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Optics Express

Cascaded collective decay in regular arrays of cold trapped atoms

Laurin Ostermann, Hashem Zoubi, Helmut Ritsch

Published Dec 20, 2012• 26 citations
Publisher

Abstract

Energy and lifetime of collective optical excitations in regular arrays of atoms and molecules are significantly influenced by dipole-dipole interaction. While the dynamics of closely positioned atoms can be approximated well by the Dicke superradiance model, the situation of finite regular configurations is hard to access analytically. Most treatments use an exciton based description limited to the lowest excitation manifold. We present a general approach studying the complete decay cascade of a finite regular array of atoms from the fully inverted to the ground state. We explicitly calculate all energy shifts and decay rates for two generic cases of a three-atom linear chain and an equilateral triangle. In numerical calculations we show that despite fairly weak dipole-dipole interactions, collective vacuum coupling allows for superradiant emission as well as subradiant states in larger arrays through multi-particle interference. This induces extra dephasing and modified decay as important limitations for Ramsey experiments in lattice atomic clock setups as well as for the gain and frequency stability of superradiant lasers.

DOI
10.1364/oe.20.029634

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Energy and lifetime of collective optical excitations in regular arrays of atoms and molecules are significantly influenced by dipole-dipole interaction. While the dynamics of closely positioned atoms can be approximated well by the Dicke superradiance model, the situation of finite regular configurations is hard to access analytically. Most treatments use an exciton based description limited to the lowest excitation manifold. We present a general approach studying the complete decay cascade of a finite regular array of atoms from the fully inverted to the ground state. We explicitly calculate all energy shifts and decay rates for two generic cases of a three-atom linear chain and an equilateral triangle. In numerical calculations we show that despite fairly weak dipole-dipole interactions, collective vacuum coupling allows for superradiant emission as well as subradiant states in larger arrays through multi-particle interference. This induces extra dephasing and modified decay as important limitations for Ramsey experiments in lattice atomic clock setups as well as for the gain and frequency stability of superradiant lasers.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.
Recent advances in generating well controlled dense arrangements of individual atoms in free space have generated interest in understanding how the extended nature of these systems influences superradiance phenomena. Here, we provide an in-depth analysis on how space-dependent light shifts and decay rates induced by dipole-dipole interactions modify the steady-state properties of coherently driven arrays of quantum emitters. We characterize the steady-state phase diagram, with particular focus on the radiative properties in the steady state. Interestingly, we find that diverging from the well-established Dicke paradigm of equal all-to-all interactions significantly modifies the emission properties. In particular, the prominent quadratic scaling of the radiated light intensity with particle number in the steady state—a hallmark of steady-state Dicke superradiance—is entirely suppressed, resulting in only linear scaling with particle number. We show that this breakdown of steady-state superradiance occurs due to the emergence of additional dissipation channels that populate not only superradiant states but also subradiant ones. The additional contribution of subradiant dark states in the dynamics leads to a divergence in the time scales needed to achieve steady states. Building on this, we further show that measurements taken at finite times for extended atom ensembles reveal properties closely mirroring the idealized Dicke scenario. Published by the American Physical Society 2024
The recoil of atoms in arrays due to the emission or absorption of photons is studied for subwavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low-intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. They arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a subradiant collective decay is substantially larger than that from independent atom decay. A method to calculate the rate of recoil when steady state has been achieved with a constant influx of photons is also described.
Fully inverted atoms placed at exactly the same location synchronize as they deexcite, and light is emitted in a burst (known as "Dicke's superradiance"). We investigate the role of finite interatomic separation on correlated decay in mesoscopic chains and provide an understanding in terms of collective jump operators. We show that the superradiant burst survives at small distances, despite Hamiltonian dipole-dipole interactions. However, for larger separations, competition between different jump operators leads to dephasing, suppressing superradiance. Collective effects are still significant for arrays with lattice constants of the order of a wavelength, and lead to a photon emission rate that decays nonexponentially in time. We calculate the two-photon correlation function and demonstrate that emission is correlated and directional, as well as sensitive to small changes in the interatomic distance. These features can be measured in current experimental setups, and are robust to realistic imperfections.
We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.
The recoil of atoms in arrays due to the emission or absorption of photons is studied for subwavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low-intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. They arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a subradiant collective decay is substantially larger than that from independent atom decay.