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Physical Review Applied

Stabilizing two-photon frequency to reduce the decoherence rate of Rydberg-state electromagnetically induced transparency

Chia-Yu Hsu, Bongjune Kim, M. Xie, Ko-Tang Chen, Yu-Chih Tseng, M.-S. Chang, Ite A. Yu

Published Dec 16, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physrevapplied.22.064056

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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 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.
We herein develop and demonstrate a stable frequency-locking scheme for Rydberg atomic experiments. We use the Zeeman effect to modulate the three-level ladder-type Rydberg electromagnetically induced transparency (EIT) signal to lock the laser frequency of the coupling light for transition from its intermediate state to a Rydberg state. The effects of polarization of the probe and coupling lights, and the amplitude of the AC modulated magnetic field B 0 on the EIT and the corresponding dispersive error signal, are both analyzed. The results show that both the EIT signal and dispersive error signal are the strongest when the polarizations of coupling and probe fields are circular and equal. The signal-to-noise ratio of the dispersive error signal increases with B 0 . The slope of the dispersive error signal increases first and then decreases with B 0 , which is related to the increase of the EIT linewidth caused by the higher B 0 . The linewidth of the laser is significantly less than 500 kHz after frequency locking, which satisfies the requirements of most experiments involving Rydberg atoms. The method proposed herein can generally be applied to any cascade system of Rydberg atoms.
The power broadening of a coupling laser can be converted into two-photon detuning by electromagnetically induced transparency (EIT), resulting in a residual Doppler effect. The residual Doppler effect in a ladder-type EIT in a room-temperature atom ensemble is further amplified through a wavelength mismatch effect between the probe and coupling laser beams, which reduces the atomic coupling of light or microwaves. We measured the Rydberg spectra of the electric dipole (E1) and electric quadrupole (E2) microwave transitions, demonstrating that the reduction in the Rydberg EIT signal can be recovered through far-off-resonance E2 microwave transition dressing and achieving an 8-dB enhancement in the Rydberg EIT signal. The frequency-dependent dressing of the E2 transition enables the shift of the dressed Rydberg states to be tuned, thereby providing a scalable approach to optimize the interaction between the Rydberg state and microwave field.
We present a laser frequency locking to Rydberg transition with electromagnetically induced transparency (EIT) spectra in a room-temperature cesium vapor cell. Cesium levels 6S 1/2 , 6P 3/2 , and the n D 5/2 state, compose a cascade three-level system, where a coupling laser drives Rydberg transition, and probe laser detects the EIT signal. The error signal, obtained by demodulating the EIT signal, is used to lock the coupling laser frequency to Rydberg transition. The laser frequency fluctuation, ∼0.7 MHz, is obtained after locking on, with the minimum Allan variance to be 8.9 × 10 −11 . This kind of locking method can be used to stabilize the laser frequency to the excited transition.
Abstract Combination of the electromagnetically-induced-transparency (EIT) effect and Rydberg-state atoms has attracted great attention recently due to its potential application in the photon-photon interaction or qubit operation. In this work, we studied the Rydberg-EIT spectra with room-temperature 87Rb atoms. Spectroscopic data under various experimental parameters all showed that the contrast of EIT transparency as a function of the probe field intensity is initially enhanced, reaches a maximum value and then decays gradually. The contrast of spectral profile at the optimum probe field intensity is enhanced by 2–4 times as compared with that at weakest intensity. Moreover, the signal-to-noise ratio of the spectrum can potentially be improved by 1 to 2 orders of magnitude. We provided a theoretical model to explain this behavior and clarified its underlying mechanism. Our work overcomes the obstacle of weak signal in the Rydberg-EIT spectrum caused by an apparent relaxation rate of the Rydberg polariton and weak coupling transition strength, and provides the useful knowledge for the Rydberg-EIT study.
Frequency locking to reference atomic lines using Rydberg electromagnetically induced transparency (EIT) has been recently introduced as an inexpensive and reliable technique for laser frequency stabilization. In this work, we carry out a systematic study of this technique using heterodyne beat spectroscopy. Two different commercial semi-conductor lasers are locked to the same reference frequency using EIT locking, and their relative frequency stability is analyzed and continuously monitored in real time. A substantial improvement in the laser frequency stability is achieved through searching for the optimal proportional–integral settings and EIT probe laser powers. The results show that the cutoff frequency of the beat signal can be lowered to less than 500 kHz. We also compare the frequencies of free running lasers with that of a locked laser and characterize their frequency drifts. This study is important in assessing the use of Rydberg EIT locking in atomic electrometers.