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International Electronic Conference on Applied Sciences (ASEC)

Multilevel Phase Switch Generation in Alkali Vapors

Abu Mohamed Alhasan, Salah Abdulrhmann

Published Dec 12, 2022• 1 citation
Publisher

Abstract

We attempt to demonstrate optical phase switches in a typical light storage experiment. We computed propagation dynamics of light pulses in sodium-23, rubidium-87, and potassium-39 vapors. These vapors have the same tensorial sets of the density matrix with a nuclear spin I = 3/2. The energy scheme is known as the double-Λ system. We considered an excitation mechanism in which one of two Λ systems was excited by two-color pulses, probe, and drive, following the standard electromagnetically induced transparency configuration. The probe channel contains delayed two pulses after the first probe pulse. Gain is generated through the drive channel and is exposed during propagation. We further investigated the spatiotemporal phase variations in the pulses and found discrete phase distribution for different vapors. The spatiotemporal evolution of the irreducible tensorial sets defines structural differential equations. Additionally, it is particularly suitable for parallel processing. We hope our study finds an application in comparison to alkali vapor magnetometry.

DOI
10.3390/asec2022-13849

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We attempt to demonstrate optical phase switches in a typical light storage experiment. We computed propagation dynamics of light pulses in sodium-23, rubidium-87, and potassium-39 vapors. These vapors have the same tensorial sets of the density matrix with a nuclear spin I = 3/2. The energy scheme is known as the double-Λ system. We considered an excitation mechanism in which one of two Λ systems was excited by two-color pulses, probe, and drive, following the standard electromagnetically induced transparency configuration. The probe channel contains delayed two pulses after the first probe pulse. Gain is generated through the drive channel and is exposed during propagation. We further investigated the spatiotemporal phase variations in the pulses and found discrete phase distribution for different vapors. The spatiotemporal evolution of the irreducible tensorial sets defines structural differential equations. Additionally, it is particularly suitable for parallel processing. We hope our study finds an application in comparison to alkali vapor magnetometry.
We theoretically demonstrated optical phase switches in light storage-like experiments. Typical light storage (LS) and retrieval experiments consist of the probe field in the probe channel with writing and reading fields across the drive branch, as well as its recovery. The probe and first drive pulses as the standard electromagnetically induced transparency (EIT) effect of storing light are used in the proposed scheme for the atomic excitations. A train of probe pulses is used after a short storage period to induce Raman gain in the drive channel. The proposed scheme was applied to alkali-metal atoms such as 23Na, 87Rb, and 39K vapours. Spatiotemporal phase variations for generated drive pulses were found to shape in the form of discrete phase distributions. The proposed approach in the process of obtaining phase discrete distributions for different irradiation intensities was tested. For weak fields, the discrete distributions were distinct as a result of the differences in the upper hyperfine structure (hf) and the atomic relaxations. However, for moderate fields, the discrete phase distributions are smeared by the atomic relaxations.
This paper describes a comparable study on the influence of frequency-sweep on the discrete and continuous phase distributions associated with pulse excitations for a double-lambda atomic system in alkali-metal vapours with a hyperfine structure. The excitation dynamics provided a different scheme of sigmoidal types, and the optical pulses were assumed to be Gaussians. We focused on the set-up of electromagnetically induced transparency (EIT). The phases of optical fields show similarities to discrete square wave distributions influenced by ramping. The results showed significant control of discrete phase distributions and temporal ramping by the implementation of sigmoidal membership functions. The relevant equations are the reduced Maxwell equations for the radiation fields, and the density matrix equation in the Liouville space governs the time evolution.
Electromagnetically induced transparency (EIT) has led to several quantum optics effects such as lasing without inversion or squeezed light generation. More recently quantum memories based on EIT have been experimentally implemented in different systems such as alkali metal atoms. In this system the excited state of the optical transition splits into several sublevels due to the hyperfine interaction. However, most of the theoretical models used to describe the experimental results are based on a Λ-system with only one excited state. In this article, we present a theoretical model for the Λ-type interaction of two light, fields and an atomic system with multiple excited state. In particular we show that if the control and probe fields are orthogonally circularly polarized the EIT effect in an alkali-metal vapor can almost disappears. We also identify the reasons of this reduction and propose a method to recover the transparency via velocity selective optical pumping.
In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.
Based in the effect of the Electromagnetically Induced Transparency (EIT) and the storage of light in atomic medium, we propose multi-wavelength optical pulse conversion. Starting from coupled Maxwell-Bloch equations, we simulate the propagation of the optical pulses resonant with electric dipole transition in the atomic system. Considering a three level Λ-type atomic system, we investigate the effect of the storage of light under EIT and we approach the wavelength conversion process using a double-Λ system. Generalizing the process for a triple-Λ system, we show the possibility of multi-wavelength conversion of a field previously stored in the atomic system. In this last case, we simulate the propagation of the six fields interacting resonantly, where three of the fields are called control fields and others are probe fields. First only two fields are incident in the medium, a probe Field and a control field, thus we establish the EIT regime. When we turn off the control field, the probe field is stored in the medium as a collective excitation between the lower energy levels which corresponds to a dark state of the atomic system. Depending on the choice of the control field which is turned on, we show that it is possible to store a field for a given a time and later to release it in differents wavelengths.
Through numerical simulations we show that the propagation of pairs of optical pulses in a double-\ensuremath{\Lambda} configuration is favorable for the attainment of electromagnetically induced transparency with matched pulses, even through a long absorbing sample. The double-\ensuremath{\Lambda} configuration allows a flexible and precise control of the amplitudes and phases for the propagating pulses. Different atomic and field configurations based on a double-\ensuremath{\Lambda} system in rubidium atoms have been explored.