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arXiv:1909.10396 · Physical Review A

Theoretical study of a memory-based optical converter with degenerate Zeeman states

Pin-Ju Tsai, Yan-Cheng Wei, Bo‐Han Wu, Sheng-Xiang Lin, Ying-Cheng Chen

Published Dec 26, 2019• 4 citations
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Abstract

Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\ensuremath{\Lambda}}$ system and retrieving in another $\mathrm{\ensuremath{\Lambda}}$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\ensuremath{\sigma}}^{+}$-polarized pulse and retrieving with ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.

DOI
10.1103/physreva.100.063843

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Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system and retrieving in another \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a \ensuremathσ+{\ensuremath{\sigma}}^{+}\ensuremathσ+-polarized pulse and retrieving with \ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ\ensuremath− polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.
Memory-based optical polarization conversion in a double-Λ\LambdaΛ atomic system with degenerate Zeeman states
Abstract Optical memory based on the electromagnetically induced transparency (EIT) in a double- Λ\LambdaΛ Λ atomic system provides a convenient way to convert the frequency, bandwidth or polarization of an optical pulse by storing it in one Λ\LambdaΛ Λ channel and retrieving it from another. This memory-based optical converter can be used to bridge the quantum nodes which have different physical properties in a quantum network. However, in real atoms, each energy level usually contains degenerate Zeeman states, which may lead to additional energy loss, as has been discussed in our recent theoretical paper (Tsai et al. in Phys. Rev. A 100, 063843). Here, we present an experimental study on the efficiency variation in the EIT-memory-based optical polarization conversion in cold cesium atoms under Zeeman-state optical pumping. The experimental results support the theoretical predictions. Our study provides quantitative knowledge and physical insight useful for practical implementation of an EIT-memory-based optical converter.
We have studied the role of degenerate Zeeman states in the storage and retrieval of light pulses in the three-level $\ensuremath{\Lambda}$-type system of electromagnetically induced transparency. A probe pulse with the ${\ensuremath{\sigma}}_{+}$ polarization is stored in the medium and subsequently released with the ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarization. However, the manipulation of the retrieved polarization causes an energy loss. Our study shows that the incompatibility between the stored ground-state coherence and the ratio of the probe and coupling Clebsch-Gordan coefficients is responsible for the energy loss. Such energy loss can be avoided as long as all population accumulates in a single Zeeman state. We provide the useful knowledge for the light-storage technique and demonstrate that the degenerate Zeeman states should be considered in the relevant applications.
Quantum memories, devices that can store and retrieve photonic quantum states on demand, are essential components for scalable quantum technologies. It is desirable to push the memory towards the broadband regime in order to increase the data rate. Here, we present a theoretical and experimental study of broadband optical memory based on the electromagnetically induced transparency (EIT) protocol. We first provide a theoretical analysis of the issues and requirements needed to achieve broadband EIT memory. We then present our experimental efforts for the movement of EIT memory in cold atoms towards the broadband or short-pulse regime. A storage efficiency of $\ensuremath{\sim}80%$ with a pulse duration of 30 ns (corresponding to a bandwidth of 14.7 MHz) is realized. Due to limitations of the available intensity of the control beam, we could not achieve an optimal storage for the even shorter pulses but were still able to obtain an efficiency of greater than 5050%50 with a pulse duration of 14 ns (31.4 MHz). The time-bandwidth product achieved at an efficiency of 5050%50 is 1267(89).
We theoretically studied the implementation of a quantum memory and an optical transistor in a system composed by a single atom trapped inside a high finesse cavity. In order to store and map the quantum state of an input pulse onto internal states of the single atom (quantum memory) we employ the electromagnetically induced transparency (EIT) phenomenon (which can work out as an optical transistor) where the information can be transferred to the dark state of the atom modelled by a three-level system in a Λ-type configuration. In our model we consider a suitable temporal shape for the control field that ensures the adiabaticity of the storage process and retrieval of the probe pulse. The dynamic of the field inside the cavity was obtained by master equation approach, while the outside field was calculated by input-output formalism. We have analysed two different setups: i) two-sided and ii) single-sided cavities. While the first setup is the most appropriate and commonly used to observe cavity-EIT in the transmission spectrum, thus the best configuration for the optical transistor, the maximum quantum memory efficiency can not reach reasonable values, being limited to 50% for symmetric cavities. On the other hand, with single-sided cavity the quantum memory efficiency increases considerably and can reach values close to 100% in the strong atom-field coupling regime. However this specific setup is not favourable to observe the cavity-EIT effect in the transmission spectrum and then it is not appropriate to control the transmission of light pulses.
We report on a detailed theoretical investigation of optical information storage in an atomic ensemble modeled by a four-level N-type system, in a nonlinear regime of interaction, where one of the writing fields is large enough to saturate the optical transition. We study the optical pulse generated from a medium in condition of electromagnetically induced absorption (EIA) or electromagnetically induced transparency (EIT). We show that in the EIA condition the energy and the maximum intensity of the pulse extracted are much larger than in the EIT condition. When the information is stored in the EIA condition the full width at half maximum (FWHM) of the optical pulse generated is larger than when extracted in the EIT condition. The energy and maximum intensity of the optical pulse generated are found to have the same decay time whether the information was stored in EIA or EIT conditions. Our work demonstrates a higher efficiency in extracting energy in the saturated regime from an atomic memory based on EIA than from one in EIT condition.
We consider the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=1$ transition between the ground and excited hyperfine levels in alkali-metal vapor interacting with $\ensuremath{\sigma}$ linearly polarized control and probe fields whose polarizations can be either parallel or perpendicular to each other. We develop a matrix formulation that allows a solution of the Bloch equations to all orders in the pump and probe Rabi frequencies. Using this formalism, we calculate the steady-state probe absorption spectrum, the coherent population oscillations (CPOs), and two-photon coherence, in the absence (degenerate case) and presence (nondegenerate case) of a longitudinal magnetic field. We then calculate the probe storage when the pump is switched off and on again. We are particularly interested in whether the probe regains its original temporal shape when the pump is switched on again for the case of identical pump and probe frequencies. We show that, in the nondegenerate case, the restored probe does not regain its original shape whereas, in the degenerate case, the original shape is restored. This can be explained by considering the relative magnitudes of the CPOs which do not remember the temporal shape of the probe and the two-photon coherence oscillations which store the probe shape when the pump is switched off, as in electromagnetically induced transparency memories. In the nondegenerate case, the CPOs are much stronger than the two-photon coherence oscillations whereas, in the degenerate case, they are of similar magnitudes. Thus it is the two-photon coherence oscillations that are responsible for the restoration of the temporal shape of the probe in the degenerate case.