We theoretically investigate the enhancement of the charging power in a Dicke quantum battery which consists of an array of N two-level systems (TLS)coupled to a single mode of cavity photons. In the limit of small N , we analytically solve the time evolution for the full charging process. The eigenvectors of the driving Hamiltonian are found to be pseudo-Hermite polynomials and the evolution is thus interpreted as harmonic oscillator like behaviour. Then we demonstrate the average charging power using a collective protocol is N times larger than that of the parallel protocol when transferring the same amount of energy. Unlike previous studies, we point out that such quantum advantage does not originate from entanglement but is due to the coherent cooperative interactions among the TLSs. Our results provide intuitive quantitative insight into the dynamic charging process of a Dicke battery and can be observed under realistic experimental conditions.
We theoretically investigate the enhancement of the charging power in a Dicke quantum battery which consists of an array of N two-level systems (TLS)coupled to a single mode of cavity photons. In the limit of small N , we analytically solve the time evolution for the full charging process. The eigenvectors of the driving Hamiltonian are found to be pseudo-Hermite polynomials and the evolution is thus interpreted as harmonic oscillator like behaviour. Then we demonstrate the average charging power using a collective protocol is N times larger than that of the parallel protocol when transferring the same amount of energy. Unlike previous studies, we point out that such quantum advantage does not originate from entanglement but is due to the coherent cooperative interactions among the TLSs. Our results provide intuitive quantitative insight into the dynamic charging process of a Dicke battery and can be observed under realistic experimental conditions.
Quantum batteries, which are quantum systems to be used for the storage and transformation of energy, have been recently attracting research interest. A promising candidate for their investigation is the Dicke model, which describes an ensemble of two-level systems interacting with a single-mode electromagnetic wave in a resonator cavity. In order to charge the battery, a coupling between the ensemble of two-level systems and resonator cavity should be turned off at a certain moment of time. This moment of time is chosen in such a way that the energy gets fully stored in an ensemble of two-level systems. In our previous works we have investigated a bound-luminosity superradiant state of the extended Dicke model and found analytical expressions for the dynamics of coherent energy transfer between the superradiant condensate and the ensemble of two-level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power $P\ensuremath{\sim}{N}^{3/2}$ as a function of the number N of two-level systems in the battery, and also the N dependence for the charging time ${t}_{c}\ensuremath{\sim}{N}^{\ensuremath{-}1/2}$. The N exponent 3/2 of the charging power is in quantitative correspondence with the recent result 1.541 obtained numerically by other authors. The physics of Dicke quantum battery charging is considered in detail.
We consider a collection of two level systems, such as qubits, embedded into a microwave cavity as a promising candidate for the realization of high power quantum batteries. In this perspective, the possibility to design devices where the conventional single-photon coupling is suppressed and the dominant interaction is mediated by two-photon processes is investigated, opening the way to an even further enhancement of the charging performance. By solving a Dicke model with both single- and two-photon coupling we determine the range of parameters where the latter unconventional interaction dominates the dynamics of the system leading to better performances both in the charging times and average charging power of the QB compared to the single-photon case. In addition, the scaling of the maximum stored energy, fluctuations and charging power with the finite number of qubits N is inspected. While the energy and fluctuations scale linearly with N, the quadratic growth of the average power leads to a relevant improvement of the charging performance of quantum batteries based on this scheme with respect to the purely single-photon coupling case. Moreover, it is shown that the charging process is progressively faster by increasing the coupling from the weak to the ultra-strong regime.
Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like sqrt[N] for N≫1.
In the Letter [Physical Review Letters 120, 117702 (2018)], Ferraro \emph{et al.} claimed a quantum advantage in the Dicke quantum battery (QB), whereby N two-level systems (TLS) are coupled to a common photonic mode of a cavity. They argued that compared with the so-called Rabi QB, the Dicke QB exhibits a N quantum enhancement in the charging power because of the entanglement created by the common photonic mode. In this Comment, however, we demonstrate that the apparent N enhancement actually comes from the stronger cavity electric (or magnetic) field under the setup discussed in [Physical Review Letters 120, 117702 (2018)]. This is a trivial classical effect, and there is no true "quantum advantage" in the charging power of the Dicke QB. While somewhat similar questions regarding the origin of the claimed "quantum advantage" have been raised before, here we would like to make it clear that the N enhancement in [Physical Review Letters 120, 117702 (2018)] is purely a classical effect, not attributable to quantum entanglement or collective phenomena. Therefore, we believe that using the term "quantum battery" in this context may be inappropriate and misleading.
In this dissertation, we investigate the charging and discharging dynamics of a quantum battery composed of a collectively driven ensemble of N identical two level systems coupled to a structured electromagnetic environment. The system is described using collective angular momentum operators in the Dicke basis, which provides a compact and physically transparent framework for analyzing collective light-matter interactions. Rather than treating dissipation as an unwanted source of loss, we explicitly use it as a mechanism for energy storage and work extraction. Starting from a coherently driven ensemble coupled to common reservoirs, we derive a master equation in Lindblad form under the Born-Markov and secular approximations. In the dressed-state basis, spontaneous emission induces irreversible transitions that can increase the energy stored in the bare basis. We obtain analytic expressions for the steady state, including the stored energy and the ergotropy, and identify parameter regimes where substantial collective coherence is generated. A central result of this work is the demonstration that, in the extensive regime where the total energy scales linearly with N and relative fluctuations vanish, the charging power scales as N2. This quadratic enhancement scaling exceeds the N3/2 limit previously established for purely Hamiltonian charging protocols of noninteracting Dicke batteries in the same regime. We show that this enhancement is consistent with quantum speed limits for open-system dynamics and originates from collectively enhanced dissipative processes analogous to superradiance. We further analyze the extraction process and show that the charged steady state stores not only energy but a macroscopic collective dipole moment. This coherence enables rapid energy release through either collective spontaneous emission or stimulated emission driven by an external coherent field. In the appropriate large N extensive regime, the stored energy can become fully extractable in principle, and the discharging power also exhibits N2 scaling. These results establish that dissipative protocols can provide a genuine collective advantage over Hamiltonian schemes in the extensive regime, while also highlighting the interplay between enhanced collective power and the conditions required to achieve high extractable energy.
We demonstrate a quadratic enhancement of power in a battery consisting of N two-level systems or spins interacting with two photonic cavity modes, where one of the modes is in the dispersive regime. In contrast to Dicke batteries, the power enhancement arises from a N2 scaling of both quantum correlations and speed of evolution, thus highlighting genuine quantum advantage. Moreover, this hybrid setup is experimentally realizable and ensures that power enhancement is not achieved at significant cost to energy efficiency, while allowing for greater tunability and stable operation in the presence of noise.