Abstract
Atoms subject to weak coherent incident light can be treated as coupled classical linear oscillators, supporting subradiant and superradiant collective excitation eigenmodes. We identify the limits of validity of this \emph{linear classical oscillator model} at increasing intensities of the drive by solving the quantum many-body master equation for coherent and incoherent scattering from a chain of trapped atoms. We show that deviations from the linear classical oscillator model depend sensitively on the resonance linewidths $\upsilon_\alpha$ of the collective eigenmodes excited by light, with the intensity at which substantial deviation occurs scaling as a powerlaw of $\upsilon_\alpha$. The linear classical oscillator model then becomes inaccurate at much lower intensities for subradiant collective excitations than superradiant ones, with an example system of seven atoms resulting in critical incident light intensities differing by a factor of 30 between the two cases. By individually exciting eigenmodes we find that this critical intensity has a $\upsilon_\alpha^{2.5}$ scaling for narrower resonances and more strongly interacting systems, while it approaches a $\upsilon_\alpha^3$ scaling for broader resonances and when the dipole-dipole interactions are reduced. The $\upsilon_\alpha^3$ scaling also corresponds to the semiclassical result whereby quantum fluctuations between the atoms have been neglected. We study both the case of perfectly mode-matched drives and the case of standing wave drives, with significant differences between the two cases appearing only at very subradiant modes and positions of Fano resonances.
Highlights
Light incident on closely spaced resonators can scatter coherently multiple times between the resonators, resulting in strong lightmediated, long-range interactions
We explore light scattering from onedimensional atomic chains [9,10,12,13,37,38,39,40,41,42,43,64,65,66,67] of subwavelength-spaced two-level atoms via simulations of the full quantum many-body master equation
In a Mott-insulator state, demonstrating subradiant resonance narrowing [15]. By simulating both coherent and incoherent scattering for the atomic chain as a function of drive strength, we identify the regimes of validity of the linear classical oscillator model
Summary
Light incident on closely spaced resonators (atoms, metamolecules, quantum dots, etc.) can scatter coherently multiple times between the resonators, resulting in strong lightmediated, long-range interactions. In the limit of low light intensity, the model of the coupled linear classical oscillators for coherently driven two-level atoms. The precise limits of validity of the linear classical oscillator model and the onset of quantum fluctuations in the low-excitation regime have not been addressed in strongly coupled many-atom systems. In a Mott-insulator state, demonstrating subradiant resonance narrowing [15] By simulating both coherent and incoherent scattering for the atomic chain as a function of drive strength, we identify the regimes of validity of the linear classical oscillator model.
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