In the standard quantum theory, the causal order of occurrence between events is prescribed, and must be definite. This has been maintained in all conventional scenarios of operation for quantum batteries. In this study we take a step further to allow the charging of quantum batteries in an indefinite causal order (ICO). We propose a nonunitary dynamics-based charging protocol and experimentally investigate this using a photonic quantum switch. Our results demonstrate that both the amount of energy charged and the thermal efficiency can be boosted simultaneously. Moreover, we reveal a counterintuitive effect that a relatively less powerful charger guarantees a charged battery with more energy at a higher efficiency. Through investigation of different charger configurations, we find that ICO protocol can outperform the conventional protocols and gives rise to the anomalous inverse interaction effect. Our findings highlight a fundamental difference between the novelties arising from ICO and other coherently controlled processes, providing new insights into ICO and its potential applications.
In the standard quantum theory, the causal order of occurrence between events is prescribed, and must be definite. This has been maintained in all conventional scenarios of operation for quantum batteries. In this study we take a step further to allow the charging of quantum batteries in an indefinite causal order (ICO). We propose a nonunitary dynamics-based charging protocol and experimentally investigate this using a photonic quantum switch. Our results demonstrate that both the amount of energy charged and the thermal efficiency can be boosted simultaneously. Moreover, we reveal a counterintuitive effect that a relatively less powerful charger guarantees a charged battery with more energy at a higher efficiency. Through investigation of different charger configurations, we find that ICO protocol can outperform the conventional protocols and gives rise to the anomalous inverse interaction effect. Our findings highlight a fundamental difference between the novelties arising from ICO and other coherently controlled processes, providing new insights into ICO and its potential applications.
Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal order is found to have the capability of accomplishing tasks that are not possible without it. Specifically, we show how this novel class of resource comes into play in quantum batteries by first, combining two static unitary chargers into a coherently superposed one to fully charge an empty battery even if in the presence of battery's local Hamiltonian. Then we demonstrate for a non-unitary charging protocol, the indefinite causal order version charger yields a charged battery with higher energy over its classical counterpart under any conditions. We also have a finding that runs counter to our intuition which, roughly speaking, has the implication that a relatively less powerful charger guarantees a charged battery with higher energy. Finally, to reduce the cost imposed by a measurement-based protection scheme, indefinite causal order shows its potential to fulfill this goal.
Enhancement of quantum battery performance is a popular subject in quantum thermodynamics. An interesting phenomenon is the quick charging effect [Phys. Rev. Res. 6, 023136 (2024)], which has been explored by utilizing a quantum interferometric technique known as superposition of trajectories. A similar technique used to boost quantum battery performance is indefinite causal order. Here, we propose a new charging protocol that utilizes cyclic indefinite causal order, whereby N charging sequences are superposed when utilizing N chargers. We observe charging efficiency bursts when implementing our cyclic indefinite charging protocol. The duration of these bursts increase with N. Additionally, we present a circuit model to implement our charging protocol for the two-charger scenario and perform proof-of-concept demonstrations on IonQ, Quantinuum and IBMQ quantum processors. The results validate the existence of charging efficiency bursts as shown by our theoretical analysis and numerical simulations.
In recent years, quantum battery (QB) models have emerged as crucial platforms for exploring the connections between quantum effects and energy within the framework of quantum thermodynamics. Inspired by the physical implementation of quantum switch (QS), we, in this work, present a simple QB model in which a two-level system as battery, under a series of coherent chargers, performs the indefinite causal order (ICO) charging by introducing a control qubit as QS. Within the energy-preserving collision interaction framework, we analyze the charging ICO and conventional definite causal order (DCO) dynamics, respectively, and discover the underlying connection between the final charged states of battery in ICO and DCO charging modes. That is, the ICO charged state can be understood as a split of the DCO charged state, accompanied by an offset caused by the interference component characterizing the ICO effect. That provides direct theoretical evidence that the ICO effect positively influences the ergotropy (i.e., the maximum extractable work) of QB only when quantum coherence is present in the charging process, and it is independent of the average stored energy of the QB. By combining numerical simulations, we examine that quantum coherence in our model is a strong quantum resource contributing to the ergotropy of QB, while the ICO effect plays a catalyst-like role, assisting quantum coherence in further enhancing the ergotropy of the battery. In addition, we also demonstrate that increasing the number of chargers also benefits the optimal ergotropy of QB. Finally, we reveal that, when the coherent chargers are subject to the dephasing channel, the ICO charging mode is more robust against dephasing noise than the DCO charging mode. This investigation deepens our understanding of quantum coherence and the ICO effect in the context of quantum thermodynamics.
In the classical world, physical events always happen in a fixed causal order.However, it was recently revealed that quantum mechanics allows events to occur with indefinite causal order (ICO).In this study, we use an optical quantum switch to experimentally investigate the application of ICO in thermodynamic tasks.Specifically, we simulate the working system interacting with two identical thermal reservoirs in an ICO, observing the quantum heat extraction even though they are in thermal equilibrium where heat extraction is inaccessible by traditional thermal contact.Using such a process, we simulate an ICO refrigeration cycle and investigate its properties.We also show that by passing through the ICO channel multiple times, one can extract more heat per cycle and thus obtain a higher refrigeration performance.Our results suggest that the causal nonseparability can be a powerful resource for quantum thermodynamic tasks.
Indefinite causal order (ICO), in which the order of quantum operations is placed in a coherent superposition, has been demonstrated to enhance various information-processing tasks. Here, we investigate its impact on the thermodynamic processes generated by thermalizing quantum channels. We consider a two-level system interacting with two thermal baths under a quantum SWITCH, with the channel order controlled coherently by an ancillary qubit. We derive closed-form expressions for the effective inverse temperature βf of the postselected system state for both identical and distinct bath temperatures, and identify the control-qubit parameters that maximize heating or cooling. Our analysis reveals how the diagonal and coherent components of the control-qubit state contribute separately to the temperature shift, and how their interplay enables departures from the thermal response attainable under protocols with a definite causal order within the thermodynamic setting considered here. Bath asymmetry enhances these effects, while reduced purity of the control qubit state suppresses them. These results provide a systematic framework for assessing SWITCH-based thermalization in the setting of indefinite causal order, and identify control-qubit coherence as a tunable resource.
Arbitrary energy transfer is only feasible in nondissipative charger-battery systems; in realistic processes, however, energy dissipation prevents this. In this work, we introduce a novel charging technique in which the coherent charger-battery interaction is replaced by a dissipative interaction via an engineered reservoir. We demonstrate that exploiting the collective effects of the engineered reservoir allows for additional optimization, giving rise to an optimal redistribution of energy. This not only significantly enhances the efficiency of the charging process but also remarkably enables the quantum battery to accumulate unlimited energy---limited only by the natural energy scale of the device. This phenomenon cannot occur in conventional charger-battery schemes. The article unveils the intricacies of built-in detuning within the context of a shared environment, offering a deeper understanding of the charging mechanisms involved. These findings apply naturally to quantum circuit battery architectures, suggesting the feasibility of efficient energy storage in these systems. The superoptimal charging mechanism offers a practical avenue for boosting the capacity of the battery through charger-battery configurations.