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Results in Optics

The refractive index of a single atom experienced by a single photon

Yuri V. Rostovtsev, Jacob Emerick, Anil K. Patnaik

Published Oct 20, 2023• 8 citations
Publisher

Abstract

The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.

DOI
10.1016/j.rio.2023.100568

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The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
We study the propagation of a quantum field composed of a few photons interacting with a three-level Λ -atom driven by a coherent classical field. The quantum field acquires a phase shift, which can be interpreted as a dispersion effect on the photon wave packet and described by the refractive index for quantum fields down to the single-photon level. In this paper, we demonstrate that the phases acquired by quantum fields depend on the number of photons in the quantum states. Notably, the phases differ between single- and two-photon states, enabling the separation of multiphoton states. This finding highlights new applications related to the dispersion of three-level atoms, which are important in advancing quantum information processing and enhancing quantum communication technologies. The results are crucial for long-distance quantum communication and hold potential for developing quantum field-based linear devices such as beam splitters, lenses, and quantum prisms capable of separating different components of quantum fields. The findings can have interesting applications for manipulating and assembling of multiphoton entanglement states.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown, however, that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analysis to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level two-photon system but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
The propagation of quantum field interacting with a single two-level atom has been studied. Using the Gaussian quantum mode functions, we calculate evolution of the quantum state that includes atomic and field variable. We demonstrated the phase and group velocities of the single photon propagation that can be of great importance for long quantum communications. The results can be used for controlling quantum field propagation, and for design of optical elements such as a quantum prism and a quantum lens.
The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 1011{}^{11}11 atoms/cm3{}^{3}3 and detunings of order 1011{}^{11}11 s${}^{\ensuremath{-}1}$, both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.
The two-level atom can, for good reason, be considered the basic material structure for the study of quantum optics [1]. The two-level atom has played a fundamental role in studies of physical processes, including self-induced transparency (SIT), photon echoes, optical nutation, saturation spectroscopy, and, most recently, slow- and fast-light research. This latter field has recently been the subject of great activity, as researchers have learned how to utilize various physical processes to exert control over the velocity of propagation of light pulses through material systems [2]. This interest stems both from the intellectual intrigue in situations in which the velocity of light can be speeded up or slowed down by many orders of magnitude and the promise that such techniques might be useful for applications in fields such as telecommunications and optical computing [3‐6]. Most of the recent work in this field has made use of the process of electromagnetically induced transparency (EIT) to induce a narrow transparency region in an otherwise highly absorbing optical material [7, 8]. The rapid variation of the refractive index n associated with this transparency window then leads to a strong modification of the group velocity n g in accordance with the standard relation