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Accumulation phenomenon of dipole-dipole interaction induced by dark Rydberg atoms

Ko-Tang Chen, Bongjune Kim, Chia-Chen Su, Shih-Si Hsiao, Shou-Jou Huang, Wen-Te Liao, Ite A. Yu

Published Oct 13, 2021• 0 citations
OpenAlex

Abstract

We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light in a laser-cooled electromagnetically-induced-transparency (EIT) medium with the Rydberg state of $|32D_{5/2}\rangle$. The present effect of attenuation and distortion was caused by the dipole-dipole interaction between Rydberg atoms in a weak-interaction regime, i.e., the mean distance between Rydberg atoms was far greater than the dipole blockade radius. Our observation can be attributed to the atoms self-accumulated in dark Rydberg states other than those in the bright Rydberg state $|32D_{5/2}\rangle$ driven by the coupling field. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to dark Rydberg states. In the theoretical model, we included the decay process from the bright to dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. The systematic study presented in this work provides a better understanding of the Rydberg-EIT system.

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Increasing the decoherence rate of Rydberg polaritons due to accumulating dark Rydberg atoms

Ko-Tang Chen, Bongjune Kim, Chia-Chen Su +4 more

We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state $|32{D}_{5/2}\ensuremath{\rangle}$ in the weak-interaction regime. The present effect of attenuation and distortion cannot be explained by considering only the dipole-dipole interaction (DDI) between Rydberg atoms in $|32{D}_{5/2}\ensuremath{\rangle}$. Our observation can be attributed to the atoms in the dark Rydberg states rather than those in the bright Rydberg state, i.e., $|32{D}_{5/2}\ensuremath{\rangle}$, driven by the coupling field. The dark Rydberg states are all the possible states in which the population decaying from $|32{D}_{5/2}\ensuremath{\rangle}$ accumulated over time, and they were not driven by the coupling field. Consequently, the DDI between the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg polaritons. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to the dark Rydberg states. In the theoretical model, we included the decay process from the bright to the dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. This study points out an additional decoherence rate in the Rydberg-state electromagnetically induced transparency effect and provides a better understanding of the Rydberg-polariton system.

arXiv:2110.06600•Physical Review Research•Apr 8, 2022•4 citations

Nonlinear absorption and density-dependent dephasing in Rydberg electromagnetically-induced-transparency media

Martin Gärttner, Jörg Evers

Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.

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Effect of laser-frequency fluctuation on the decay rate of Rydberg coherence

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The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derive an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula is experimentally verified by using the $\mathrm{\ensuremath{\Lambda}}$-type EIT system of laser-cooled $^{87}\mathrm{Rb}$ atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also include the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\mathrm{\ensuremath{\Lambda}}$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\ensuremath{\mu}\mathrm{K}$, we study the decoherence rate in the Rydberg-EIT system involving the state of $|32{D}_{5/2}\ensuremath{\rangle}$. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}48$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.3$ MHz.

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The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

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Abstract The combination of Rydberg atoms and electromagnetically induced transparency (EIT) has been extensively studied in the strong-interaction regime. Here we proposed utilizing an EIT medium with a high optical depth (OD) and a Rydberg state of low principal quantum number to create a many-body system of Rydberg polaritons in the weak-interaction regime. The phase shift and attenuation induced by the dipole–dipole interaction (DDI) were still significant, and can be viewed as the consequences of elastic and inelastic collisions among Rydberg polaritons. We further observed that the width of the transverse momentum distribution of Rydberg polaritons at the exit of the system became notably smaller as compared with that at the entrance. The observation demonstrates the cooling effect in this system. The μs-long interaction time due to the high-OD EIT medium plus the μm2-size collision cross section due to the DDI suggests a feasible platform of polariton Bose–Einstein condensation.

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Electromagnetically Induced Transparency In Rydberg Atomic Medium

Li Deng, Cong Lu, Aixi Chen

Due to possessing big principal quantum number, Rydberg atom has some unique properties, for example: its radiative lifetime is long, dipole moment is large, and interaction between atoms is strong and so on. These properties make one pay attention to Rydberg atoms. In this paper we investigate the effects of Rydberg dipole-dipole interactions on electromagnetically induced transparency (EIT) schemes and group velocity in three-level systems of ladder type, which provides theoretical foundation for exploring the linear and nonlinear characteristics of light in a Rydberg electromagnetically-induced-transparency medium.

IOP Conference Series Materials Science and Engineering•Mar 1, 2018•2 citations
We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light in a laser-cooled electromagnetically-induced-transparency (EIT) medium with the Rydberg state of ∣32D5/2⟩|32D_{5/2}\rangle∣32D5/2​⟩. The present effect of attenuation and distortion was caused by the dipole-dipole interaction between Rydberg atoms in a weak-interaction regime, i.e., the mean distance between Rydberg atoms was far greater than the dipole blockade radius. Our observation can be attributed to the atoms self-accumulated in dark Rydberg states other than those in the bright Rydberg state ∣32D5/2⟩|32D_{5/2}\rangle∣32D5/2​⟩ driven by the coupling field. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to dark Rydberg states. In the theoretical model, we included the decay process from the bright to dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. The systematic study presented in this work provides a better understanding of the Rydberg-EIT system.
We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state $|32{D}_{5/2}\ensuremath{\rangle}$ in the weak-interaction regime. The present effect of attenuation and distortion cannot be explained by considering only the dipole-dipole interaction (DDI) between Rydberg atoms in $|32{D}_{5/2}\ensuremath{\rangle}$. Our observation can be attributed to the atoms in the dark Rydberg states rather than those in the bright Rydberg state, i.e., $|32{D}_{5/2}\ensuremath{\rangle}$, driven by the coupling field. The dark Rydberg states are all the possible states in which the population decaying from $|32{D}_{5/2}\ensuremath{\rangle}$ accumulated over time, and they were not driven by the coupling field. Consequently, the DDI between the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg polaritons. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to the dark Rydberg states. In the theoretical model, we included the decay process from the bright to the dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. This study points out an additional decoherence rate in the Rydberg-state electromagnetically induced transparency effect and provides a better understanding of the Rydberg-polariton system.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derive an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula is experimentally verified by using the $\mathrm{\ensuremath{\Lambda}}$-type EIT system of laser-cooled 87Rb^{87}\mathrm{Rb}87Rb atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also include the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\mathrm{\ensuremath{\Lambda}}$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\ensuremath{\mu}\mathrm{K}$, we study the decoherence rate in the Rydberg-EIT system involving the state of $|32{D}_{5/2}\ensuremath{\rangle}$. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}48$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.3$ MHz.
The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.
Abstract The combination of Rydberg atoms and electromagnetically induced transparency (EIT) has been extensively studied in the strong-interaction regime. Here we proposed utilizing an EIT medium with a high optical depth (OD) and a Rydberg state of low principal quantum number to create a many-body system of Rydberg polaritons in the weak-interaction regime. The phase shift and attenuation induced by the dipole–dipole interaction (DDI) were still significant, and can be viewed as the consequences of elastic and inelastic collisions among Rydberg polaritons. We further observed that the width of the transverse momentum distribution of Rydberg polaritons at the exit of the system became notably smaller as compared with that at the entrance. The observation demonstrates the cooling effect in this system. The μs-long interaction time due to the high-OD EIT medium plus the μm2-size collision cross section due to the DDI suggests a feasible platform of polariton Bose–Einstein condensation.
Due to possessing big principal quantum number, Rydberg atom has some unique properties, for example: its radiative lifetime is long, dipole moment is large, and interaction between atoms is strong and so on. These properties make one pay attention to Rydberg atoms. In this paper we investigate the effects of Rydberg dipole-dipole interactions on electromagnetically induced transparency (EIT) schemes and group velocity in three-level systems of ladder type, which provides theoretical foundation for exploring the linear and nonlinear characteristics of light in a Rydberg electromagnetically-induced-transparency medium.