Timing Quantum Emission Reveals Hierarchy: Coherence, Superradiance, and Entanglement in Order

The precise timing of light emission from multiple quantum sources remains a fundamental challenge in quantum physics, and a team led by Nur Fadhillah Binti Rahimi of the University of Otago, Norman Koo Tze Wei from the National University of Singapore, and Daniel Schumayer of the University of Sydney now reveals a clear sequence of events governing this process. Building upon the established theory of superradiance, originally proposed in 1954, the researchers demonstrate that coherence develops before the peak of correlated light emission, followed by minimal dephasing, and ultimately, correlated dephasing itself. This work, also involving contributions from Christopher Gies, Leong Chuan Kwek, and David A. W. Hutchinson, establishes a distinct temporal hierarchy, showing that enhanced coherence initiates correlated emission when dephasing is minimal, and fundamentally advances understanding of how quantum systems collectively emit light.

Entanglement’s Role in Dicke Superradiance Dynamics

This research explores the dynamics of Dicke superradiance, a collective emission of light from many atoms, with a particular focus on the emergence of entanglement and its role in the process. Scientists investigate how entanglement evolves during superradiance and how it relates to the overall efficiency and characteristics of the emitted light. The study also delves into the theoretical framework for understanding these phenomena, employing quantum mechanical tools and numerical simulations to model the process. It considers experimental realizations and potential applications of superradiance in emerging quantum technologies.

Dicke superradiance is a cooperative emission of light from a collection of two-level atoms, or qubits, driven by an external field, resulting in a burst of coherent light much stronger than that from independent atoms. Researchers investigated the conditions under which superradiance occurs and how parameters such as the number of atoms, the driving field strength, and the geometry of the atomic ensemble influence it. A central theme is the connection between entanglement and superradiance, with the study arguing that entanglement is not necessarily a prerequisite for superradiance and that its growth during the process is often limited. The authors explore the evolution of entanglement measures to understand how it contributes to the overall dynamics, finding that while entanglement can be generated, it often saturates or even decreases as the process evolves, suggesting that coherence and correlations may be more important drivers of emission.

The study employs theoretical tools including the Dicke Hamiltonian, which describes the collective dynamics of two-level atoms, and quantum master equations, used to model the system’s evolution in the presence of dissipation and decoherence. Numerical simulations are used to obtain quantitative results, and various entanglement measures, such as concurrence and negativity, are used to quantify the amount of entanglement present. Experimental platforms where superradiance has been observed include cold atoms trapped in optical lattices or magnetic traps, solid-state systems like semiconductor microcavities, and arrays of quantum dots. Potential applications include quantum information processing, quantum metrology, and the development of new laser technologies.

A key finding is that entanglement does not necessarily grow during superradiance, challenging some previous assumptions. The study emphasizes the importance of coherence, the phase relationship between atoms, in driving superradiance, potentially more so than entanglement. Dissipation and decoherence limit the growth of entanglement and affect the overall dynamics of superradiance. In essence, the paper provides a nuanced and critical examination of the role of entanglement in Dicke superradiance, challenging conventional wisdom and highlighting the importance of other factors, such as coherence and dissipation.

Temporal Hierarchy of Superradiance and Dephasing

Scientists investigated the dynamics of superradiance, a phenomenon involving coherent emission from closely spaced emitters, building upon the foundational work of Dicke from 1954. The study pioneers a detailed analysis of the sequential emergence of coherence, superradiance, and correlated dephasing, revealing a distinct temporal hierarchy in their peak values. Researchers established that relative coherence develops initially, followed by the peak of correlated emission, then minimal correlated dephasing, and finally, correlated dephasing itself. To model this process, the team employed the Tavis-Cummings Hamiltonian, describing the interaction of identical two-level emitters with photons, and extended it to account for realistic open quantum systems.

This involved incorporating incoherent processes like decay, photon loss, and pure dephasing within a Markovian approximation and Lindblad master equation, allowing for a comprehensive description of emitter dynamics and interaction with the electromagnetic field. The team solved this equation using two distinct approaches, selecting the method based on system size. For systems with fewer than ten emitters, they performed exact calculations, suitable for experimental setups utilizing superconducting qubits, quantum dots, or silicon-on-insulator platforms. For larger systems, up to sixty emitters, they implemented an optimised numerical approach leveraging permutation invariance.

The study initiated the system with all emitters in their ground state and a resonant mode populated with half the total number of photons. Scientists then investigated the temporal evolution of four key quantities: correlated emission, the von Neumann entropy, relative entropy of coherence, and an entanglement witness. Correlated emission and the von Neumann entropy were chosen as basis-independent measures, while the entanglement witness and relative entropy of coherence provided complementary insights. To quantify the temporal evolution, the team introduced characteristic times, measuring when each quantity reached its extremal value, and compared these times to predict the sequence of events during superradiant emission. This detailed analysis revealed that, in the collective regime, the characteristic timescale for superradiant emission scales inversely with the number of emitters.

Superradiance Reveals Temporal Hierarchy of Coherence

This work investigates the temporal dynamics of superradiance, focusing on the sequential emergence of coherence, superradiant emission, and entanglement in closely spaced emitters. Researchers discovered a distinct temporal hierarchy, demonstrating that relative coherence develops first, followed by the peak of correlated emission, and finally, minimal correlated dephasing. These findings reveal that enhanced relative coherence initiates correlated emission, particularly when correlated dephasing is negligible, tightly linking these two processes in time. The team measured the behavior of time delays as a function of the number of emitters, N, and the decay parameter, γ.

Results demonstrate that the time delay diminishes as ln(N)/N α, where α is approximately 1 for γ = 0 and 1. 2 for γ = 2. This behavior is analogous to a damped harmonic oscillator, where increased mechanical damping shifts the first extremal deflection to earlier times. Measurements confirm that the time difference between coherence measures, τCrel and τC0, is consistently smaller than the time difference between coherence and entanglement, τW, and that all time differences vanish as the light-matter coupling strength increases. Further analysis of time differences between measures, as a function of coupling strength, revealed that τW is always larger than τC0.

The team established a clear temporal order: τCrel ≤ τC0 ≤ τW ≤ τCzz, demonstrating that enhanced relative coherence drives correlated emission. Specifically, when correlated dephasing is approximately zero, entanglement and correlated emission become directly linked, with their time gap vanishing. These findings suggest that current experimental capabilities are sufficient to verify these predictions in small systems in the near future, opening avenues for further exploration of superradiance dynamics.