Transitionless quantum driving based wireless power transfer

TL;DR

The paper addresses efficient wireless power transfer between two inductively coupled coils by leveraging transitionless quantum driving (TQD) to surpass the slow, adiabatic limit. It builds a two-coil, non-Hermitian, coupled-mode model and derives both the adiabatic and transitionless driving Hamiltonians, introducing an auxiliary term that cancels non-adiabatic transitions and yields an effective coupling $κ_{ ext{eff}}$. Numerical results show that TQD substantially improves energy transfer efficiency and robustness against variations in coupling strength, distance, and intrinsic losses, compared to adiabatic following. The findings suggest that STA-based TQD can enable fast, loss-tolerant wireless power transfer in practical coil systems, with potential applicability to other non-ideal quantum-inspired energy transfer platforms.

Abstract

Shortcut to adiabaticity (STA) techniques have the potential to drive a system beyond the adiabatic limits. Here, we present a robust and efficient method for wireless power transfer (WPT) between two coils based on the so-called transitionless quantum driving (TQD) algorithm. We show that it is possible to transfer power between the coils significantly fast compared to its adiabatic counterpart. The scheme is fairly robust against the variations in the coupling strength and the coupling distance between the coils. Also, the scheme is found to be reasonably immune to intrinsic losses in the coils.

Figures (6)

• Figure 1: (Color online) (a) Typical wireless power transfer system consists of two coils separated by a distance $d$, (b) Schematic of the coils. Two lossy $LC$ circuits, Source and Drain with losses $\Gamma_s$ and $\Gamma_d$ respectively, coupled to each other by inductive coupling. The resonant frequencies are $\omega_s$ and $\omega_d$ and also $\omega_s \ne \omega_d$.
• Figure 2: (Color online) Evolution of energy from the Source coil (solid red) to the Drain coil (dash-dotted blue) with $\Gamma_s=\Gamma_d=4\times 10^{3}s^{-1}$, $\delta=2\times 10^{5}s^{-1}$. (a) Adiabatic evolution for the time window $2t_0$ where $\kappa_0 = 4\times 10^{4}s^{-1}$, $\beta=3\times 10^{9}s^{-2}$ and $t_0 = 10^{-4}s$, followed by energy evolution using TQD with weaker coupling strenght $\kappa_0 = 4 \times 10^{2} s^{-1}$ and decreasing time windows (b) $\beta = 3\times 10^{9}s^{-2}$ and $t_0 = 10^{-4}s$, (c) $\beta = 3\times 10^{10}s^{-2}$ and $t_0 = 10^{-5}s$, (d) $\beta = 3\times 10^{11}s^{-2}$ and $t_0 = 10^{-6}s$,
• Figure 3: (Color online) Frequency sweep of $\omega_s(t)$ (or $\Delta(t)$ when $\omega_d =$ constant). The sweep is linear with slope $\beta$ according to L-Z model. For adiabatic evolution $|\beta| = \beta_{adiabatic}$ is small (solid red) and $|\beta| = \beta_{TQD}$ is high for the TQD method. Time period required for adiabatic case is large accordingly i.e. $T_{TQD}<T_{Adiabatic}$.
• Figure 4: (Color online) Comparison of efficiency ($\eta$) as a function of $\delta$ between adiabatic (dashed-dotted) and tqd based methods (solid) for different $\kappa_0 / \Gamma_{s,d}$ values: $\kappa_0 / \Gamma_{s,d}=10$ (red), $\kappa_0 / \Gamma_{s,d}=50$ (purple), $\kappa_0 / \Gamma_{s,d}$=100 (green) where $\Gamma_w=10^4 s^{-1}$. Time windows ($T$) for the evolution are as follows: (a) $T=200 \mu s$, (b) $T=2 \mu s$.
• Figure 5: (Color online) Dependence on the distance $d$ of the (a) coupling $\kappa(d)$ between the source and the drain coil (dash-dotted blue), additional coupling $\kappa_a(d)$ (dotted brown) and effective coupling $\kappa_{eff}(d)$ for TQD (solid red), (b) efficiency $\eta(d)$ for adiabatic method (dash-dotted blue) and for TQD (solid brown) .