Bosonic Systems Switch Emission Modes, Mirroring Superradiance Despite Complexity

A bosonic system mirroring the Dicke model of superradiance exhibits nuanced emission behaviours dependent on interaction strength. Bennet Windt of ICFO, University of Copenhagen, Max Planck Institute of Quantum Optics, Google, The Barcelona Institute of Science and Technology, and colleagues reveal a transition from Dicke-like superradiance at strong interactions to subradiant emission with weaker interactions. Notably, the dynamics in the weaker interaction regime align with rate equations similar to the original Dicke model, despite a complex bosonic state space. These findings, supported by analytical calculations and thorough numerical simulations using the system’s symmetry, offer insights relevant to circuit QED experiments.

Exploiting permutational symmetry to reduce Hilbert space dimensionality

Permutational symmetry proved central to analysing this complex bosonic system. The system remained unchanged under rearrangements of its energy particles, owing to the high degree of symmetry in the interactions between bosonic modes. Consequently, a dramatic reduction in the size of the mathematical ‘Hilbert space’ occurred, transforming an intractable dimension into one manageable for large-scale numerical simulations. Calculations were simplified without sacrificing accuracy by focusing solely on the symmetric subspace, the portion of the Hilbert space respecting the system’s inherent symmetries, revealing previously hidden dynamics.

A bosonic system mirroring the Dicke model of superradiance was investigated, concentrating on interactions between bosonic modes exhibiting permutational symmetry. Rather than specifying parameters like qubit count or temperature, the investigation focused on the qualitative behaviour of these bosonic interactions. This approach proved favourable over full simulations due to the complete system’s intractable size.

Permutational symmetry unlocks simplified rate equation modelling of collective decay

Ten bosonic modes undergoing collective decay have revealed a surprising simplification in the subradiant regime. Emission dynamics can now be modelled using rate equations, a method previously limited to strong interaction, Dicke-like scenarios. This advance is significant, as accurately describing the complex dynamics of these systems previously demanded computationally intensive methods due to the vastness of the ‘Hilbert space’, a mathematical representation of all possible states.

The system’s emission dynamics simplify considerably in the subradiant regime, even with ten interacting bosonic modes undergoing collective decay. Specifically, the collective emission rate, denoted R(t), exhibits initial oscillations with amplitude Nγ/U and frequency U around the Dicke solution, decaying over a timescale of approximately (Nγ)−1. Analysis reveals that, in the weak interaction limit, excitations scatter within a ‘dark subspace’, states inaccessible to direct decay, but the overall dynamics remain accurately modelled using rate equations. These rate equations are confined to a ground state manifold of just N+1 states, mirroring the simplicity observed in strong interaction scenarios, despite the accessible bosonic Hilbert space’s vastness. The plateau emission rate, arising from the initial state’s decay, is approximately Rd ≈ (4U)2/(Nγ), demonstrating a clear relationship between parameters and observed behaviour.

Symmetry’s role in collective energy release and implications for quantum technology

Understanding energy dissipation from complex systems is fundamental to designing efficient quantum devices. This investigation offers a new understanding of collective decay, where multiple energy sources release energy together, potentially improving the performance of technologies reliant on precise energy control. However, the current work concentrates on scenarios with perfect symmetry, a simplification that may not hold true in real-world applications where imperfections and asymmetries are commonplace.

It is important to acknowledge that this investigation simplifies real-world complexity with its focus on perfect symmetry. Many practical quantum systems exhibit imperfections and asymmetries that could alter these decay dynamics. Nevertheless, understanding behaviour in this idealised scenario provides a vital baseline for future investigations, allowing scientists to build upon this foundation to model and mitigate the effects of asymmetry, ultimately designing more robust and efficient quantum technologies.

The strength of interactions between energy sources dictates how energy release occurs; strong interactions resemble a cascade, while weaker ones lead to a slower release. Exploiting the symmetry inherent in multi-particle systems simplifies the modelling of collective decay, a process where energy is released from multiple sources simultaneously. Scientists demonstrated that even complex interactions between these energy particles, known as bosons, can be understood using relatively simple equations mirroring those developed for superradiance, a highly coordinated form of emission. This achievement overcomes a significant hurdle, as accurately describing these systems previously required extensive computational resources due to the vast number of potential states. The investigation establishes a foundation for investigating more intricate quantum systems and opens questions regarding how imperfections and asymmetries influence these emission dynamics.

The research revealed that the manner in which energy is released from interacting systems depends on the strength of those interactions, ranging from rapid cascades to slower emissions. This is significant because understanding collective decay, where multiple energy sources release energy together, is fundamental to designing efficient quantum devices. Scientists were able to describe the dynamics of these complex bosonic systems using simplified rate equations, despite the large number of possible states. The authors suggest this work provides a baseline for future investigations into how imperfections and asymmetries affect these emission dynamics.