Disordered Waveguide QED Maintains Superradiance with Scaling As, Demonstrating Robust Collective Emission

The collective emission of light from multiple atoms, known as superradiance, typically requires precise atomic arrangement, but new research demonstrates its surprising resilience to disorder. Xin H. Zhang from the Technical University of Munich, alongside Daniel Malz from the University of Copenhagen and Peter Rabl also from the Technical University of Munich, investigates how superradiance behaves when atoms are randomly positioned within a waveguide. Their work reveals that this collective emission remains robust even with significant disorder, and importantly, the atoms spontaneously organise themselves to enhance the effect. This discovery resolves a long-standing question about superradiance in realistic, imperfect systems and offers valuable insights into controlling collective optical phenomena for future technologies.

Disorder’s Impact on Superradiant Spin Ordering

This supplemental material details research into superradiance and spontaneous spin ordering within disordered waveguide quantum electrodynamics systems. Scientists utilized a truncated Wigner approximation to model the interactions of numerous atoms coupled to a waveguide, focusing on how disorder influences superradiant emission and the development of collective spin order. The study demonstrates that detuning has a negligible effect on the superradiant rate when a large number of atoms are present, confirming the accuracy of the modeling approach. Supplementary plots illustrate a smooth transition from ordered to disordered spin states as disorder increases, and comparisons between regular and irregular lattices reveal the sensitivity of spin ordering to structural arrangement.

Further analysis of propagating phases and relative spin angles demonstrates uniform phase distribution and concentrated spin angle values. The data confirms the accuracy of the truncated Wigner approximation and reveals a logarithmic scaling of burst time with the number of atoms. These findings collectively demonstrate robust superradiance, spontaneous spin ordering, and the accuracy of the chosen modeling technique.

Disordered Superradiance via Quantum State Diffusion

The study investigates superradiant emission from disordered arrays of two-level atoms coupled to a one-dimensional waveguide. Researchers developed large-scale semiclassical methods, including a discrete truncated Wigner approximation and a quantum state diffusion approach, to model the collective decay of excited atoms, overcoming limitations of exact numerical simulations. These techniques enabled systematic investigation of superradiance for increasing numbers of atoms, even with strong spatial disorder, revealing subtle differences in scaling behavior compared to perfectly ordered systems. By tracing out the waveguide modes, scientists derived a master equation describing atomic dynamics, incorporating both coherent photon-mediated interactions and incoherent losses.

Simulations, initialized with all atoms in an excited state, monitored collective decay, focusing on the characteristic N² scaling of superradiance, where N represents the number of atoms. To account for disorder, atomic positions were randomly offset, introducing phase variations. Researchers introduced a product-state ansatz to establish an upper bound for the maximal collective decay rate, revealing a mechanism for robustness against disorder, where atomic spins spontaneously organize, aligning relative orientations based on position, enabling constructive interference. The team confirmed that even with strong disorder, the N² scaling of superradiance is asymptotically recovered, demonstrating persistent collective behavior.

Disorder Preserves Strong Superradiant Emission Rates

This work presents a detailed study of superradiance, a phenomenon of accelerated collective emission, in a disordered array of two-level atoms coupled to a one-dimensional waveguide. Scientists employed large-scale semiclassical simulations and analytical methods to investigate how disorder affects this collective behavior, revealing surprising robustness. Experiments demonstrate that even with strong disorder, the characteristic superradiant burst maintains a peak emission rate scaling with N², where N represents the number of atoms, confirming the persistence of collective effects despite disruptive influences. To understand this behavior, the team developed a product-state ansatz, a mathematical description of the atomic dipole configuration at the peak emission time, providing a tight upper bound for the maximal collective decay rate and explaining how atoms self-organize to optimize constructive interference.

Results show that atoms spontaneously align according to their positions, even in disordered arrangements, enhancing collective emission. The simulations and analysis reveal subtle differences in numerical prefactors as the system approaches the N² scaling limit, providing new insights into superradiance dynamics. This research successfully addresses a long-standing question regarding the survival of Dicke superradiance in disordered quantum systems, demonstrating that the characteristic N² scaling of the peak emission rate is asymptotically recovered, even with strong disorder, delivering a deeper understanding of collective optical phenomena and offering valuable insights for applications such as superradiant lasers and quantum metrology.

Disorder Surprisingly Enhances Superradiant Light Emission

Researchers have demonstrated the surprising robustness of superradiance, a collective emission of light, even when atoms are arranged in a highly disordered fashion within a waveguide. The team employed large-scale semiclassical simulations to investigate how disorder affects the characteristic burst of light emitted during superradiance, finding that the key signature of this phenomenon persists despite significant spatial and spectral irregularities in the atomic arrangement. Importantly, the simulations reveal a tendency for atoms to self-organize spontaneously, optimizing constructive interference and maintaining efficient light emission. This work resolves longstanding questions regarding the existence of superradiance in disordered systems and provides valuable insight into collective optical phenomena in realistic, imperfect environments.

The researchers developed an analytical estimate to bound the numerical results, further clarifying how disorder shapes the collective decay process and demonstrating the emergence of mirror-asymmetric correlations in the superradiant emission. While the simulations accurately capture the system’s behaviour, the authors acknowledge that the semiclassical approach represents an approximation, and that fully quantum mechanical simulations would be necessary to explore certain subtle effects. Future research directions include investigating non-Markovian effects and exploring the behaviour of the system with increased complexity and dimensionality.