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arXiv:2406.08856 · Atoms

Cooperative Decay of an Ensemble of Atoms in a One-Dimensional Chain with a Single Excitation

N. Piovella

Published Aug 28, 2024• 3 citations
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Abstract

We present an analytic calculation of the cooperative decay of a one-dimensional chain of N two-level atoms in the single-excitation configuration. Whereas the subradiant decay is zero for infinite lattices, we prove that for finite lattice the subradiant decay rate decreases as 1/N. We compare the results obtained using the scalar and the vectorial model. The calculations provide simple analytic expressions for the decay rate of the excitation, for arbitrary lattice spacing.

DOI
10.3390/atoms12090043

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We present an analytic calculation of the cooperative decay of a one-dimensional chain of N two-level atoms in the single-excitation configuration. Whereas the subradiant decay is zero for infinite lattices, we prove that for finite lattice the subradiant decay rate decreases as 1/N. We compare the results obtained using the scalar and the vectorial model. The calculations provide simple analytic expressions for the decay rate of the excitation, for arbitrary lattice spacing.
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Recently, the subradiant states of one-dimensional two-level atom chains coupled to light modes were found to have decay rates obeying a universal scaling, and an unexpected fermionic character of the multiply excited subradiant states was discovered. In this Letter, we theoretically obtain the singly excited subradiant states, and by eliminating the superradiant modes, we demonstrate a relation between the multiply excited subradiant states and the Tonks-Girardeau limit of the Lieb-Liniger model which explains the fermionic behavior. In addition, we identify a new family of subradiant states with correlations different from the fermionic ansatz.
We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.
Atomic arrays can exhibit collective light emission when the transition wavelength exceeds their lattice spacing. Subradiant states take advantage of this phenomenon to drastically reduce their overall decay rate, allowing for long-lived states in dissipative open systems. We build on previous work to investigate whether or not disorder can further decrease the decay rate of a singly excited atomic array. More specifically, we consider spatial disorder of varying strengths in a one-dimensional (1D) half waveguide and in 1D, two-dimensional (2D), and three-dimensional (3D) atomic arrays in free space and analyze the effect on the most subradiant modes. While we confirm that the dilute half waveguide exhibits an analog of Anderson localization, the dense half waveguide and free-space systems can be understood through the creation of close-packed, few-body subradiant states similar to those found in the Dicke limit. In general, we find that disorder provides little advantage in generating darker subradiant states in free space on average and will often accelerate decay. However, one could potentially change interatomic spacing within the array to engineer specific subradiant states.
We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance x21{x}_{21}x21​. We obtain collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, producing cooperative effects even when the atoms are far apart. The decay rates and the energy oscillate with the distance x21{x}_{21}x21​. Depending on x21{x}_{21}x21​, the decay rates will either decrease, vanish, or increase as compared with the one-atom decay rate. We have sub- and superradiance at periodic intervals. Our model may be used to study two-cavity electron waveguides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.