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Photonics & Electromagnetics Research Symposium - Spring (PIERS-Spring)

Collective behavior of multiple atoms in general electromagnetic environments: Dressed atom fields and bound states

Aiyin Y. Liu, Weng Cho Chew

Published May 1, 2017• 2 citations
Publisher

Abstract

The fully quantized Hamiltonian of multiple harmonic oscillator atoms coupled via dipole interaction to a general lossless electromagnetic environment is factorized into dressed atom fields. Both the rotating wave and counter rotating wave terms are considered. Atom field bound states are found and their effects on collective spontaneous emission studied.

DOI
10.1109/piers.2017.8262143

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The fully quantized Hamiltonian of multiple harmonic oscillator atoms coupled via dipole interaction to a general lossless electromagnetic environment is factorized into dressed atom fields. Both the rotating wave and counter rotating wave terms are considered. Atom field bound states are found and their effects on collective spontaneous emission studied.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
The spectrum of cooperative light emission from ensembles of multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The effects of counter-rotating terms are included using a unitary transformation method. The spectra are analyzed and interpreted in terms of the radiative eigenmodes of the atom ensemble. We further show how the qualitative features arise from the structure of the underlying two-particle dipole-dipole interaction induced by the the vacuum field. We predict that for a suitable modification of the ensemble properties, the sign of the cooperative Lamb shift can be reversed, while still maintaining strong superradiant emission. Finally, we discuss the effects of finite detection resolution and of averaging over many realizations of the random distribution of atoms for given ensemble parameters.
Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
We study the contributions of off-resonant transitions to the dynamics of a system of N multi-level atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The rotating wave approximation significantly simplifies the derivation of the equations of motion describing the collective atomic dynamics, but it leads to an incorrect expression for the dispersive part of the atom–atom interaction terms. For the case of two-level atoms and a scalar electromagnetic field, it turns out that the atom–atom interaction can be recovered correctly if integrals over the photon mode frequencies are extended to incorporate negative values. We explicitly derive the atom–atom interaction for multi-level atoms, coupled to the full vector electromagnetic field, and we recover also in this general case the validity of the results obtained by the extension to negative frequencies of the formulas derived with the rotating wave approximation.