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arXiv:1902.09845 · Physical Review A

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

Bongjune Kim, Ko-Tang Chen, Chia-Yu Hsu, Shih-Si Hsiao, Yu-Chih Tseng, Chin-Yuan Lee, Shih-Lun Liang, Yi-Hua Lai, Julius Ruseckas, Gediminas Juzeliūnas, Ite A. Yu

Published Jul 9, 2019• 12 citations
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Abstract

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.

DOI
10.1103/physreva.100.013815

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Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.

•Jan 1, 2014•1 citation
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 \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-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 \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 \ensuremathμK\ensuremath{\mu}\mathrm{K}\ensuremathμK, we study the decoherence rate in the Rydberg-EIT system involving the state of ∣32D5/2\ensuremath⟩|32{D}_{5/2}\ensuremath{\rangle}∣32D5/2​\ensuremath⟩. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of 2\ensuremathπ\ifmmode×\else\texttimes\fi482\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}482\ensuremathπ\ifmmode×\else\texttimes\fi48 kHz at a moderate coupling Rabi frequency of 2\ensuremathπ\ifmmode×\else\texttimes\fi4.32\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.32\ensuremathπ\ifmmode×\else\texttimes\fi4.3 MHz.
Two-photon frequency stabilization is a critical step for experiments related to the Rydberg-state electromagnetically induced transparency (EIT) effect, as it exploits both the high optical nonlinearity of the EIT effect and the strong electric dipole-dipole interaction among Rydberg-state atoms. Fluctuations in the two-photon frequency cause decoherence in the Rydberg-EIT system, degrading its optical nonlinearity. Here, we propose and experimentally demonstrate a counterintuitive method to enhance the stability of the two-photon frequency of probe and coupling using atomic transitions. This method leverages increased probe power or intensity beyond the power broadening threshold. This improvement in the two-photon frequency stability consequently reduces the decoherence rate of Rydberg-EIT in laser-cooled atoms. By employing the double-resonance scheme with a moderate 480-nm coupling power of 64 mW or a Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.1$ MHz, the resulting fluctuation of the two-photon frequency lock was 170 kHz at an optimum 780 nm probe Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}15.6$ MHz. Concurrently, the observed frequency fluctuation-induced decoherence rate was $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}12$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.8$ MHz for the Rydberg-EIT transition with cold atoms. This work represents a pivotal advancement, as it furnishes sufficient stability in the two-photon frequency to meet the demands of most Rydberg-EIT applications.
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.
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.
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.
We perform spectroscopic measurements of electromagnetically induced transparency (EIT) in a strongly interacting Rydberg gas. We observe a significant spectral shift and attenuation of the transparency resonance due to the presence of interactions between Rydberg atoms. We characterize the attenuation as the result of an effective dephasing and show that the shift and the dephasing rate increase versus atomic density, probe Rabi frequency, and principal quantum number of Rydberg states. Moreover, we find that the spectral shift is reduced if the size of a Gaussian atomic cloud is increased and that the dephasing rate increases with the EIT pulse duration at large-parameter regimes. We simulate our experiment with a semianalytical model, which yields results in good agreement with our experimental data.
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.