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Applied Sciences

Multiple Phase Stepping Generation in Alkali Metal Atoms: A Comparative Theoretical Study

Abu Mohamed Alhasan, Abeer S. Altowyan, Aysh Y. Madkhli, Salah Abdulrhmann

Published Mar 13, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.3390/app13063670

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arXiv:quant-ph/0404018•Physical Review A•Nov 30, 2004•68 citations
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.
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.
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.
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 system with only one excited state. In this article, we present a theoretical model for the 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 iden tify the reasons of this reduction and propose a method to recover the transparency via velocity selective opti cal pumping. DOI: 10.1134/S0030400X1111021X Λ Λ COHERENT EFFECTS IN OPTICAL AND ATOMIC–MOLECULAR PROCESSES
This thesis set out to investigate light storage based on dynamic electromagnetically induced transparency (EIT) in a room-temperature atomic ensemble of rubidium as a means to provide a quantum memory for single-photons created by a single rubidium atom coupled to a high-finesse optical resonator. Setting up the light storage medium presented a new addition to the research group's portfolio of experimental techniques and led to investigations of EIT, slow light and stored light in warm rubidium-87 vapour. Lambda level schemes connecting Zeeman or hyperfine substates on the D1 and D2 lines were addressed in rubidium vapour cells containing different buffer gases and different isotopic fractions of rubidium-87 and rubidium-85. Single beam spectroscopy with a weak probe was used to characterise the vapour cells. A numerical method to fit the D line spectrum to a theoretical model to include isotopic fractions and collisional broadening of a buffer gas has been implemented. Temperature and isotopic fractions could be reliably extracted from the fit parameters. For an offset-stabilisation of two lasers to address a lambda level scheme connecting the two different hyperfine groundstates in rubidium a phase locked loop including a frequency divider has been designed and implemented. Light storage and retrieval has been demonstrated using a Zeeman scheme on the D1 line. Two microsecond long classical light pulses containing one million photons on average were stored and retrieved with an efficiency of 15% after a delay of one microsecond. Several methods of attenuating the strong co-propagating control laser beam to allow for lowering the signal pulse intensity in future experiments are discussed.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb^{87}\mathrm{Rb}87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.