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arXiv:2505.13146 · Physical Review Letters

Exponential Linewidth Narrowing and Enhancement of Sensitivity in Ramsey Interferometry with an Optically Thick Ensemble of Atoms

Sergey A. Moiseev, K. I. Gerasimov, Mansur M. Minnegaliev, Ivan Brekotkin, E. S. Moiseev

Published May 20, 2026• 0 citations
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Abstract

Ramsey resonance is a high-resolution technique used in spectroscopy, precise measurement of time and frequency, and the creation of modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid backaction of atoms on excitation pulses. In contrast to latter belief, we predict and experimentally show that in optically thick resonant media, the backaction can lead to the highly enhanced narrowing of Ramsey resonance. The linewidth narrowing and corresponding precision of the frequency measurement scale exponentially with an increase in optical depth of a sample and can reach the limits set by homogeneous broadening. We show that this effect is caused by a nonlinear interference of multiple echoes formed inside the atomic medium, which is experimentally confirmed with ^{167}Er^{3+} ions in Y_{2}SiO_{5} crystal. Our findings open new opportunities for sensitivity enhancement of the Ramsey technique, as well as providing researchers with an additional method to investigate fundamental issues of coherent nonlinear interaction of light pulses with resonant atomic ensembles and numerous applications.

DOI
10.1103/bqzh-gy4n

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Ramsey resonance is a high-resolution technique used in spectroscopy, precise measurement of time and frequency, and the creation of modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid backaction of atoms on excitation pulses. In contrast to latter belief, we predict and experimentally show that in optically thick resonant media, the backaction can lead to the highly enhanced narrowing of Ramsey resonance. The linewidth narrowing and corresponding precision of the frequency measurement scale exponentially with an increase in optical depth of a sample and can reach the limits set by homogeneous broadening. We show that this effect is caused by a nonlinear interference of multiple echoes formed inside the atomic medium, which is experimentally confirmed with ^{167}Er^{3+} ions in Y_{2}SiO_{5} crystal. Our findings open new opportunities for sensitivity enhancement of the Ramsey technique, as well as providing researchers with an additional method to investigate fundamental issues of coherent nonlinear interaction of light pulses with resonant atomic ensembles and numerous applications.
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.
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.
Ramsey spectroscopy serves as a key tool for frequency measurement. Although entanglement can enhance the measurement precision, the atom-atom interaction required for entanglement generation may lead to a frequency shift. In addition, the spectra also suffer from light shift caused by the interaction between light and atoms. Thus, it is difficult to achieve high precision without inducing additional systematic errors. Here, we propose to realize high-precision entanglement-enhanced Ramsey spectroscopy with composite pulses. First, we utilize spin-squeezed states generated by one-axis twisting (OAT) dynamics to enhance the measurement precision. We find that by applying a suitable pulse after OAT, the resonant frequency can be inferred and the light shift can be reduced by using composite pulses. To increase the signal slope, we use anti-OAT dynamics to perform interaction-based readout after interrogation. By designing suitable composite pulses, it can significantly increase the signal response and further improve the measurement precision. Although both schemes can mitigate the light shift, it cannot be entirely eliminated. Thus, we develop the autobalanced entanglement-enhanced Ramsey spectroscopy. By using combination of different sequences with short and long interrogation times and feedback control, the light shift of both our protocols can be completely suppressed, which increases the measurement accuracy. Besides, we also investigate the effects of background atom-atom interaction and find that it only reduces the measurement precision without introducing additional frequency shift. Our study offers an alternative method for achieving precise frequency measurement, which has the potential to be of significant application in quantum sensors such as atomic clocks.
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Rydberg Raman-Ramsey (R3{}^33) resonances in atomic vapor
The sensitivity of electric field sensors based on two-photon electromagnetically induced transparency (EIT) involving highly excited Rydberg states in thermal atoms is often limited by the residual Doppler effect and optical power broadening. Here, we propose a method to reduce the EIT spectral linewidth using a Ramsey interrogation approach, allowing multiple interrogations of atomic coherence, using either temporally or spatially separated laser beams. Our theoretical calculations predict that the linewidth of such Raman-Ramsey spectral features can be substantially reduced compare to a standard Doppler-broadened EIT, opening a possibility to improved sensitivity of Rydberg atomic vapor-based sensors. We also discuss some preliminary experimental efforts toward observing Raman-Ramsey resonances for both spatially and temporally separated interrogation approaches and associated technical challenges.
We propose an effective method to decrease the Ramsey linewidth of microwave atomic clock by tracking the coherent atomic phase through nondestructive measurement. The free evolution time T between two Ramsey pulses is divided into N subsections. In each subsection, the coherent phase of the atomic ensemble is probed by an additional large-detuning laser. The probed phase in the previous subsection is used to change the phase of the microwave pulse in the following subsection. After tracking the coherent atomic phase for N-1 times, the final linewidth of Ramsey fringe decreases quickly as N/(2N-1). We then demonstrate this proposal in a vapor cell atomic clock. The linewidth of the Ramsey fringe is decreased down to 27 Hz after 5 successive sub-interrogations, which is much narrower than the linewidth of 142 Hz obtained by normal Ramsey spectroscopy.