Measurement of the time-domain Landau–Zener–Stückelberg–Majorana interference sidebands in an <sup>87</sup>Sr optical lattice clock
Authors: XIA Jingjing  , LIU Weixin  , ZHOU Chihua  , TAN Wei  , WANG Tao  , CHANG Hong  ,   1 Key Laboratory of Time Reference and Applications, National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;,   2 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China;,   3 Hefei National Laboratory, Hefei 230088, China;,   4 Department of Physics, Xinzhou Normal University, Xinzhou 034000, China;,   5 Department of Physics, and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing, 401331, China;,   6 Center of Modern Physics, Institute for Smart City of Chongqing University in Liyang, Liyang, 213300, China
Published: February 2025

Landau-Zener-Stückelberg-Majorana (LZSM) interference has significant application value in quantum state manipulation, extending quantum state lifetimes, and suppressing decoherence. Optical lattice clocks, with long coherence times, increases the likelihood of experimentally observing time-domain LZSM interference. While time-dominant Landau-Zener (LZ) Rabi oscillations have already been observed in optical lattice clock, the time-dominant LZSM interference sidebands in optical lattice clock remain unexplored. This paper is based on an <sup>87</sup>Sr optical lattice clock. By periodically modulating the frequency of the 698 nm clock laser and optimizing the parameters of the optical clock system, LZ transitions were achieved under the fast-passage limit (FPL). During the clock detection, two acoustic optical modulators (AOMs) were employed: AOM1 compensates for the frequency drift of the clock laser and operates continuously throughout the experiment, while AOM2 performs conventional clock transition detection and generates a cosine modulation signal using an external trigger from the RF signal generator in Burst mode. Ultimately, the periodically modulated 698nm clock laser with frequency of $\omega(t)=\cos \left[\int\left(\omega_p-A \omega_s \cos \omega_s t\right) d t\right]$ is used to probe atoms, and the Hamiltonian is $\hat{H}_{\vec{n}}(t)=\frac{h}{2}\left[\delta+A \omega_s \cos \left(\omega_s t\right)\right] \hat{\sigma}_z+\frac{h g_{\vec{n}}}{2} \hat{\sigma}_x$. As the modulated laser interacts with the atoms, exhibiting interference phenomena in the time domain, adjusting the clock laser detuning allows for probing the time-domain LZSM interference sideband spectra at different detection times. The results show that the time-domain LZSM interference sideband consists of multiple sidebands. Specifically, ±<i>kth</i> order sidebands can be observed at <i>δ</i>/<i>ω<sub>s</sub></i>=<i>k</i>, where <i>k</i> is an integer, indicating that constructive interference. Additionally, the excitation fraction of different sidebands varies due to the differing LZ Rabi oscillation periods for each sideband, leading to different excitation fraction for the sidebands at the same clock detection time. Scanning the frequency of the clock laser, when detection time is an integer period, small interference peaks appear next to the +1<i>st</i>, +4<i>th</i>, +5<i>th</i>, +6<i>th,</i> -3<i>th</i> and -4<i>th</i> order sidebands. These peaks all appear on the right side of the sidebands, breaking the symmetry of LZSM interference sidebands. In contrast, when the detection time is a half-integer period, the interference sidebands exhibit symmetric distribution. This phenomenon mainly arises from the effective dynamical phase accumulated during the LZSM interference evolution. Moreover, the excitation fraction is higher than that at half-integer, which holds potential application value in state preparation research. The experimental results are in excellent agreement with theoretical simulations, confirming the feasibility of conducting time-domain LZSM interference studies on the optical lattice clock. In the future, by further suppressing clock laser noise, the optical lattice clock will provide an ideal experimental platform for studying the effects of noise on LZ transition.