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arXiv:1410.8171 · Physical Review A

Controlling the magnetic-field sensitivity of atomic-clock states by microwave dressing

L. Sárkány, P. Weiss, H. Hattermann, József Fortágh

Published Nov 13, 2014• 53 citations
arXivHTMLPDF

Abstract

We demonstrate control of the differential Zeeman shift between clock states of ultracold rubidium atoms by means of nonresonant microwave dressing. Using the dc field dependence of the microwave detuning, we suppress the first- and second-order differential Zeeman shift in magnetically trapped $^{87}\mathrm{Rb}$ atoms. By dressing the state pair $5{S}_{1/2}$ $F=1$, ${m}_{F}=\ensuremath{-}1$ and $F=2$, ${m}_{F}=1$, a residual frequency spread of $<0.1$ Hz in a range of 100 mG around a chosen magnetic offset field can be achieved. This is one order of magnitude smaller than the shift of the bare states at the magic field of the Breit-Rabi parabola. We further identify double magic points, around which the clock frequency is insensitive to fluctuations both in the magnetic field and in the dressing Rabi frequency. The technique is compatible with chip-based cold-atom systems and allows the creation of clock and qubit states with reduced sensitivity to magnetic-field noise.

DOI
10.1103/physreva.90.053416

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We demonstrate control of the differential Zeeman shift between clock states of ultracold rubidium atoms by means of nonresonant microwave dressing. Using the dc field dependence of the microwave detuning, we suppress the first- and second-order differential Zeeman shift in magnetically trapped 87Rb^{87}\mathrm{Rb}87Rb atoms. By dressing the state pair 5S1/25{S}_{1/2}5S1/2​ F=1F=1F=1, mF=\ensuremath−1{m}_{F}=\ensuremath{-}1mF​=\ensuremath−1 and F=2F=2F=2, mF=1{m}_{F}=1mF​=1, a residual frequency spread of <0.1<0.1<0.1 Hz in a range of 100 mG around a chosen magnetic offset field can be achieved. This is one order of magnitude smaller than the shift of the bare states at the magic field of the Breit-Rabi parabola. We further identify double magic points, around which the clock frequency is insensitive to fluctuations both in the magnetic field and in the dressing Rabi frequency. The technique is compatible with chip-based cold-atom systems and allows the creation of clock and qubit states with reduced sensitivity to magnetic-field noise.
We demonstrate engineering of a narrow microwave transition between trappable states in radio-frequency-dressed 87^{87}87rubidium, reducing the static field dependence. A single-frequency, off-resonant microwave field allows for the suppression of the differential Zeeman shift arising from the nuclear magnetic moment to at least first order. The field dependence can be suppressed further with additional dressing fields, which we demonstrate experimentally with two microwave frequencies. The engineered transition can thus be used in a range of cold atom schemes that rely on coherent state superpositions.
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.
A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a nonresonant radio-frequency field. For fermionic species as (87)Sr, (171)Yb, and (199)Hg, particular ratios between the radio-frequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first-order magnetic variations are produced within a relative uncertainty below the 10(-18) level. An Autler-Townes continued fraction describing a semiclassical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher-order magnetic field corrections to the dressed energies.
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We study the spectral signatures and coherence properties of radio-frequency-dressed hyperfine Zeeman sublevels of 87Rb^{87}\mathrm{Rb}87Rb. Experimentally, we engineer combinations of static and RF magnetic fields to modify the response of the atomic spin states to environmental magnetic field noise. We demonstrate analytically and experimentally the existence of ``magic'' dressing conditions where decoherence due to electromagnetic field noise is strongly suppressed. Building on this result, we propose a bichromatic dressing configuration that reduces the global sensitivity of the atomic ground states to low-frequency noise, and enables the simultaneous protection of multiple transitions between the two ground hyperfine manifolds of atomic alkali species. Our methods produce protected transitions between any pair of hyperfine sublevels at arbitrary (low) DC-magnetic fields.
When the cold atom clock operates in microgravity around the near-earth orbit, its performance will be affected by the fluctuation of magnetic field. A strategy is proposed to suppress the fluctuation of magnetic field by additional coils, whose current is changed accordingly to compensate the magnetic fluctuation by the linear and incremental compensation. The flight model of the cold atom clock is tested in a simulated orbital magnetic environment and the magnetic field fluctuation in the Ramsey cavity is reduced from 17 nT to 2 nT, which implied the uncertainty due to the second order Zeeman shift is reduced to be less than 2 × 10 −16 . In addition, utilizing the compensation, the magnetic field in the trapping zone can be suppressed from 7.5 μT to less than 0.3 μT to meet the magnetic field requirement of polarization gradients cooling of atoms.