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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Dispersion in a four level N-scheme atomic system with co- and counter- propagating beams

Jon P. Davis, Frank A. Narducci

Published Feb 7, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.914722

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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.
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.
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.
In this paper, we investigate theoretically the effect of the relative phase ($\ensuremath{\phi}$) between the probe and driving fields on gain (absorption) and dispersion of the probe field in a Doppler-broadened NNN-type four-level system with spontaneously generated coherence from different respects. It is shown that gain (absorption) and dispersion are very sensitive to variations in the relative phase, and changing the Doppler width also has an obvious effect on the phase-dependent gain (absorption) and dispersion. When the probe and driving fields have the same propagation directions (copropagating), for the same Doppler width, the dispersion curve with $\ensuremath{\phi}=\ensuremath{\alpha}$ is the same as the gain (absorption) curve with $\ensuremath{\phi}=\ensuremath{\alpha}+\ensuremath{\pi}/2$; however, when the probe and driving fields have opposite propagation directions (counterpropagating), the dispersion curve and gain (absorption) curve are different and the difference becomes more considerable with an increase in Doppler width. In the co- and counterpropagating cases, gain (absorption) and dispersion always vary periodically with varying $\ensuremath{\phi}$, and the period is 2\ensuremath{\pi}. By adjusting the value of $\ensuremath{\phi}$, the largest gain (absorption) and dispersion can be obtained, and a large index of refraction without absorption can be realized. Generally speaking, gain decreases with an increase in Doppler width, but by adjusting value of $\ensuremath{\phi}$, at some special values of Doppler width, a larger gain than that without Doppler broadening can be obtained. Our study also shows that gain in the copropagating case is much larger than that in the counterpropagating case.
In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.
A numerical method is introduced that solves the optical Bloch equations describing a two-level atom interacting with a strong polychromatic pump field with an equidistant spectrum and an arbitrarily intense monochromatic probe field. The method involves a transformation of the optical Bloch equations into a system of equations with time-independent coefficients at steady state via double harmonic expansion of the density-matrix elements, which is then solved by the method of matrix inversion. The solutions so obtained lead immediately to the determination of the polarization of the atomic medium and of the absorption and dispersion spectra. The method is applied to the case when the pump field is bichromatic and trichromatic, and the physical interpretation of the numerically computed spectra is given.