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Physical Review A

Raman-Ramsey resonances in atomic vapor cells: Rabi pulling and optical-density effects

Salvatore Micalizio, Aldo Godone

Published Apr 26, 2019• 12 citations
Publisher

Abstract

Raman-Ramsey interference has proved a very effective technique to implement compact and high performing vapor cell frequency standards. In this paper, we theoretically characterize Raman-Ramsey resonances in an optically thick atomic vapor. Specifically, some parameters of interest for frequency standards applications, like contrast and linewidth of the central Raman-Ramsey fringe, are evaluated at different temperatures for $^{133}\mathrm{Cs}$ and $^{87}\mathrm{Rb}$ vapor cells with buffer gas. Density narrowing and broadening effects are described and explained in terms of a three-level theory where laser field propagation through the atomic medium is taken into account. Also, we investigate light shift both in low and high atomic density regimes. Light shift, which potentially degrades the medium- to long-term stability of Raman-Ramsey clocks, is composed of two contributions. The first is a pulling effect exerted by the wide Rabi profile enclosing the interference pattern on the central Raman-Ramsey fringe. The second light-shift term is strictly related to the detection time. Calculations derived from our model well describe already existing experimental results and new behaviors are predicted.

DOI
10.1103/physreva.99.043425

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Raman-Ramsey interference has proved a very effective technique to implement compact and high performing vapor cell frequency standards. In this paper, we theoretically characterize Raman-Ramsey resonances in an optically thick atomic vapor. Specifically, some parameters of interest for frequency standards applications, like contrast and linewidth of the central Raman-Ramsey fringe, are evaluated at different temperatures for 133Cs^{133}\mathrm{Cs}133Cs and 87Rb^{87}\mathrm{Rb}87Rb vapor cells with buffer gas. Density narrowing and broadening effects are described and explained in terms of a three-level theory where laser field propagation through the atomic medium is taken into account. Also, we investigate light shift both in low and high atomic density regimes. Light shift, which potentially degrades the medium- to long-term stability of Raman-Ramsey clocks, is composed of two contributions. The first is a pulling effect exerted by the wide Rabi profile enclosing the interference pattern on the central Raman-Ramsey fringe. The second light-shift term is strictly related to the detection time. Calculations derived from our model well describe already existing experimental results and new behaviors are predicted.
Determining light shift in Raman–Ramsey (RR) interference is important for the development of atomic frequency standards based on a vapor cell. We have accurately calculated light shift in RR interference using the density-matrix equations for a three-level system without invoking the adiabatic approximation. Specifically, phase shifts associated with coherent density-matrix terms are studied as they are relevant to the detection of RR interference in transmission (or absorption) through the medium. For the single-velocity case, the numerically computed results are compared with the analytical results obtained using the adiabatic approximation. The result shows light shift suppression in conformity with the closed-form analytic solutions. The computational studies have also been extended to investigate RR interference for a Doppler-broadened vapor medium. Importantly, a velocity-induced frequency shift is found at the fringe center as an additional source of frequency error for a vapor cell Raman clock.
We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature, and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed regime. We report also that the central fringe line-width is commonly narrower than the expected Ramsey line-width given by 1/(2TR), with TR the free-evolution time, for short values of TR. The clock demonstrates a short-term fractional frequency stability at the level of 2.3×10−13 τ−1/2 up to 100 s averaging time, mainly limited by the laser amplitude modulation noise. Comparable performances are obtained in the conventional continuous wave regime, with the use of an additional laser power stabilization setup. The pulsed interaction allows to reduce significantly the clock frequency sensitivity to laser power variations, especially for high values of TR. This pulsed CPT clock, ranking among the best microwave vapor cell atomic frequency standards, could find applications in telecommunication, instrumentation, defense or satellite-based navigation systems.
Pulsed coherent population trapping in atomic vapor provides a convenient method for generating frequency narrowed atomic resonance using Ramsey interference. Here, we present our experimental results showing high-contrast and sub-kilohertz Ramsey interference fringes produced by coherently prepared 85Rb atoms using Raman excitation formed in D1 line transitions. A test system for atomic clock has been constructed to measure light shift for both continuous and pulsed Raman excitation cases. Our measurements show that light shift measured using pulsed Raman excitation, is reduced compared to the continuous excitation case. Our ability to measure light shift is currently limited by the resolution of the frequency counter, and performance of the locking electronics used.
In this paper we describe a few phenomena that may affect the linewidth and/or the line shape of Ramsey fringes observed in an alkali-metal vapor cell with buffer gas. Experiments are performed on a vapor-cell--microwave-cavity arrangement in which 87Rb{}^{87}\mathrm{Rb}87Rb atoms successively experience laser pumping preparation (through a D2{D}_{2}D2​ line), microwave interrogation with a couple of coherent pulses, and clock signal detection by means of laser absorption. We show that the linewidth of the Ramsey central fringe is influenced by the Rabi pattern produced by a single microwave pulse. Moreover, cycle memory and atomic density effects can modify the shape of the Ramsey central fringe from the common sinusoidal behavior. A simple three-level model well reproduces the experimental observations.
The phenomenon of all-optical Ramsey interference using pulsed coherent population trapping (CPT) beams provides a new avenue for developing frequency standards using atomic vapor. In this study, we show that frequency narrowed Ramsey fringes can be produced in rubidium vapor without the effect of power broadening. We observed fringes of width as narrow as 1 kHz using a buffer-gas filled rubidium cell. A compact injection-locked laser (ILL) system was used to generate CPT beams. Studies also show that ac Stark effect on Ramsey fringes can be reduced, and higher frequency stability can be achieved in a clock application. The results are encouraging to propose an architecture for development of a pulsed CPT Ramsey clock. In this paper, we also provide related discussions on clock frequency stability, and our plans for future experiments.