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Scientific Reports

Transport of Photonic Bloch Wave in Arrayed Two-Level Atoms

Chih-Chun Chang, Lee Lin, Guang-Yin Chen

Published Jan 18, 2018• 4 citations
Publisher

Abstract

In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.

DOI
10.1038/s41598-018-20023-x

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In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.
We investigate interactions between two (parallel) arrays of two-level atoms (2LA) via photons through quantum electrodynamical interaction with one array (the source array) connected to a particle source, and we study the (photo-)resistivity of the other array (the measured array). The wave function of the interacted photon propagating in an array is a Bloch wave with a gap in its eigenvalue (the photonic dispersion). Due to interactions between arrayed 2LA and the dressed photonic field with non-linear dispersion, the conduction behaviors of the measured array can be very diversified according to the input energy of the particle source connected to the source array, and their relative positions. As a result, the resistivity of the measured array can be zero or negative, and can also be oscillatory with respect to the incoming energy of the particle source of the source array, and the separation between arrays.
In a quantum electrodynamics (QED) system of arrayed two-level atoms interacting with light, because the energy of the photon is around the spacing between two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Our theoretical study shows that coherent phasing of atomic states occurs when the photons are in the attenuated mode. The existence of this ordered state is a result of a quantum phase transition induced by the mediation of the attenuated photonic field. By tuning the intensity of the light, the ordered state can be manipulated so that two-level atoms can be in an arbitrary uniform linear combination of the single-atom ground state and the excited state. Potential applications of this phenomenon are quantum computation, lasing physics, optical lattices and related subjects in nanotechnology. Similar phase transitions induced by the mediation of transmuted intermediate boson-like phonons, magnons or other fields may also occur in condensed-matter systems.
We present a unified and transparent theoretical framework for two longstanding phenomena in light-matter systems: collective emission and anomalous transport. Although both subjects have been extensively studied, we revisit them using a field-theoretical approach that solves the dressed Bloch wave functions of photons and electrons in an irradiated array of two-level atoms. This treatment reveals that the evolution of emission with irradiation frequency-from subradiance to superradiance-is directly encoded in the dressed photon momentum, which captures radiative decay and coherence. At the same time, photon-mediated interactions give rise to unconventional transport responses, including near-zero and even negative resistivity, whose microscopic origin can be consistently explained through the self-energy of the dressed electron. Framed in terms of Bloch polaritons, our results establish a direct link between radiative decay, cooperative interference, and transport anomalies, providing fresh insights into engineered light-matter platforms with tunable emission and transport properties.
Spontaneous emission from a two-level atom embedded in photonic crystals was investigated in this paper. Due to the photon localization and the quantum interference between the two dressed states, some changes in the radiation field take place: when the excited level moves from the gap to the band, the energy of the localized field is transferred to the propagating field through the diffusion field. If the localized field and the propagating field could coexist, the population evolution in the excited level would exhibit quasi-oscillation behavior. If they could not coexist, there would be no quasi-oscillation. The steady-state trapped atom population in the excited level is changed also. All these characteristics depend not only on the relative position δ of the excited level ω _1 with respect to the band-edge ω _c but also on the photon density of states ρ(ω_k) (or the band-edge smoothing parameter e ) near the band edge.
We investigate the interactions between an array of three-level atoms and two photon fields with distinct frequencies employing quantum electrodynamics (QED). The control beam, as expected, has a considerably higher intensity than the probe beam, and the probe photon's eigenstate notably then appears as a distinctive dressed Bloch wave. We calculate the dispersion relation and quantum amplitude of the probe photons for their transmission. At positions predicting electromagnetically induced transparency (EIT) phenomena, we unveil remarkable enhancements in the transmission of the probe beam. Crucially, these enhancements are intricately linked to the unique characteristics of the dressed Bloch wave eigenstate. Moreover, we demonstrate that modulating frequency and intensity of the control beam and the lattice constant would further tune these enhancements. Our study highlights the crucial role of the dressed Bloch wave eigenstate in substantially amplifying targeted light beams, thereby significantly enhancing the detection sensitivity for minute electromagnetic signals and emphasizing its pivotal role in unveiling intriguing phenomena.
We investigate spontaneous emission from a two-level atom embedded in photonic crystals. Due to the photon localization and the quantum interference between the two dressed states, some changes of the radiation field happen, and the energy is transferred among the excited atom, the localized field, the propagating field and the diffusion field. If there is a localized field, it appears quasi-oscillation behaves of the population evolution in the excited level. If there isn't a localized field, it appears no quasi-oscillation. Moreover, there have some steady-state trapped atom populations in the excited level, and the spontaneous emission spectrum near the forbidden gap edge is different from that in the vacuum. All these characteristics depend not only on the relative position of the excited level from the band-edge but also on the photon density of states (or the band-edge smoothing parameter) near the band edge.