Wireless energy transfer in non-Hermitian quantum battery

TL;DR

This work addresses wireless energy transfer from non-Hermitian quantum batteries (QBs) by exploiting PT-symmetric schemes. It analyzes two regimes—linear gain with $g=\gamma$ and nonlinear saturable gain—via coupled-mode models mapped from two magnetically coupled resonators with gain and loss, deriving analytic transfer-energy $E$ and storage-energy $E_A$ expressions across parameter regions. Key findings include real eigenfrequencies and Rabi-like oscillations in the unbroken region, exponential/hyperbolic growth in the broken region, and, under nonlinear gain, steady-state energy due to saturable feedback; robustness to separation distance and ultrafast responses to sudden movements are demonstrated. The results suggest practical pathways for wireless energy transfer in quantum batteries with potential applications ranging from wireless charging to medical devices and beyond.

Abstract

The extraction of energy is one of fundamental challenges in realizing quantum batteries (QBs). Here, we propose two wireless transfer schemes with parity-time symmetries to efficiently extract the energy stored in non-Hermitian QBs to consumption centers. For linear cases, the transfer energy oscillates periodically in the unbroken symmetry region and grows hyperbolically in the broken region. For nonlinear cases, the transfer energy eventually reach and remain steady-state values arising from the feedback mechanism of the nonlinear saturable gain. Furthermore, we show the significant robustness and the ultrafast response of the wireless transfer schemes to sudden movements around one metre. Our work overcomes energy bottlenecks for wireless transfer schemes in QBs and may provide inspirations for practical applications of QBs.

Figures (8)

• Figure 1: (a) The schematic diagram of the non-Hermitian QB with wireless transfer scheme, in which two resonators acts as the battery and the consumption-hub (CH). (b) The classical simulator consisting of two magnetically coupled LRC circuits is used to verify $\mathcal{PT}$ symmetries in non-Hermitian QBs. The effective negative resistor is provided by a voltage-doubling buffer $(\times2)$. (c) The nonlinear gain as a function of the field amplitude in left resonator, where the intrinsic loss rate and gain rate are $\gamma_{1}=0.05\omega_{0},~g_{1}=3\omega_{0}$. (d) The dependence of the coupling strength on the separation distance between two coaxially aligned coils Assawaworrarit2017. The resonant frequency is taken as $\omega_{0}=1$.
• Figure 2: The non-Hermitian QB with linear gain. (a), (b) The real and imaginary parts of the eigenfrequencies $\omega$ in dependence on the loss rate $\gamma$. The parameter space around the EP can be divided into unbroken and broken $\mathcal{PT}$-symmetry regions depending on whether the eigenfrequency is purely real. (c), (d) The time evolution of the energy $E$ and the power $P$ for different values of the loss rate $\gamma$. Because of the nonorthogonality of the eigenvectors, the transfer dynamics shows a pseudo-closed oscillation in the unbroken region and grows exponentially in the broken region.
• Figure 3: The non-Hermitian QB with nonlinear gain. (a)-(c) The eigenfrequencies $\omega$ and the saturated gain $g_{sat}$ in dependence on the loss rate $\gamma$. The saturated gain increases proportionally in the unbroken region while decreases inversely in the broken region, and the numerical result matches perfectly with the analytical result. (d)-(f) The time evolution of the nonlinear gain $g$ and the dynamics of the consumption-hub for different values of the loss rate $\gamma$. The feedback mechanism of the nonlinear saturable gain causes the consumption-hub to reach and remain at steady states.
• Figure 4: The robustness and the transient response of the wireless transfer processes versus the separation distance. (a)-(d) Contour plots of the maximum energy $E_{max}$, the stable energy $E_{s}$ and the maximum power $P_{max}$ as functions of the separation distance $d$ and the loss rate $\gamma$. The left and right sides of the gray curves indicate the unbroken and broken regions, respectively. (e), (f) The effect of sudden changes in the separation distance $d$ on the energy $E$ transferred from the nonlinear non-Hermitian QB to the consumption-hub, where the loss rate $\gamma=0.04\omega_{0}$. The consumption-hub can settle into steady states within an instant when the separation distance suddenly shifts between $20~{\rm cm}$ to $120~{\rm cm}$.
• Figure 5: The storage energy of non-Hermitian QBs with linear and nonlinear gains. The storage energy has the same advantages as the transfer energy although the battery has small initial energy and the parameters are the same as those in Fig. \ref{['fig2']} and Fig. \ref{['fig3']}.