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:1412.0977 · Physical Review A

Magic radio-frequency dressing for trapped atomic microwave clocks

Georgy A. Kazakov, Thorsten Schumm

Published Feb 4, 2015• 22 citations
arXivHTMLPDF

Abstract

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 ${}^{87}\mathrm{Rb}$ 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.

DOI
10.1103/physreva.91.023404

Related papers

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

L. Sárkány, P. Weiss, H. Hattermann +1 more

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.

arXiv:1410.8171•Physical Review A•Nov 13, 2014•53 citations

Magic Radio-Frequency Dressing of Nuclear Spins in High-Accuracy Optical Clocks

T. Zanon-Willette, Emeric de Clercq, E. Arimondo

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.

arXiv:1206.7091•Physical Review Letters•Nov 30, 2012•18 citations

Multi-Frequency Coherence Control of Radio-Frequency-Dressed States

Bethany Foxon, Sindhu Jammi, T. Fernholz

We demonstrate engineering of a narrow microwave transition between trappable states in radio-frequency-dressed $^{87}$rubidium, 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.

arXiv:2504.17143•Apr 23, 2025•0 citations

Decoherence-free radio-frequency-dressed subspaces

G. Sinuco-León, Hèctor Mas, S Pandey (9349130) +3 more

We study the spectral signatures and coherence properties of radio-frequency-dressed hyperfine Zeeman sublevels of Rb87. 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.

•Sep 1, 2021•0 citations

Decoherence-free radio-frequency-dressed subspaces

G. A. Sinuco-Leon, H. Mas, S. Pandey +3 more

We study the spectral signatures and coherence properties of radio-frequency-dressed hyperfine Zeeman sublevels of $^{87}\mathrm{Rb}$. 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.

arXiv:2007.15730•Physical Review A•Sep 7, 2021•5 citations

Microwave spectroscopy of radio-frequency-dressed Rb87

G. Sinuco-León, B. M. Garraway, Hèctor Mas +8 more

We study the hyperfine spectrum of atoms of $^{87}\mathrm{Rb}$ dressed by a radio-frequency field and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap, and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant sidebands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum using a semiclassical model in the low-field limit and the rotating-wave approximation for alkali-metal-like species, in general, and $^{87}\mathrm{Rb}$ atoms, in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.

arXiv:1904.12073•Physical Review A•Nov 22, 2019•16 citations
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.
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, ${m}_{F}=\ensuremath{-}1$ 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.
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.
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.
We study the spectral signatures and coherence properties of radio-frequency-dressed hyperfine Zeeman sublevels of Rb87. 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.
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.
We study the hyperfine spectrum of atoms of 87Rb^{87}\mathrm{Rb}87Rb dressed by a radio-frequency field and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap, and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant sidebands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum using a semiclassical model in the low-field limit and the rotating-wave approximation for alkali-metal-like species, in general, and 87Rb^{87}\mathrm{Rb}87Rb atoms, in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.