Experimental challenges and prospects for quantum-enhanced energy conversion: Stationary Fano coherence in V-type qutrits interacting with polarized incoherent radiation

TL;DR

This work develops a first-principles Bloch-Redfield framework for a V-type three-level system driven by polarized incoherent radiation, showing that steady-state Fano coherence between the excited states can persist beyond strict degeneracy. By retaining non-secular terms and employing a partial secular approach, the authors demonstrate how polarization-induced interference survives across weak- and strong-pumping regimes, with stationary coherence favored by small $Δ$ and higher incoherent pumping. They provide detailed dynamical equations in linear form and identify regimes where the coherence magnitude, relative to excited-state populations, is maximized, including a theoretical bound on coherence under pumping. The paper further discusses experimental feasibility with Rubidium-87, outlining a concrete D1-line implementation and predicting parameter ranges (e.g., bandwidth $50$–$500$ MHz) where stationary Fano coherence could be observed, paving the way for coherence-assisted energy conversion and storage technologies.

Abstract

Quantum coherence offers potential for energy conversion technologies. It influences light absorption and emission, affecting energy conversion limits and efficiency. As a result, quantum coherence is being harnessed to boost performance in quantum heat engines, photocells, and photosynthetic-inspired platforms. Of particular interest in this context is the generation of Fano coherences, i.e., the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. We aim to formalize mathematically the possibility of achieving steady-state Fano coherence in a V-type three-level quantum system using polarized incoherent radiation, without requiring the energy difference between the excited levels to tend to zero. We perform this analysis by deriving the Bloch-Redfield equation from first-principles by quantizing the incoherent radiation. The resulting reduced dynamics of the system are analysed, so as to determine the lifetime of Fano coherence and identify the conditions under which it becomes stationary. We characterise distinct dynamical regimes, ranging from weak to strong pumping, in which steady-state Fano coherence emerges, and we quantitatively determine its magnitude. For each regime, we analyse the generation of Fano coherence as a function of both the intensity of the incoherent pumping and the energy splitting between the excited levels. We also assess how obtaining Fano coherence is modified by symmetric or asymmetric decay rates. These findings indicate that a three-level quantum system driven by polarized incoherent light can act as a robust resource for coherence-assisted energy conversion and storage. Finally, we discuss the experimental challenges associated with the implementation of the proposed model using an ensemble of Rubidium atoms.

Figures (5)

• Figure 1: Pictorial representation of the V-type three-level system considered in our analysis. Its energy level configuration consists of two nearly degenerate excited levels, denoted as $|a\rangle$ and $|b\rangle$ with a frequency splitting of $\rm \Delta$. These levels are incoherently pumped, at rates ${\rm r}_a$ and ${\rm r}_b$ respectively, from the ground level $|c\rangle$. Both $|a\rangle$ and $|b\rangle$ can decay to the ground level at rates $\gamma_a$ and $\gamma_b$.
• Figure 2: Dimensionless time evolution of both the excited levels populations and module of quantum coherence $|\rho_{ab}|$. (a): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=1$, $\Delta/\bar{\gamma}=10$, $\bar{n}=0.06$; (b): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=1$, $\Delta/\bar{\gamma}=0.1$, $\bar{n}=0.06$; (c): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=1$, $\Delta/\bar{\gamma}=0.1$, $\bar{n}=100$; (d): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=10$, $\Delta/\bar{\gamma}=10$, $\bar{n}=0.06$; (e): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=10$, $\Delta/\bar{\gamma}=0.1$, $\bar{n}=0.06$; (f): $\gamma_{a}^{\rm iso}/\gamma_{b}^{\rm iso}=10$, $\Delta/\bar{\gamma}=0.1$, $\bar{n}=100$. The panels in the first row refer to symmetric systems, while the panels in the second row are related to asymmetric ones.
• Figure 3: Excited state coherence $\rho_{ab}$ in the long-time limit $t\rightarrow\infty$ as a function of $\bar{n}$ and $\Delta/\bar{\gamma}$. (a) Plot of $|\rho_{ab}|_{\rm steady}$ varying $\bar{n}$, for different values of $\Delta/\bar{\gamma}$ in a symmetric system. (b) Plot of $|\rho_{ab}|_{\rm steady}$ varying $\Delta/\bar{\gamma}$, for different values of $\bar{n}$ in a symmetric system. (c) Plot of $|\rho_{ab}|_{\rm steady}$ varying $\bar{n}$, for different values of $\Delta/\bar{\gamma}$ in an asymmetric system ($\gamma_a^{\rm iso}/\gamma_b^{\rm iso}=10$). (d) Plot of $|\rho_{ab}|_{\rm steady}$ varying $\Delta/\bar{\gamma}$, for different values of $\bar{n}$ in an asymmetric system ($\gamma_a^{\rm iso}/\gamma_b^{\rm iso}=10$).
• Figure 4: V-type three level system within the D1 line transition of $^{87}$Rb. The ground state $|c\rangle$ corresponds to the hyperfine magnetic sublevel $|F=1 \,, m_F=0\rangle$, while the two excited states $|a\rangle$ and $|b\rangle$ are represented by the levels $|F'=1 \,, m_{F'}=-1\rangle$ and $|F'=1 \,, m_{F'}=+1\rangle$, respectively. The red arrows denote the radiation processes involved: spontaneous emission from levels $|a\rangle$ and $|b\rangle$ to level $|c\rangle$ at rates $\gamma_{a}^{\rm iso}=\gamma_{b}^{\rm iso}$ respectively; incoherent pumping and stimulated emission involving transitions $|a\rangle \leftrightarrow |c\rangle$ and $|b\rangle \leftrightarrow |c\rangle$ at rates $r_a^{\rm pol}=r_b^{\rm pol}$, respectively. The parameter $\Delta$ is the energy splitting between the excited levels: $\Delta=\omega_{ac}-\omega_{bc}$. In the figure, the wavevector ${\bf k}$ of the radiation and the uniform magnetic field vector ${\bf B}$ are reported, as well as the frequency difference between the hyperfine manifolds of the $D1$ line.
• Figure 5: (a) Stationary magnitude of the quantum coherence $|\rho_{ab}|$ as a function of the mean photon number $\bar{n}$ and of the normalized excited state splitting $\Delta/\bar{\gamma}$. (b) Stationary coherence normalized with respect to the excited state populations, as a function of $\bar{n}$ and $\Delta/\bar{\gamma}$. The V-type three-level system is driven by a linearly polarized radiation field along the $x$-axis.