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arXiv:2210.01355 · Physica Scripta

Quench dynamics in the Jaynes-Cummings-Hubbard and Dicke models

Andrew R. Hogan, A. Martin

Published Feb 29, 2024• 6 citations
arXivHTMLPDF

Abstract

Abstract Both the Jaynes-Cummings-Hubbard (JCH) and Dicke models can be thought of as idealised models of a quantum battery. In this paper we numerically investigate the charging properties of both of these models. The two models differ in how the two-level systems are contained in cavities. In the Dicke model, the N two-level systems are contained in a single cavity, while in the JCH model the two-level systems each have their own cavity and are able to pass photons between them. In each of these models we consider a scenario where the two-level systems start in the ground state and the coupling parameter between the photon and the two-level systems is quenched. Each of these models display a maximum charging power that scales with the size of the battery N and no super charging was found. Charging power also scales with the square root of the average number of photons per two-level system m for both models. Finally, in the JCH model, the power was found to charge inversely with the photon-cavity coupling κ.

DOI
10.1088/1402-4896/ad2efd

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Abstract Both the Jaynes-Cummings-Hubbard (JCH) and Dicke models can be thought of as idealised models of a quantum battery. In this paper we numerically investigate the charging properties of both of these models. The two models differ in how the two-level systems are contained in cavities. In the Dicke model, the N two-level systems are contained in a single cavity, while in the JCH model the two-level systems each have their own cavity and are able to pass photons between them. In each of these models we consider a scenario where the two-level systems start in the ground state and the coupling parameter between the photon and the two-level systems is quenched. Each of these models display a maximum charging power that scales with the size of the battery N and no super charging was found. Charging power also scales with the square root of the average number of photons per two-level system m for both models. Finally, in the JCH model, the power was found to charge inversely with the photon-cavity coupling κ.
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 NNN is inspected. While the energy and fluctuations scale linearly with NNN, 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.
Abstract We present a quantum battery model comprising two lossless cavities that interact through a controlled photon–hopping mechanism, each housing an isolated two-level atom. This study explores the possibility of influencing the interaction between cavities within the traditional two single–cavity working modes, thereby paving the way for enhanced charging performance. By solving the generalized double Jaynes–Cummings model with cavity–cavity interactions, we demonstrate the positive impact of such interactions on battery charging, enabling the quantum battery to outperform the single–cavity case in terms of charging time and average charging power. Additionally, we investigate the influence of different cavity–cavity interaction strengths on charging efficiency and attempt to explain the underlying mechanisms by analyzing the entanglement within the system.
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 NNN of two-level systems in the battery, and also the NNN dependence for the charging time ${t}_{c}\ensuremath{\sim}{N}^{\ensuremath{-}1/2}$. The NNN exponent 3/23/23/2 of the charging power is in quantitative correspondence with the recent result 1.5411.5411.541 obtained numerically by other authors. The physics of Dicke quantum battery charging is considered in detail.
The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two-level system which can be tuned in resonance with the cavity. Here, we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where intercavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread over many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.
We investigate the performances of multiphoton anisotropic Dicke quantum battery (QB), which couples a finite number NNN of identical and independent two-level systems (TLSs) to a unique cavity mode. Each transition of TLS is accompanied by the absorption or emission of lll photons from the cavity mode. In this model, the coupling constants of rotating and counterrotating wave terms are independent. Therefore, we utilize this interesting property to investigate the role of counterrotating wave terms and find that the higher the proportion of counterrotating wave terms, the higher the average power. Moreover, it is shown that the charging process is progressively faster by increasing the coupling strength from the weak to the ultrastrong and deep strong coupling regime. In the deep strong regime, the anti-Tavis-Cummings (ATC) coupling can almost achieve the optimal energy storage in a short time, which can be used to realize the feasibility of QB. Furthermore, we also analyze the effects of multiphoton interaction and single-multiphoton mixing process on the battery performances.
In this paper, we consider a quantum battery, namely a miniaturized device able to store energy and release it on-demand. In the so-called Dicke configuration, it is made of [Formula: see text] two-level systems embedded into a cavity which plays the role of charger. In this context, we compare two different situations, namely: the resonant regime, where the energy of the two-level systems is the same as the one of the photons trapped in the cavity, and the off-resonant regime, where the photons are way more energetic. We observe that, while the energy stored per two-level system is comparable in the two cases, the average charging power, despite showing the same asymptotic superextensive scaling, is strongly suppressed in the latter. This analysis will help to orient future experimental implementations of these devices.