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

arXiv:physics/0608024 · Physical Review A

Analysis of a magnetically trapped atom clock

Demascoth Kadio, Y. B. Band

Published Nov 8, 2006• 14 citations
arXivHTMLPDF

Abstract

We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.

DOI
10.1103/physreva.74.053609

Related papers

Analysis of a trapped atom clock with losses

Valentin Ivannikov

We present a number of analytical means for the analysis of the evolution of an atom clock, emphasizing the role of many-body processes in the population and coherence loss. A master equation with one-body and two-body losses included is presented for a thermal cloud ensemble, suitable for modelling atom clock evolution. Approximate solutions for the coupled rate equations with one-body and two-body losses are obtained for the case of Ramsey free evolution, and their validity is analyzed. An approach is suggested to combine the analytical trap-induced fringe envelope function with a numerically evaluated many-body envelope function. A set of Ramsey and spin echo models is offered with analytical solutions for the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. An interferometric fringe in long evolution experiments is typically measured with a visibility decay primarily due to phase diffusion, phase instability, trapping effects and many-body losses. It constitutes a problem to extract parameters from a fringe obtained in the time domain because of the growing uncertainty of the fringe amplitude and phase. This visibility loss can be compensated for systems with unequal state population losses, as the one we have, by tailoring the pulse durations. Methods are suggested for the one-body and many-body cases.A comprehensive set of experiments is conducted on the characterization of the stability of the trapped atom clock: with condensate and thermal cloud ensembles, with phase-domain Ramsey and spin echo interferometries, with synchronization from a rubidium frequency standard and from an oven-controlled quartz oscillator. The types of noise present in the system are identified by means of an Allan deviation analysis. Despite the 50 times different cloud densities of the condensate and the thermal clouds, an equality of the phase stability in the Ramsey interferometry with BEC and thermal clouds is demonstrated. The spin echo interferometry has shown a slightly superior stability with the thermal clouds as compared to the BEC.

•Jan 1, 2024•0 citations

Spin Waves and Collisional Frequency Shifts of a Trapped-Atom Clock

W. Maineult, Christian Deutsch, Kurt Gibble +2 more

We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.

arXiv:1204.1150•Physical Review Letters•Jul 13, 2012•31 citations

Preliminary results of the trapped atom clock on a chip

Clément Lacroûte, Friedemann Reinhard, F. Ramírez-Martínez +4 more

We present an atomic clock based on the interrogation of magnetically trapped (87)Rb atoms. Two photons, in the microwave and radiofrequency domain, excite the clock transition. At a magnetic field of 3.23 G the clock transition from |F = 1, m(F) = -1> to |F = 2, m(F) = 1> is 1st-order insensitive to magnetic field variations. Ramsey interrogation times longer than 2 s can be achieved, leading to a projected clock stability in the low 10(-13) at 1 s for a cloud of 10(5) atoms. We use an atom chip to cool and trap the atoms. A coplanar waveguide is integrated to the chip to carry the Ramsey interrogation signal, making the physics package as small as (5 cm)(3). We describe the experimental setup and show preliminary Ramsey fringes of line width 1.25 Hz.

IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control•Jan 1, 2010•20 citations

Preliminary results of the trapped atom clock on a chip

Clément Lacroûte, F. Ramírez-Martínez, P. Rosenbusch +4 more

We present an atomic clock based on the interrogation of magnetically trapped87Rb atoms. Two photons, in the microwave and radiofrequency domain excite the clock transition. At a magnetic field of 3.23 G the clock transition from |F=1, mF=-1rang to |F=2, mF=1rang is 1storder insensitive to magnetic field variations. Long Ramsey interrogation times can thus be achieved, leading to a projected clock stability in the low 10-13at 1 s. We use an atom chip to cool and trap the atoms. A coplanar waveguide has been integrated to the chip to carry the Ramsey interrogation signal, making the physics package as small as (5 cm)3. We describe the experimental setup and show preliminary Ramsey fringes of line width 1.25 Hz.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Apr 1, 2009•4 citations

Optically trapped atom interferometry using the clock transition of large87Rb Bose–Einstein condensates

P. A. Altin, Gordon McDonald, D. Döring +7 more

In our original paper (Altin et al 2011 New J. Phys. 13 065020), we presented the results from a Ramsey atom interferometer operating with an optically trapped sample of up to 10 6 Bose-condensed 87 Rb atoms in the m F = 0 clock states. We were unable to observe projection noise fluctuations on the interferometer output, which we attribute to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross–Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions accounts for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 × 10 4 atoms, we observe a coherence time of τ = 1.0 +0.5 −0.3 s.

New Journal of Physics•Nov 29, 2011•13 citations

Exploring the Use of Ramsey-CPT Spectroscopy for a Microcell-Based Atomic Clock

Clément Carlé, Michael Petersen, Nicolas Passilly +3 more

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 and$450~\mu \text{s}$, 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 of$450~\mu \text{s}$, a clock fractional frequency stability of$3.8 \times 10^{-12}$at 104s is obtained, in comparison with the level of$8\times 10^{-11}$obtained 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.

IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control•Jun 2, 2021•17 citations
We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.
We present a number of analytical means for the analysis of the evolution of an atom clock, emphasizing the role of many-body processes in the population and coherence loss. A master equation with one-body and two-body losses included is presented for a thermal cloud ensemble, suitable for modelling atom clock evolution. Approximate solutions for the coupled rate equations with one-body and two-body losses are obtained for the case of Ramsey free evolution, and their validity is analyzed. An approach is suggested to combine the analytical trap-induced fringe envelope function with a numerically evaluated many-body envelope function. A set of Ramsey and spin echo models is offered with analytical solutions for the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. the off-resonant and on-resonant regimes with one-body population loss and phenomenological dephasing. Their detuning spectra are presented and the difference between them and the standard Ramsey model is shown: the Rabi pedestal in the present model has no spectral ripples due to the pi/2-pulse duration equal to a quarter of a Rabi oscillation, even off resonance, in contrast to the Ramsey method where the pi/2-pulse duration is not corrected off resonance and causes spectral ripples. An interferometric fringe in long evolution experiments is typically measured with a visibility decay primarily due to phase diffusion, phase instability, trapping effects and many-body losses. It constitutes a problem to extract parameters from a fringe obtained in the time domain because of the growing uncertainty of the fringe amplitude and phase. This visibility loss can be compensated for systems with unequal state population losses, as the one we have, by tailoring the pulse durations. Methods are suggested for the one-body and many-body cases.A comprehensive set of experiments is conducted on the characterization of the stability of the trapped atom clock: with condensate and thermal cloud ensembles, with phase-domain Ramsey and spin echo interferometries, with synchronization from a rubidium frequency standard and from an oven-controlled quartz oscillator. The types of noise present in the system are identified by means of an Allan deviation analysis. Despite the 50 times different cloud densities of the condensate and the thermal clouds, an equality of the phase stability in the Ramsey interferometry with BEC and thermal clouds is demonstrated. The spin echo interferometry has shown a slightly superior stability with the thermal clouds as compared to the BEC.
We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.
We present an atomic clock based on the interrogation of magnetically trapped (87)Rb atoms. Two photons, in the microwave and radiofrequency domain, excite the clock transition. At a magnetic field of 3.23 G the clock transition from |F = 1, m(F) = -1> to |F = 2, m(F) = 1> is 1st-order insensitive to magnetic field variations. Ramsey interrogation times longer than 2 s can be achieved, leading to a projected clock stability in the low 10(-13) at 1 s for a cloud of 10(5) atoms. We use an atom chip to cool and trap the atoms. A coplanar waveguide is integrated to the chip to carry the Ramsey interrogation signal, making the physics package as small as (5 cm)(3). We describe the experimental setup and show preliminary Ramsey fringes of line width 1.25 Hz.
We present an atomic clock based on the interrogation of magnetically trapped87Rb atoms. Two photons, in the microwave and radiofrequency domain excite the clock transition. At a magnetic field of 3.23 G the clock transition from |F=1, mF=-1rang to |F=2, mF=1rang is 1storder insensitive to magnetic field variations. Long Ramsey interrogation times can thus be achieved, leading to a projected clock stability in the low 10-13at 1 s. We use an atom chip to cool and trap the atoms. A coplanar waveguide has been integrated to the chip to carry the Ramsey interrogation signal, making the physics package as small as (5 cm)3. We describe the experimental setup and show preliminary Ramsey fringes of line width 1.25 Hz.
In our original paper (Altin et al 2011 New J. Phys. 13 065020), we presented the results from a Ramsey atom interferometer operating with an optically trapped sample of up to 10 6 Bose-condensed 87 Rb atoms in the m F = 0 clock states. We were unable to observe projection noise fluctuations on the interferometer output, which we attribute to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross–Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions accounts for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 × 10 4 atoms, we observe a coherence time of τ = 1.0 +0.5 −0.3 s.
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.