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Quantum batteries (QBs) exploit principles of quantum mechanics to accelerate the charging process and aim to achieve optimal energy storage. However, analytical results for investigating these problems remain lacking due to the challenges associated with nonequilibrium dynamics. In this work, we analytically investigate a central-spin QB model in which $N_b$ spin-1/2 battery cells interact with $N_c$ spin-1/2 charger units, using $m$ initially excited charger units as a resource. By employing the invariant subspace method and the shifted Holstein-Primakoff (HP) transformation, we identify four scenarios in which optimal energy storage can be achieved: 1) $N_b\!\ll\!m\!\ll\!N_c$; 2) $m\!\ll\!N_b\!\ll\!N_c$; 3) $m\!\ll\!N_c\!\ll\!N_b$; and 4) $N_b\!\ll\!m\!=\!kN_c$ [$k\!\in\!(0,1)$]. In these cases, optimal storage is ensured by the SU(2) symmetry emerging from the charging dynamics. The first three cases map the central-spin QB to different Tavis-Cummings (TC) QBs, while the fourth corresponds to the non-TC limit. We analytically determine the charging time and demonstrate that in the fully charging cases (1) and (4), the collective charging exhibits an $N_b$-fold enhancement in speedup compared to the parallel charging scheme. Additionally, we numerically observe a unified charging behavior when $m\!=\!N_c$, showing that asymptotically optimal energy storage is possible when $N_b\!=\!m\!=\!N_c$. In this case, we find a collective charging enhancement scaling as $N_b^{0.8264}$. Our results highlight the crucial role of dynamically emergent SU(2) symmetry in providing an analytical understanding of non-equilibrium charging dynamics in QBs., Comment: 8 pages, 5 figures

The Tavis-Cummings (TC) model, which serves as a natural physical realization of a quantum battery, comprises $N_b$ atoms as battery cells that collectively interact with a shared photon field, functioning as the charger, initially containing $n_0$ photons. In this study, we introduce the invariant subspace method to effectively represent the quantum dynamics of the TC battery. Our findings indicate that in the limiting case of $n_0\!\gg\! N_b$ or $N_b\!\gg\! n_0$, a distinct SU(2) symmetry emerges in the dynamics, thereby ensuring the realization of optimal energy storage. We also establish a negative relationship between the battery-charger entanglement and the energy storage capacity. As a result, we demonstrate that the asymptotically optimal energy storage can be achieved in the scenario where $N_b\!=\!n_0\!\gg\! 1$. Our approach not only enhances our comprehension of the algebraic structure inherent in the TC model but also contributes to the broader theoretical framework of quantum batteries. Furthermore, it provides crucial insights into the relation between energy transfer and quantum correlations., Comment: 8 pages, 4 figures

We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining maximally incoherent work. Examples ranging from the central-spin battery and the Tavis-Cummings battery to the spin-chain battery are given to illustrate these results., Comment: 6+1 pages, 2 figures

We consider a central-spin battery where $N_b$ central spins serve as battery cells and $N_c$ bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time $\propto 1/N_c$, large extractable work, and $\sqrt{N_c}$-improvement of charging power compared with the battery in the Tavis-Cummings limit. The above-mentioned results have also been numerically verified in multi-cell batteries. Our results pave the way to improve extractable work storage in the central-spin battery and highlight a competitive relation between the extractable work and the battery-charger entanglement., Comment: 8 pages, 4 figures

We study an extended central spin model with an isotropic nearest-neighbour spin-exchange interaction among the bath spins. The system is controllable by external magnetic fields applied on the central spin and the bath, respectively. We construct a basis set of the Hilbert space and express the Hamiltonian of the extended model into a series of $2\times2$ block matrices to obtain the exact solution of the model successfully. Therefrom, the coherence and the spin polarization of the central spin are investigated. We find that if the couplings among the bath spins are antiferromagnetic, the central spin has good coherence and polarization at low temperatures. Moreover, the decoherence is greatly suppressed at the critical point where the strengthes of the central and the bath magnetic field take the same value. A dephasing phenomenon is identified when the initial state of the central spin is unpolarized.

Recent experiments have tuned the monolayer 1T'-WTe2 to be superconducting by electrostatic gating. Here, we theoretically study the phonon-mediated superconductivity in monolayer 1T'-WTe2 via charge doping. We reveal that the emergence of soft-mode phonons with specific momentum is crucial to give rise to the superconductivity in electron-doping regime, whereas no such soft-mode phonons and no superconductivity emerge in hole-doping regime. We also find a superconducting dome, which can be attributed to the change of Fermi surface nesting condition as electron doping. By taking into account the experimentally established strong anisotropy of temperature-dependent upper critical field H_{c2} between the in-plane and out-of-plane directions, we show that the superconducting state probably has the unconventional equal-spin-triplet pairing in A_{u} channel of C_{2h} point group. Our studies provide a promising understanding to the doping dependent superconductivity and strong anisotropy of H_{c2} in monolayer 1T'-WTe2., Comment: 14 pages, 4 figures

Maintaining coherence of a qubit is of vital importance for realizing a large-scale quantum computer in practice. In this work, we study the central spin decoherence problem in the $XXX$ central spin model (CSM) and focus on the quantum states with different initial entanglement, namely intra-bath entanglement or system-bath entanglement. We analytically obtain their evolutions of fidelity, entanglement, and quantum coherence. When the initial bath spins constitute an $N$-particle entangled state (the Greenberger-Horne-Zeilinger-bath or the $W$-bath), the leading amplitudes of their fidelity evolutions both scale as $\mathcal O(1/N)$, which is the same as the case of a fully polarized bath. However, when the central spin is maximally entangled with one of the bath spins, the amplitude scaling of its fidelity evolution declines from $\mathcal O(1/N)$ to $\mathcal O(1/N^2)$. That implies appropriate initial system-bath entanglement is contributive to suppress central spin decoherence. In addition, with the help of system-bath entanglement, we realize quantum coherence-enhanced dynamics for the central spin where the consumption of bath entanglement is shown to play a central role., Comment: 17 pages, 1 figures

Monolayer WTe2 attracts rapidly growing interests for its large-gap quantum spin Hall effect,which enables promising apllications in flexible logic devices. Due to one-dimensional W-W chains,1T'-WTe2 exhibits unique anisotropic structure and promising properties, which can be modified by simply applying strains. Based on the first-principles simulations, we show that phonon branch undergoes soft down to negative frequency at special q points under different critical strains, i.e., epsilon_a = 11.55 percent along a-axis (with W-W chains) direction, epsilon_b = 7.0 percent along b-axis direction and epsilon_ab = 8.44 percent along biaxial direction. Before each critical strain, the Raman-shift of A1_g, A3_g, and A4_g modes, corresponding to the main peaks in Raman spectra of 1T'-WTe2 , shows anisotropic response to uniaxial strain but most sensitive to biaxial strain. Interestingly, we find that the frequency shift of A3_g mode show parabolic characters of strained 1T'-WTe2, then we split it into two parts and it shows a Raman-shift transition at about 5 percent strains. While for the A1_g and A4_g modes,the frequencies change linearly. Through careful structure and vibration analysis, we try to explain these Raman irregularity in strained 1T'-WTe2., Comment: 13 pages, 5 figures

We identify that quantum coherence is a valuable resource in the quantum heat engine, which is designed in a quantum thermodynamic cycle assisted by a quantum Maxwell's demon. This demon is in a superposed state. The quantum work and heat are redefined as the sum of coherent and incoherent parts in the energy representation. The total quantum work and the corresponding efficiency of the heat engine can be enhanced due to the coherence consumption of the demon. In addition, we discuss an universal information heat engine driven by quantum coherence. The extractable work of this heat engine is limited by the quantum coherence, even if it has no classical thermodynamic cost. This resource-driven viewpoint provides a direct and effective way to clarify the thermodynamic processes where the coherent superposition of states cannot be ignored., Comment: 18 pages; 4 figures