Unifying Collective Effects in Emission, Absorption, and Transfer

TL;DR

This work unifies emission, absorption, and transfer collective effects (CEEAT) within a single Dicke framework, resolving disparate community definitions and extending the formalism to harmonic oscillators and mixed degrees of freedom. It derives explicit scaling laws for spin and HO Dicke states: SR and SA scale as $igO(N^2)$ for spins and as unbounded $igO(R)$ for HO excitations, while ST can reach $igO(N_D^2N_A^2)$ (or $igO(N^4)$ when donor and acceptor sizes are equal); mixed spin–HO cases yield product-like enhancements. Robustness to disorder and noise is demonstrated to arise from intra-aggregate couplings, with criteria such as $V_{DD}igg rto au_c^{-1}$ and $ ext{var}( ext{site energies}) \\lesssim eta_0$ maintaining delocalisation. The framework also points to broader extensions (anharmonic/other degrees of freedom, driven/steady-state regimes) and potential experimental implementations, offering a versatile blueprint for designing resilient quantum devices leveraging CEEAT.

Abstract

Collective effects, such as superradiance and subradiance are central to emerging quantum technologies -- from sensing to energy storage -- and play an important role in light-harvesting. These effects enhance or suppress rates of dynamic processes (absorption, emission, and transfer) due to the formation of symmetric or antisymmetric collective states. However, collective effects in different contexts -- absorption, emission, and transfer -- have often been defined disparately, especially across different communities, leading to results that are not immediately transferable between different contexts. Here, we describe all three types of collective effects using a common Dicke framework that resolves the apparent discrepancies between different approaches. It allows us to generalise previously known collective effects involving spins into new ones involving aggregates of harmonic oscillators or other degrees of freedom. It also explains how collective effects can be engineered to be robust against both disorder and noise, paving the way for more resilient quantum devices.

Figures (5)

• Figure 1: Collectively enhanced and suppressed rate processes, illustrated using super- and subradiance from a donor aggregate of four sites (blue) to an acceptor field. (a) Emission from a localised donor excitation to the acceptor field occurs with rate $\gamma_0$. Dotted lines indicate couplings, including stronger intra-donor couplings (thicker) and weaker donor-acceptor couplings (thinner). (b) Superradiance: symmetrically delocalised excitations can increase emission rates. (c) Subradiance: anti-symmetrically delocalised excitations can suppress the emission.
• Figure 2: Classification of collective enhancements in emission, absorption, and transfer. The donor (blue) and the acceptor (red) may consist of spins, harmonic oscillators (HOs), or a field. Superradiance is the enhanced emission from spins or HOs into a field, while superabsorption is the inverse process of enhanced absorption from a field. Supertransfer is the enhanced transfer between one aggregate of spins or HOs and another. An analogous table could classify the suppressed collective effects into subradiance, subabsorption, and subtransfer.
• Figure 3: Scaling of the rate $\gamma$ for Dicke states of spins and HOs.(a) Dicke states of an aggregate of $N$ spins are labelled $\ket{\ell,m}$; shown is only the Dicke ladder of the bright states with $\ell=N$ because the other states are dark. Going up the ladder, the enhancement increases from $\mathcal{O}(N)$ at $m=1$ to the maximum value of $\mathcal{O}(N^2)$ at half-filling ($m=N/2$) before decreasing back to $\mathcal{O}(N)$ for the fully excited aggregate. (b) Time evolution of the rate out of a spin aggregate for different initial states. For initial states in the bottom half of the Dicke ladder, the rate decreases over time as excitations are lost. Initial states in the upper half, illustrated with $m=4$, show the characteristic bump in time, where the rate increases until the state passes through the middle of the ladder. (c) Dicke states of an aggregate of HOs are characterised by the occupation numbers of the collective modes, one bright with occupation number $R$ (the one shown) and $N-1$ dark ones, with occupation number vector $\mathbf{d}$. The bright mode emits with a rate that increases without bound as $N_\mathrm{D} R$. (d) Time evolution of the rate out of an HO aggregate for different initial states. Unlike the spin case, no bump is present for any initial $R$.
• Figure 4: Robust CEEAT due to intra-aggregate couplings in a four-spin donor aggregate ($N_{\mathrm{D}}=4$), initialised in the half-filled Dicke state. (a) Samples of Ornstein--Uhlenbeck noise with strength $\Lambda=\gamma_0$ and a range of correlation times. (b,c) The rate enhancement $\gamma/\gamma_0$, obtained from the emission $\gamma_0\langle J^{+} J^{-} \rangle$ averaged over evolution up to $t=1/\gamma_0$. Maximal enhancement $\gamma_{\max}/\gamma_0 = 6$ is achieved when the intra-aggregate coupling $V_{\mathrm{D}\mathrm{D}}$ is large compared to both the noise strength $\Lambda_\mathrm{D}$ and the inverse correlation time $\tau_\mathrm{c}$, i.e., $V_{\mathrm{D}\mathrm{D}} \gg \Lambda_\mathrm{D},\tau_\mathrm{c}^{-1}$. (b) Rate enhancement as a function of $V_{\mathrm{DD}}$ and $\Lambda_{\mathrm{D}}$ at fixed $\tau_\mathrm{c}=0.33\,\gamma_0^{-1}$. An additional way to preserve CEEAT occurs when $\Lambda_{\mathrm D} \ll \gamma_0$, even for no coupling. (c) Rate enhancement as a function of $V_{\mathrm{DD}}$ and $\tau_\mathrm{c}^{-1}$ at fixed $\Lambda_{\mathrm D}=5\gamma_0$.
• Figure 5: Robust delocalisation due to intra-aggregate couplings in a disordered four-spin donor aggregate ($N_\mathrm{D}=4$). The average participation ratio (PR) of the two-particle eigenstates as a function of intra-aggregate coupling $V_{\mathrm{D}\mathrm{D}}$ and the variance $\Lambda$ of the static energetic disorder. A higher PR, up to a maximum of $\mathrm{PR_{max}}=6$, indicates greater delocalisation of the states, and is obtained when $\Lambda_\mathrm{D} \ll V_{\mathrm{D}\mathrm{D}}$.