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Journal of Physics B Atomic Molecular and Optical Physics

Dephasing in sodium Ramsey interferometry under a weak inhomogeneous magnetic field

Keisuke Nakamura, Motoyuki Murakami, Atsuo Morinaga

Published Mar 17, 2015• 1 citation
Publisher

Abstract

Abstract In Ramsey interference of the clock transition of cold sodium atoms, we observed dephasing of the visibility, which was based on the frequency fluctuation due to the second-order Zeeman effect for inhomogeneity of the magnetic field within the atomic cloud. The frequency fluctuation was enhanced with increased strength of the quantization magnetic field, causing the dephasing of the visibility to become large. The theoretical dephasing function with frequency fluctuation was in good agreement with experimental values.

DOI
10.1088/0953-4075/48/7/075001

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Abstract In Ramsey interference of the clock transition of cold sodium atoms, we observed dephasing of the visibility, which was based on the frequency fluctuation due to the second-order Zeeman effect for inhomogeneity of the magnetic field within the atomic cloud. The frequency fluctuation was enhanced with increased strength of the quantization magnetic field, causing the dephasing of the visibility to become large. The theoretical dephasing function with frequency fluctuation was in good agreement with experimental values.
The $\ensuremath{\pi}$-phase shift between ∣F=1,mF=0⟩|F=1,{m}_{F}=0⟩∣F=1,mF​=0⟩ and ∣F=2,mF=0⟩|F=2,{m}_{F}=0⟩∣F=2,mF​=0⟩ states for an adiabatic rotation of a magnetic field observed in Ramsey atom interferometry arises from the negative sign of the transition amplitude between the ∣1,0⟩|1,0⟩∣1,0⟩ and ∣2,0⟩|2,0⟩∣2,0⟩ states when the wave functions are rotated to the opposite direction. Using a two-photon Raman atom interferometer with a cold ensemble of sodium atoms, the phase shift for a half-rotation of the magnetic field was confirmed to be $\ensuremath{\pi}\text{ }\text{rad}$ with an uncertainty of 4%, and the phase shift for a noncyclic adiabatic rotation of the magnetic field was investigated.
In this article, taking advantage of the special magnetic shieldings and the optimal coil design of a transportable Rb atomic fountain clock, the intensity distribution in space and the fluctuations with time of the quantization magnetic field in the Ramsey region were measured using the atomic magneton-sensitive transition method. In an approximately 310 mm long Ramsey region, a peak-to-peak magnetic field intensity of a 0.74 nT deviation in space and a 0.06 nT fluctuation with time were obtained. These results correspond to a second-order Zeeman frequency shift of approximately (2095.5±5.1)×10-17. This is an essential step in advancing the total frequency uncertainty of the fountain clock to the order of 10-17.
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Summary form only given. Spatial coherences are measured by means of a new atom interferometry technique. First, a coherent superposition of the Zeeman components of the atom is built by means of well-controlled magnetic interactions. Second, pulsed inhomogeneous magnetic fields are employed to coherently separate and reunite the atomic substates via the Stern-Gerlach induced forces. Finally, atomic interference fringes are recorded on the state-selected outcoming sample by changing the spatial separation. This method bears strong similarities with the Fourier-transform spectroscopy of light. The interferogram visibility curve yields the atom sample spatial coherences. For example, when the applied magnetic gradients are parallel to the atom trajectory, one gets the coherence length by varying the overlap of the separated wavepackets. Several experiments on cold cesium atoms have been performed and are presented. Furthermore, we have used our magnetic cooling method to prepare the atom cloud upstream from the interferometer. Large enhancements of the coherence length are demonstrated.
We investigate Ramsey interferometry for two separated fields oscillating with different frequencies. It is shown that the interplay between average and relative detuning leads to interference effects not present in the standard, single-frequency setup. For a large free-flight time of ground-state atoms before entering the first field region, the Ramsey fringes with respect to the relative detuning become much narrower than the usual ones. The stability of these effects with respect to phase or velocity fluctuations is discussed.
It has been proposed to use magnetically trapped atomic ensembles to enhance the interrogation time in microwave clocks. To mitigate the perturbing effects of the magnetic trap, near-magic-field configurations are employed, where the involved clock transition becomes independent of the atom's potential energy to first order. Still, higher order effects are a dominating source for dephasing, limiting the performance of this approach. Here we propose a simple method to cancel the energy dependence to both first and second order, using weak radio-frequency dressing. We give values for dressing frequencies, amplitudes, and trapping fields for 87Rb{}^{87}\mathrm{Rb}87Rb atoms and investigate quantitatively the robustness of these second-order-magic conditions to variations of the system parameters. We conclude that radio-frequency dressing can suppress field-induced dephasing by at least one order of magnitude for typical experimental parameters.