and discussed through representative examples. We believe that our study will, on the one hand, be useful for understanding fluctuations in energy extracted from and injected into quantum batteries based on quantum measurements and, on the other hand, contribute to the foundations of quantum thermodynamics. More generally, our results can be applied beyond the three-stroke cycle considered here, especially to quantum batteries subject to environmental noise and decoherence.
Recently, we have considered a single-qubit quantum Otto cycle based on arbitrary (non-unitary) unital channels as a heat source. We showed similarly to some works in literature that the ratio of the fluctuations of work (W) and heat absorbed (QM) is lower-and-upper bounded. In this paper, we drive this line of research further and consider the fluctuations of the stochastic heat exchanged (denoted by QC′) with the cold bath. In general, there is another stochastic quantity, which we denote by QC, that gives the same average as QC′− but not higher cumulants. While QC′ is defined through the two-point measurement scheme, i.e., by measuring the energy of the working medium in all four strokes, QC follows from imposing the first of thermodynamics at the stochastic level. Our work has two important results: (i) first, we prove that the measurement of the working medium during three strokes is sufficient to construct the distribution of QC′ (ii) and that the cumulants of the stochastic entropy production denoted by Σ can be inferred from the cumulants of QC.
Abstract We introduce a cyclic quantum battery QB model, based on an interacting bipartite system, weakly coupled to a thermal bath. The working cycle of the battery consists of four strokes: system thermalization, disconnection of subsystems, ergotropy extraction, and reconnection. The thermal bath acts as a charger in the thermalization stroke, while ergotropy extraction is possible because the ensuing thermal state is no longer passive after the disconnection stroke. Focusing on the case of two interacting qubits, we show that phase coherence, in the presence of non-trivial correlations between the qubits, can be exploited to reach working regimes with efficiency higher than 50% while providing finite ergotropy. Our protocol is illustrated through a simple and feasible circuit model of a cyclic superconducting QB. Furthermore, we simulate the considered cycle on superconducting IBM quantum machines. The good agreement between the theoretical and simulated results strongly suggests that our scheme for cyclic QBs can be successfully realized in superconducting quantum hardware.
We investigate the energetic and thermodynamic performance of an interacting two-qubit system serving as both a quantum battery and a quantum Otto heat engine. The working medium is described by an anisotropic Heisenberg Hamiltonian supplemented by a dipolar interaction, a symmetric spin--orbit interaction, and an external magnetic field. Within a unified microscopic framework, we first analyze a coherent unitary charging protocol and characterize the resulting energy-storage performance through the ergotropy, anti-ergotropy, charging power, storage capacity, and ℓ1-norm of quantum coherence. We investigate the effects of the dipolar interaction, temperature, and magnetic field on these quantities. We then employ the same working medium in a quantum Otto cycle and study the absorbed and released heat, net work, and thermodynamic efficiency as functions of the magnetic-field modulation, dipolar interaction, and temperature bias. A direct comparison between the two protocols reveals a pronounced contrast in their response to the dipolar interaction. In the investigated parameter regime, increasing the dipolar interaction substantially enhances the maximum ergotropy and storage capacity of the quantum battery, whereas the maximum work extracted per Otto cycle decreases. The Otto efficiency exhibits a nonmonotonic dependence on the dipolar interaction while remaining below the Carnot bound. These results demonstrate that an enhancement of quantum energy-storage capability does not necessarily imply an enhancement of heat-to-work conversion. Our findings highlight the complementary nature of quantum batteries and quantum heat engines and show how microscopic spin interactions can
be used to control different forms of quantum energy conversion within
the same physical platform.
Abstract Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.