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arXiv:1403.1779 · Physical Review B

Cooperative robustness to static disorder: Superradiance and localization in a nanoscale ring to model light-harvesting systems found in nature

G. L. Celardo, Giulio G. Giusteri, F. Borgonovi

Published Aug 8, 2014• 59 citations
arXivHTMLPDF

Abstract

We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super- and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench superradiance. We identify two different regimes: (i) weak opening, in which superradiance is quenched at the same critical disorder at which the states of the closed system localize; (ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.

DOI
10.1103/physrevb.90.075113

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We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super- and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench superradiance. We identify two different regimes: (i) weak opening, in which superradiance is quenched at the same critical disorder at which the states of the closed system localize; (ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.
We analyze a one-dimensional ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super- and subradiant behavior. Moreover, each two-level system is coupled to another independent environment, modeled by a classical white noise, simulating a dephasing bath and described by the Haken-Strobl master equation. Single-exciton superradiance, an example of a cooperative quantum coherent effect, is destroyed at a critical dephasing strength proportional to the system size, showing robustness of cooperativity to the action of the dephasing environment. We also show that the coupling to a common decay channel contrasts with the action of dephasing, driving the entanglement decay to slow down on increasing the system size. Moreover, after a projective measurement which finds the excitation in the system, the entanglement reaches a stationary value, independent of the initial conditions.
Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Localization of light in cold atomic systems presents strong differences from the standard problem of localization since one needs to deal with an open quantum wave problem in presence of long range hopping which induces strong cooperative effects, such as super and subradiance. Contrary to common believe, we show that localization of light is possible in the dilute regime for subradiant states. Additional disorder in atomic transition frequencies leads to the emergence of a mobility edge in the immagibary axis, independent of the real energy. The existence of a critical lifetime above which subradiant Dicke states are localized appears as a general feature of scalar wave localization.
Large-scale simulations of light-matter interaction in natural photosynthetic antenna complexes containing more than one hundred thousands of chlorophyll molecules, comparable with natural size, have been performed. Photosynthetic antenna complexes present in Green sulfur bacteria and Purple bacteria have been analyzed using a radiative non-Hermitian Hamiltonian, well-known in the field of quantum optics, instead of the widely used dipole-dipole Frenkel Hamiltonian. This approach allows us to study ensembles of emitters beyond the small volume limit (system size much smaller than the absorbed wavelength), where the Frenkel Hamiltonian fails. When analyzed on a large scale, such structures display superradiant states much brighter than their single components. An analysis of the robustness to static disorder and dynamical (thermal) noise shows that exciton coherence in the whole photosynthetic complex is larger than the coherence found in its parts. This provides evidence that the photosynthetic complex as a whole plays a predominant role in sustaining coherences in the system even at room temperature. Our results allow a better understanding of natural photosynthetic antennae and could drive experiments to verify how the response to electromagnetic radiation depends on the size of the photosynthetic antenna.
A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
A theoretical investigation of the effects of static disorder on the linear optical response and the degenerate four-wave-mixing signals of multiple quantum well Bragg structures is presented. It is shown that disorder leads to a finite radiative coupling strength of subradiant modes that are optically forbidden in the ideal structure. In the absorption spectrum, the subradiant modes appear as sharp resonances in the presence of barrier thickness fluctuations, whereas the disorder induced subradiant modes are inhomogeneously broadened in the presence of interface roughness. The decay of the time integrated four-wave-mixing signal at large delays is determined by the dephasing time of subradiant modes, whereas the initial fast decay is dominated by the superradiant mode. A free induction decay is observed in the presence of barrier thickness fluctuations. In contrast, even a small inhomogeneous broadening induces a photon-echo-like behavior for the subradiant modes, while the superradiant mode still exhibits a free induction decay.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.