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Advances in Physics X

Ramsey interferometry with cold atoms in coherent population trapping

Chengyin Han, Bo Lü, Chaohong Lee

Published Feb 23, 2024• 6 citations
Publisher

Abstract

The utilization of Ramsey interferometry via coherent population trapping (CPT), which enables the optical interrogation of microwave transitions without the reliance on microwave cavities, plays a crucial role in the advancement of compact and low-power quantum sensors. Particularly, high-resolution CPT-Ramsey spectroscopy of alkali-metal atoms has found extensive application in constructing miniaturized quantum sensors like atomic magnetometers and atomic clocks. Due to their well-defined environment and extended coherence time, cold atoms offer enhanced sensitivity and precision in CPT-Ramsey interferometry. This review comprehensively examines CPT-Ramsey interferometry with cold atoms, encompassing both conventional and multi-pulse techniques, and explores their potential applications in practical quantum sensors.

DOI
10.1080/23746149.2024.2317896

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The utilization of Ramsey interferometry via coherent population trapping (CPT), which enables the optical interrogation of microwave transitions without the reliance on microwave cavities, plays a crucial role in the advancement of compact and low-power quantum sensors. Particularly, high-resolution CPT-Ramsey spectroscopy of alkali-metal atoms has found extensive application in constructing miniaturized quantum sensors like atomic magnetometers and atomic clocks. Due to their well-defined environment and extended coherence time, cold atoms offer enhanced sensitivity and precision in CPT-Ramsey interferometry. This review comprehensively examines CPT-Ramsey interferometry with cold atoms, encompassing both conventional and multi-pulse techniques, and explores their potential applications in practical quantum sensors.
Coherent-population trapping (CPT) is a multilevel quantum coherence phenomenon of promising applications in atomic clocks and magnetometers. In particular, multipulse CPT Ramsey interferometry is a powerful tool for improving the performance of CPT atomic clocks. Most studies on multipulse CPT Ramsey interferometry consider periodic pulse sequence and time-independent detuning. However, to further improve the accuracy and precision, one may modify the spectrum symmetry which involves a pulse sequence with time-dependent detuning or phase shift. Here we theoretically analyze the multipulse CPT Ramsey interferometry under arbitrary pulse sequences of time-dependent detuning and obtain a general analytical formula. Using our formula, we analyze the popular CPT Ramsey interferometry schemes such as two-pulse symmetric and antisymmetric spectroscopy and multipulse symmetric and antisymmetric spectroscopy. Under periodic pulses, we quantitatively obtain the influences of pulse width, pulse period, pulse number, and Rabi frequency. Furthermore, we examine the impact of CPT pulses and Rabi frequency on the light shift in both two-pulse and multipulse CPT Ramsey interference. Our theoretical results can guide the experimental design to improve the performance of atomic clocks via multipulse CPT Ramsey interferometry.
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.
We investigate the application of Ramsey spectroscopy for the development of a microcell atomic clock based on coherent population trapping (CPT). The dependence of the central Ramsey-CPT fringe properties on key experimental parameters is first studied for optimization of the clock’s short-term frequency stability. The sensitivity of the clock frequency to light-shift effects is then studied. In comparison with the continuous-wave (CW) regime case, the sensitivity of the clock frequency to laser power variations is reduced by a factor up to 14 and 40.3 for dark times of 150 and450 μs450~\mu \text{s}450 μs, respectively, at the expense of intensity 3.75 times higher for short-term stability optimization. The dependence of the clock frequency on the microwave power is also reduced in the Ramsey case. We demonstrate that the Ramsey-CPT interrogation improves the clock Allan deviation for averaging times higher than 100 s. With a dark time of450 μs450~\mu \text{s}450 μs, a clock fractional frequency stability of3.8×10−123.8 \times 10^{-12}3.8×10−12at 104s is obtained, in comparison with the level of8×10−118\times 10^{-11}8×10−11obtained in the standard CW case, in similar environmental conditions. These results demonstrate that Ramsey-based interrogation protocols might be an attractive approach for the development of chip-scale atomic clocks (CSACs) with enhanced mid- and long-term stability.
Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in a variety of applications ranging from network synchronization and secure communications to GPS hold-over and inertial navigation. A cold-atom coherent population trapping (CACPT) clock featuring laser-cooled 87RB atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the principal frequency shifts can be controlled and the performance degradation associated with miniaturization can be overcome. In this thesis, research focused on the development of this type of compact atomic clock is presented. To address the low atom numbers obtained in small cold-atom sources, experiments were performed in which an atomic beam was decelerated with bichromatic stimulated laser forces and loaded into a mm-scale magneto-optical trap, increasing the atom number by a factor of 12.5x. A CACPT clock using the high-contrast lin||lin optical interrogation technique was developed and achieved a stability of 7 × 10-13 after one hour of integration. Doppler shifts in the clock are explained using a simple kinematic model and canceled by interrogating the atoms with a counter-propagating CPT configuration. Finally, a thorough characterization of the AC-stark effect in lin||lin CPT was performed. Observed shifts are explained in terms of contributions from coherent CPT-generating couplings and population transfer effects caused by optical pumping from incoherent light. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that reduces clock drift from light shifts to less than 10-14 for the current system.
Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $\perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ 5×10−11/τ5{\times}{10}^{-11}/\sqrt{\tau }5×10−11/τ​ with a projected quantum projection noise limit at the 10 − 13 / τ 10−13/τ{10}^{-13}/\sqrt{\tau }10−13/τ​ level.