Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Multiple π/2 pulse area operation of caesium fountains and the collisional frequency shift

S. Weyers, R. Wynands, K. Szymaniec, Witold Chałupczak

Published May 1, 2007• 2 citations
Publisher

Abstract

Typically, primary fountain frequency standards are tested at elevated microwave powers in order to check for potential frequency shifts due to, e.g., microwave leakage or cavity phase gradients. Usually such tests are performed at nπ/2 microwave pulse area (n an odd integer), where the microwave power is set to these values typically by maximizing the contrast of the central Ramsey fringe. We have experimentally demonstrated that in this case for different n a varying clock state composition after the first Ramsey interaction can be obtained, if the average microwave power seen by the expanding atom cloud is different during the first and the second transition through the Ramsey cavity. In the presence of a clock state composition dependent collisional shift, this effect gives rise to different collisional shifts for operation at different nπ/2 pulse area.

DOI
10.1109/freq.2007.4319029

Related papers

Cancellation of the Collisional Frequency Shift in Caesium Fountain Clocks

K. Szymaniec, Witold Chałupczak, Eite Tiesinga +3 more

We have observed that the collisional frequency shift in primary caesium fountain clocks varies with the clock state population composition and, in particular, is zero for a given fraction of the |F=4,mF=0) atoms, depending on the initial cloud parameters. We present a theoretical model explaining our observations. The possibility of the collisional shift cancellation implies an improvement in the performance of caesium fountain standards and a simplification in their operation.

Physical Review Letters•Apr 13, 2007•69 citations

Recoil effects in microwave atomic frequency standards: preliminary results

Peter Wolf, S. Bize, Andr  Clairon +4 more

We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). We use an interferometric description to model the frequency standards, treating simultaneously internal and external degrees of freedom. We consider multiple momentum exchanges in 3D between the atoms and the standing microwave field inside the cavity leading to a large number of wave packets that leave the cavity with different momenta. At detection, these wave packets interfere giving rise to Ramsey fringes that are modulated by the interference of the external states of the wave packets. Similar treatments have proved efficient when treating ID recoil effects in standing laser waves. We apply this theoretical model numerically to laser cooled atomic fountain frequency standards and investigate the behaviour of the observed signal as a function of the frequency standard parameters (microwave power, launching height, etc.). Finally, we discuss possible experimental methods that could be used to observe such effects.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Nov 13, 2002•1 citation

s -Wave Collisional Frequency Shift of a Fermion Clock

E.L. Hazlett, Yi Zhang, Ronald W. Stites +2 more

We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.

arXiv:1212.4385•Physical Review Letters•Apr 15, 2013•20 citations

Investigations on Microwave Power Shift in Compact Vapor-Cell Atomic Clock

William Moreno, Matthieu Pellaton, Nil Almat +3 more

We employ a three-level Bloch vector model to simulate Ramsey fringes of our Rb vapor-cell atomic clock. The residual inhomogeneity of the microwave magnetic field across the buffer-gas cell is a key ingredient for correctly modelling the behavior at high microwave powers (pulse area > π/2. We add to this model different position-dependent frequency shifts that arise from external fields, and we identify inhomogeneous light-shifts as the dominant contribution for reproducing the measured clock frequency shifts as a function of microwave power. Other frequency shifts give negligible contributions.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Apr 1, 2019•2 citations

Ramsey Spectroscopy with Displaced Frequency Jumps

M. Shuker, J. W. Pollock, Rodolphe Boudot +4 more

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.

arXiv:1812.01703•Physical Review Letters•Mar 19, 2019•38 citations

Free expanding cloud of cold atoms as an atomic standard: Ramsey fringes contrast

Stella Müller, Daniel Varela Magalhães, Aida Bebeachibuli +3 more

A compact frequency standard based on an expanding cold Cs133 cloud is under development in our laboratory. In a first experiment, Cs cold atoms were prepared by a magneto-optical trap in a vapor cell, and a microwave antenna was used to transmit the radiation for the clock transition. The signal obtained from fluorescence of the expanding cold atoms cloud is used to lock a microwave chain. In this way the overall system stability is evaluated. A theoretical model based on a two-level system interacting with the two microwave pulses enables interpretation for the observed features, especially the poor Ramsey fringes contrast.

Journal of the Optical Society of America B•May 14, 2008•9 citations
Typically, primary fountain frequency standards are tested at elevated microwave powers in order to check for potential frequency shifts due to, e.g., microwave leakage or cavity phase gradients. Usually such tests are performed at nπ/2 microwave pulse area (n an odd integer), where the microwave power is set to these values typically by maximizing the contrast of the central Ramsey fringe. We have experimentally demonstrated that in this case for different n a varying clock state composition after the first Ramsey interaction can be obtained, if the average microwave power seen by the expanding atom cloud is different during the first and the second transition through the Ramsey cavity. In the presence of a clock state composition dependent collisional shift, this effect gives rise to different collisional shifts for operation at different nπ/2 pulse area.
We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). We use an interferometric description to model the frequency standards, treating simultaneously internal and external degrees of freedom. We consider multiple momentum exchanges in 3D between the atoms and the standing microwave field inside the cavity leading to a large number of wave packets that leave the cavity with different momenta. At detection, these wave packets interfere giving rise to Ramsey fringes that are modulated by the interference of the external states of the wave packets. Similar treatments have proved efficient when treating ID recoil effects in standing laser waves. We apply this theoretical model numerically to laser cooled atomic fountain frequency standards and investigate the behaviour of the observed signal as a function of the frequency standard parameters (microwave power, launching height, etc.). Finally, we discuss possible experimental methods that could be used to observe such effects.
We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.
We employ a three-level Bloch vector model to simulate Ramsey fringes of our Rb vapor-cell atomic clock. The residual inhomogeneity of the microwave magnetic field across the buffer-gas cell is a key ingredient for correctly modelling the behavior at high microwave powers (pulse area > π/2. We add to this model different position-dependent frequency shifts that arise from external fields, and we identify inhomogeneous light-shifts as the dominant contribution for reproducing the measured clock frequency shifts as a function of microwave power. Other frequency shifts give negligible contributions.
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.
A compact frequency standard based on an expanding cold Cs133 cloud is under development in our laboratory. In a first experiment, Cs cold atoms were prepared by a magneto-optical trap in a vapor cell, and a microwave antenna was used to transmit the radiation for the clock transition. The signal obtained from fluorescence of the expanding cold atoms cloud is used to lock a microwave chain. In this way the overall system stability is evaluated. A theoretical model based on a two-level system interacting with the two microwave pulses enables interpretation for the observed features, especially the poor Ramsey fringes contrast.