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Frontiers in Optics

Stimulated Emission from a Two-Level Atom Coupled to a Waveguide

Eden Rephaeli, Shanhui Fan

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We study stimulated emission from a two-level atom coupled to a waveguide containing an incident single photon pulse. By replacing the atom with a side-coupled cavity we show that the strong photon-photon interaction induced by the atom plays a very crucial role in the stimulated emission process.
DOI
10.1364/fio.2012.fth3b.6

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Stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. Hence, the two outgoing photons are identical. In a waveguide or free space, this intuition is typically found through Fermi's Golden rule, however, this does not properly account for the wave-like nature of the photons. Here, I present an exact solution to stimulated emission from a quantum two-level atom that properly accounts for the incoming and outgoing electromagnetic modes. This result is valid over a huge range of incident photon numbers. For a single incident photon, it shows how the photon must properly mode match the two-level system to cause stimulated emission. For a Fock state drive with large photon number, the exact solution shows how a two-level system Rabi oscillates with the traveling Fock mode as it passes by. I additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two-level system's state factorizes with the electromagnetic field's coherent state. Recent advances in superconducting circuits make them an ideal platform to test these predictions.
We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherent-state photon pulse. We provide an analytical result when a short πππ pulse is incident, which shows that the atoms emit photons coherently into the output pulse, which remains a coherent state in the short pulse limit. An incident pulse is amplified in phase-preserving manner, where noise is added almost entirely in the phase direction in phase space. This property improves the ratio of intensity signal to noise after the amplification for sufficiently short pulses. This is a unique feature different from general phase-preserving linear amplifiers, where the signal-to-noise ratio deteriorates in the amplification process. We also discuss the dependence of the photon-emission probability on pulse parameters, such as the pulse area and the duration.
The area of waveguide quantum electrodynamics plays a signi cant role in many quantum technology applications. Photonic waveguides can be used to coherently transport photon pulses and can also efficiently increase the light-matter interaction strength. The work is done by Shen and Fan [1, 2] on the propagation of a photon pulse in a 1-D waveguide coupled to a single two-level emitter shows that a photon pulse can undergo complete reflection or transmission through the waveguide by controlling the coupling strength between the atom and the guided photon. We propose a V-type atomic system embedded in a 1-D waveguide and study the properties of an incoming photon pulse in the waveguide. We show that the driving field, which couples one of the atomic transitions, can be used as a controlling parameter to allow the photon pulse to be reflected or transmitted through the waveguide. As there reflection and transmission of the incident photon pulse can be externally controlled in our system, in comparison to the system suggested by Shen and Fan [1, 2], the proposed system in this thesis is more practiced than the system [1, 2]