Cooperative Effects in Quantum Systems: Superradiance and Long-Range Interactions

This Ph.D. thesis studies the interplay of cooperativity and noise in realistic systems, largely focusing on superradiance. Cooperative effects emerge from the collective interaction of an ensemble of elements to an external field. Notable examples are superconductivity, where the electron Cooper pairs interact with the lattice vibrations, plasmon excitations, arising from the collective interaction of electrons in a metal with the Coulomb field, and superradiance, that is a cooperative spontaneous emission process stemming from an aggregate of identical emitters. Cooperative effects are typically robust to disorder and noise, making them interesting for applications to quantum devices operating at room temperature. In this work, we first present a general master equation formalism that describes the collective coupling of an aggregate of emitters/absorbers to the electromagnetic field, valid both when the size of the aggregate is larger or smaller than the emitted/absorbed wavelength. Also, the formalism is valid both for weak and strong coupling of the emitters to the electromagnetic field and, most importantly, it allows to correctly describe superradiance in different regimes.

Within such formalism, the interplay of superradiance and thermal noise is studied both for molecular nanotubes (of size smaller than the transition wavelength) that are present in the antenna complexes of photosynthetic Green Sulfur Bacteria, and also for novel solid state quantum dot superlattices, having size larger than the emitted wavelength. In both cases it is shown that coherence can persist in presence of thermal noise at the temperatures where these systems have been experimentally analyzed (room temperature for molecular nanotubes, and 6 K for quantum dot superlattices). Specifically, in natural molecular nanotubes we show that the macroscopic coherent delocalization of the excitation at room temperature, covering hundreds of molecules, can be considered an emergent effect originating from the combined effect of the specific geometric disposition of the molecules and the presence of cooperatively enhanced couplings between cylinder subunits. These results open the path to new ways of engineering quantum wires robust to noise thanks to cooperativity. Moreover, our analysis of solid state systems based on perovskite (CsPbBr3) quantum dot superlattices provides a theoretical framework able to explain recent observations of superradiant emission. Based on our theory, we suggest that further experiments, using smaller quantum dots, could significantly increase the robustness of the system to thermal noise, paving the way towards room-temperature superradiance in solid-state systems. We also considered the antenna complexes of Purple Bacteria, where cooperative effects are well known to boost the transfer and storage of photo-absorbed excitations. We show how these properties can be exploited to create a bio-inspired molecular aggregate laser medium, where natural sunlight, although weak, would be used as a pumping source. The efficient energy transfer within this system would effectively focus the absorbed excitation on a suitably chosen molecular dimer, composed by a pair of interacting molecules. The orientation of the molecule transition dipole moment in each dimer is such to concentrate all the dipole strength in the highest energy level, leaving the lower excitonic state dark. A molecular dimer in such configuration, which is ideal to achieve population inversion, is called H-dimer. Such an H-dimer in our proposed architecture for a bio-inspired laser medium, is placed at the center of the bio-inspired molecular aggregates. The H-dimers, pumped by the surrounding molecular aggregates, reach population inversion and, therefore, can lase when such aggregates are placed in an optical cavity. Turning the incoherent energy supply provided by the Sun into a coherent laser beam would overcome several of the practical limitations inherent in using sunlight as a source of clean energy. For example, laser beams are highly effective at driving chemical reactions which convert sunlight into chemical energy. Further, since bacterial photosynthetic complexes tend to operate in the near-infrared spectral region, our proposal naturally lends itself for realising short-wavelength infrared lasers which would allow their beams to travel nearly losslessly over large distances, thus efficiently distributing the collected sunlight energy.

In search of a common mechanism to cooperativity and its robustness, we have compared the Cooper pair model of superconductivity and single-excitation superradiance, showing many similarities between the two: in particular, superradiant systems present an imaginary gap in the complex plane (that is, a segregation between the lifetimes of the system eigenstates) that, similarly to the superconducting gap, makes these systems robust to static disorder. More in general, we show that any long-range interaction between the constituents of a system generates collective behaviours, manifested by gaps in the excitonic spectrum. Therefore, our further analysis considers the effect of long-range interactions on excitation transport along disordered chains. We show that the presence of a gapped, collective state affects the whole spectrum of the system, generating quite counter-intuitive disorder-enhanced and disorder-independent transport regimes, that extend over many orders of magnitude of the disorder strength. We also prove that a chain strongly coupled to a cavity mode is equivalent to a long-range interacting chain, thus being very promising for future experiments and applications. Specifically, we show that realistic molecular chains, state-of-the-art trapped ions and Rydberg atoms are all able to reach the needed long-range interaction strength that would show disorder-enhanced or disorder-independent transport, aiming to the realization of dissipationless transport of energy in disordered quantum wires.