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Physical Review A

Resonances and excitation pathways in four-level N -scheme atomic systems

Tony Abi-Salloum, B. Henry, Jon P. Davis, Frank A. Narducci

Published Jul 26, 2010• 17 citations
Publisher

Abstract

In this work, we theoretically study the absorption and dispersion coefficients of a probe field in four-level N-scheme atomic systems driven by two additional fields. We separate the steady-state solution of the appropriate density matrix element into the sum of three resonances. The effect of each resonance on the overall absorption and dispersion experienced by the probe is studied as a function of the strengths of the two other fields. In the limit of low saturation, we reveal the physics of these resonances and associate them with atomic excitation pathways, which we explicitly explain in the bare-states picture.

DOI
10.1103/physreva.82.013834

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In this work, we theoretically study the absorption and dispersion coefficients of a probe field in four-level N-scheme atomic systems driven by two additional fields. We separate the steady-state solution of the appropriate density matrix element into the sum of three resonances. The effect of each resonance on the overall absorption and dispersion experienced by the probe is studied as a function of the strengths of the two other fields. In the limit of low saturation, we reveal the physics of these resonances and associate them with atomic excitation pathways, which we explicitly explain in the bare-states picture.
A four level `N-scheme' atomic system consists of a standard Λ EIT configuration with an additional level being driven by an additional switch field. We theoretically extend our earlier studies of this model to include a counter-propagating, weak probe field. Using a perturbation method, we first focus on an investigation of the dispersion experienced by the weak probe under a variety of conditions including cold and warm samples, as well as weak and strong switching fields. We find conditions in which the forward propagating probe field experiences normal dispersion while the backward propagating field experiences negative dispersion. We next turn to a similar study of absorption in this system and explore regions of high dispersion with vanishing absorption.
We motivate the study of an 'N-scheme' atomic system for the case of a bi-directional probe field. We derive the equations of motion. The equations were expanded in order of the counter-propagating field strength over the co-propagating field strength. We solve the equations numerically in steady state in a perturbative manner. The zeroth order solutions describe the dispersion and absorption of the co-propagating field, while the first order solutions describe the dispersion and absorption of the counter-propagating field. We investigate the solutions in two temperature regimes for a variety of field strengths. Regimes of similar dispersion for the co- and counter-propagating fields were found, as well as regimes of opposite behavior. In most cases, absorption of the fields is still a problem.
We discuss and analyze absorption-dispersion response for the probe field in a typical four-level atomic system with vacuum-induced coherence (VIC) arising from the cross coupling pathways associated with a pair of upper excited hyperfine levels. We find that VIC effect can preserve electromagnetically induced transparency (EIT) by using the detailed numerical simulations based on the density-matrix equations and analytical calculations in the dressed-state picture. We also show that the atomic hyperfine structure cannot be a hindrance to obtaining EIT.
We discuss and analyze absorption-dispersion response for the probe field in a typical four-level atomic system with vacuum-induced coherence (VIC) arising from the cross coupling pathways associated with a pair of upper excited hyperfine levels. We find that VIC effect can preserve electromagnetically induced transparency (EIT) by using the detailed numerical simulations based on the density-matrix equations and analytical calculations in the dressed-state picture. We also show that the atomic hyperfine structure cannot be a hindrance to obtaining EIT.
We discuss and analyze absorption-dispersion response for the probe field in a typical four-level atomic system with vacuum-induced coherence (VIC) arising from the cross coupling pathways associated with a pair of upper excited hyperfine levels. We find that VIC effect can preserve electromagnetically induced transparency (EIT) by using the detailed numerical simulations based on the density-matrix equations and analytical calculations in the dressed-state picture. We also show that the atomic hyperfine structure cannot be a hindrance to obtaining EIT.