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arXiv:1807.06877 · Physical Review A

Magic density in a self-rephasing ensemble of trapped ultracold atoms

Alexis Bonnin, Cyrille Solaro, Xavier Alauze, Franck Pereira dos Santos

Published Feb 27, 2019• 4 citations

Abstract

We investigate the collective spin dynamics of a self-rephasing bosonic ensemble of $^{87}\mathrm{Rb}$ trapped in a one-dimensional vertical optical lattice. We show that the combination of the frequency shifts induced by atomic interactions and inhomogeneous dephasing, together with the spin self-rephasing mechanism, leads to the existence of a ``magic density'': i.e., a singular operating point where the clock transition is first-order insensitive to density fluctuations. This feature is very appealing for improving the stability of quantum sensors based on trapped pseudo-spin-1/2 ensembles. Ramsey spectroscopy of the $|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=2,{m}_{F}=0\ensuremath{\rangle}$ hyperfine transition is in qualitative agreement with a numerical model based on coupled Bloch equations of motion for energy-dependent spin vectors.

DOI: 10.1103/physreva.99.023627

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We investigate the collective spin dynamics of a self-rephasing bosonic ensemble of

^{87}\mathrm{Rb}

trapped in a one-dimensional vertical optical lattice. We show that the combination of the frequency shifts induced by atomic interactions and inhomogeneous dephasing, together with the spin self-rephasing mechanism, leads to the existence of a ``magic density'': i.e., a singular operating point where the clock transition is first-order insensitive to density fluctuations. This feature is very appealing for improving the stability of quantum sensors based on trapped pseudo-spin-1/2 ensembles. Ramsey spectroscopy of the

|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=2,{m}_{F}=0\ensuremath{\rangle}

hyperfine transition is in qualitative agreement with a numerical model based on coupled Bloch equations of motion for energy-dependent spin vectors.

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of (87)Rb by applying the recently discovered spin self-rephasing [C. Deutsch et al., Phys. Rev. Lett. 105, 020401 (2010)]. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a stability of 2.4×10(-11)τ(-1/2), where τ is the integration time in seconds. Based on a set of technical improvements, the presented frequency standard is predicted to rival the stability of microwave fountain clocks in a potentially much more compact setup.

We perform Ramsey spectroscopy on the ground state of ultracold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 ± 12 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and may appear in other physical systems.

We perform Ramsey interferometry on an ultracold ^{87}Rb ensemble confined in an optical dipole trap. We use a π pulse set at the middle of the interferometer to restore the coherence of the spin ensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However, for high atomic densities, we observe the opposite behavior: the π pulse accelerates the dephasing of the spin ensemble leading to a faster contrast decay of the interferometer. We understand this phenomenon as a competition between the spin-echo technique and an exchange-interaction driven spin self-rephasing mechanism based on the identical spin rotation effect. Our experimental data are well reproduced by a numerical model.

We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 ± 12 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from the exchange interaction. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and may appear in other physical systems.

We present a compact atomic clock interrogating ultracold 87Rb magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5 s Ramsey time. The clock exhibits a fractional frequency stability of

5.8\times 10^{-13}

at 1 s and is likely to integrate into the

1\times10^{-15}

range in less than a day. A detailed analysis of 7 noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field (

5\times10^{-6}

relative fluctuations shot-to-shot) are the main noise sources together with the local oscillator, which is degraded by the 30% duty cycle. The analysis suggests technical improvements to be implemented in a future second generation set-up. The results demonstrate the remarkable degree of technical control that can be reached in an atom chip experiment.

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.