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Temporal analog of Fabry-Pérot resonator via coherent population trapping

Ruihuan Fang, Chengyin Han, Xunda Jiang, Yuxiang Qiu, Yuanyuan Guo, Minhua Zhao, Jiahao Huang, Bo Lü, Chaohong Lee

Published Sep 30, 2021• 11 citations
Publisher

Abstract

Abstract Ramsey spectroscopy via coherent population trapping (CPT) is essential in precision measurements. The conventional CPT-Ramsey fringes contain numbers of almost identical oscillations and so that it is difficult to identify the central fringe. Here we experimentally demonstrate a temporal analog of Fabry–Pérot resonator via double-Λ CPT of laser-cooled 87Rb atoms. By inserting a periodic CPT pulse train between the two CPT-Ramsey pulses, due to the constructive interference of spin coherence, the transmission spectrum appears as a comb of equidistant peaks in frequency domain and thus the central Ramsey fringe can be easily identified. From the five-level Bloch equations for our double-Λ system, we find that the multi-pulse CPT interference can be regarded as a temporal analog of Fabry–Pérot resonator. Because of the small amplitude difference between the two Landé g factors, each peak splits into two when the external magnetic field is not too weak. This splitting is exactly linear with the magnetic field strength and thus can be used for measuring a magnetic field without involving magneto-sensitive transitions.

DOI
10.1038/s41534-021-00479-y

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Abstract Ramsey spectroscopy via coherent population trapping (CPT) is essential in precision measurements. The conventional CPT-Ramsey fringes contain numbers of almost identical oscillations and so that it is difficult to identify the central fringe. Here we experimentally demonstrate a temporal analog of Fabry–Pérot resonator via double-Λ CPT of laser-cooled 87Rb atoms. By inserting a periodic CPT pulse train between the two CPT-Ramsey pulses, due to the constructive interference of spin coherence, the transmission spectrum appears as a comb of equidistant peaks in frequency domain and thus the central Ramsey fringe can be easily identified. From the five-level Bloch equations for our double-Λ system, we find that the multi-pulse CPT interference can be regarded as a temporal analog of Fabry–Pérot resonator. Because of the small amplitude difference between the two Landé g factors, each peak splits into two when the external magnetic field is not too weak. This splitting is exactly linear with the magnetic field strength and thus can be used for measuring a magnetic field without involving magneto-sensitive transitions.
Ramsey spectroscopy via coherent population trapping (CPT) is essential in precision measurements. The conventional CPT-Ramsey fringes contain numbers of almost identical oscillations and so that it is difficult to identify the central fringe. Here, we experimentally demonstrate a temporal spinwave Fabry-Pérot interferometry via double-ΛΛΛ CPT of laser-cooled 87^{87}87Rb atoms. Due to the constructive interference of temporal spinwaves, the transmission spectrum appears as a comb of equidistant peaks in frequency domain and thus the central Ramsey fringe can be easily identified. From the optical Bloch equations for our five-level double-ΛΛΛ system, the transmission spectrum is analytically explained by the Fabry-Pérot interferometry of temporal spinwaves. Due to small amplitude difference between the two Landé factors, each peak splits into two when the external magnetic field is not too weak. This peak splitting can be employed to measure an unknown magnetic field without involving magneto-sensitive transitions.
We report the results of experimental investigation of the Raman – Ramsey method of pulsed excitation of coherent population trapping (CPT) resonances in a rubidium vapour cell filled with a mixture of Ar and Ne buffer gases. For the development of compact quantum microwave frequency standards, this method is an alternative to the pulsed optical pumping method recently implemented using the same rubidium cell. Both methods have advantages over the traditional double radio-optical resonance technique, the main of which is the substantial suppression of the light shift of the clock transition frequency, since the evolution of the coherence of atomic states forming the clock transition occurs in the absence of laser radiation in the cell. The narrow (110 – 240 Hz) Raman – Ramsey resonances are obtained using the scheme of pulsed excitation of CPT resonances on the D 1 lines of the 87 Rb atom with the same linear (lin||lin) polarisations of the bichromatic laser radiation components. The process of optimising the central fringe linewidth, its contrast, and the linewidth-to-contrast ratio is described. The magnetic dependence of the Raman – Ramsey line central fringe linewidth is experimentally investigated.
We describe an experiment which combines cold87Rb atoms from a grating magneto-optical trap (GMOT) with Lin±Lin coherent population trapping (CPT) and pulsed Ramsey interrogation. The bichromatic fields required for Lin±Lin are generated by combining light from a single external cavity diode laser (ECDL) with an electro-optic modulator (EOM) and an acousto-optic modulator (AOM). With this laser system and the GMOT, we are able to produce Raman-Ramsey fringes using either the F' = 1 or the F' = 2 excited states of the87Rb Di line. As a step towards realising a frequency standard based on the GMOT, we measure the Ramsey fringe amplitude as a function of the magnetic bias field and the excited state. We observe dark state interference with F'= 1 and show that this interference is suppressed with F' = 2, as expected from prior work on CPT with87Rb in thermal vapour cells.
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.