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arXiv:1709.03437 · Physical Review A

Reducing the sensitivity of Rydberg atoms to dc electric fields using two-frequency ac field dressing

Donald W. Booth, Joshua Isaacs, Mark E. Saffman

Published Jan 26, 2018• 28 citations
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Abstract

We propose a method for reducing the sensitivity of atomic ground-to-Rydberg transitions to stray dc electric fields, using microwave-induced dressing of Rydberg states. Calculations are presented for the Cs $90{S}_{1/2}$ and $90{P}_{3/2}$ states. With zero dc bias electric field, a two-frequency ac field is used to simultaneously reduce the sensitivity of both states to dc field variations. The sensitivity reduction is a factor of 95 for the $90{S}_{1/2}$ state and a factor of 1600 for the $90{P}_{3/2},{m}_{J}=3/2$ state. We also show how the two-frequency ac field can be used to cancel both second- and fourth-order terms in the polarizability of a single Rydberg state. These results are relevant to improving the stability of experiments that seek to excite Rydberg atoms in the proximity of charged surfaces.

DOI
10.1103/physreva.97.012515

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Demonstration of a tunable interface between Rydberg atoms and superconducting microwave circuits with differential polarizability nulling

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Microwave-dressed Rydberg atoms in pairs of states that are optically accessible and engineered so that the frequency of the transition between them is tunable while exhibiting a low sensitivity to stray electric fields have been interfaced with a superconducting coplanar waveguide (CPW) microwave resonator. This was achieved with helium atoms in triplet Rydberg states with principal quantum numbers n = 55 and 56. The atoms were dressed with two strong microwave fields—a control field and a differential polarizability nulling field. The control field allowed the atoms to be coupled to the resonator using the two-color two-photon transition between the equal parity 1 s 55 s S 1 3 ≡ | 55 s 〉 and 1 s 56 s S 1 3 ≡ | 56 s 〉 Rydberg states, with one photon supplied by it and the other provided by the resonator. The nulling field was detuned from the field-free 1 s 55 s S 1 3 → 1 s 55 p P J 3 ≡ | 55 p 〉 transition to admix | 55 p 〉 character into the | 55 s 〉 state and eliminate the differential static electric dipole polarizability of the | 55 s 〉 and | 56 s 〉 states. The experiments were performed with atoms located ∼ 300 µ m above a λ / 4 niobium nitride superconducting CPW resonator operated at temperatures between 3.59 and 3.73 K . The measured ac and dc Stark shifts of the Rydberg states at this atom-circuit interface in the presence of the dressing fields are in good quantitative agreement with the results of Floquet calculations. The differential polarizability nulling fields used in the experiments allowed the difference in the Stark shifts of the | 55 s 〉 and | 56 s 〉 states over the range of dc fields offset from the residual stray field by ± 65 mV/cm to be reduced from 2 π × 2.1 MHz to 2 π × 125 kHz. Published by the American Physical Society 2024

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A microwave dressing field was used to induce resonant energy transfer in translationally cold Rydberg atoms. The Rb Rydberg atoms were obtained by laser excitation of cold atoms in a magneto-optical trap. When the amplitude of a 1.356 GHz dressing field was scanned, the two-atom dipole-dipole process 43d5/2 + 43d5/2 → 45p3/2 + 41f5/2,7/2 was enhanced due to the induced degeneracy of the initial and final states. The resulting spectrum had a series of resonant field amplitudes corresponding to different magnetic sublevels possible for the states involved. The scanned field amplitude was calibrated using microwave spectroscopy of the 43d5/2− 41f transition under the influence of non-resonant dressing fields. The calibrated resonant field amplitudes agree well with ac Stark shift calculations performed using the Floquet approach. This method for enhancing interactions is complementary to dc electric field induced resonant energy transfer, but benefits from the ability to shift energy levels in either direction by choice in frequency.

•Jan 1, 2007•0 citations
We propose a method for reducing the sensitivity of atomic ground-to-Rydberg transitions to stray dc electric fields, using microwave-induced dressing of Rydberg states. Calculations are presented for the Cs 90S1/290{S}_{1/2}90S1/2​ and 90P3/290{P}_{3/2}90P3/2​ states. With zero dc bias electric field, a two-frequency ac field is used to simultaneously reduce the sensitivity of both states to dc field variations. The sensitivity reduction is a factor of 95 for the 90S1/290{S}_{1/2}90S1/2​ state and a factor of 1600 for the 90P3/2,mJ=3/290{P}_{3/2},{m}_{J}=3/290P3/2​,mJ​=3/2 state. We also show how the two-frequency ac field can be used to cancel both second- and fourth-order terms in the polarizability of a single Rydberg state. These results are relevant to improving the stability of experiments that seek to excite Rydberg atoms in the proximity of charged surfaces.
Nonresonant dressing fields can make the transition frequency between two circular Rydberg states insensitive to second-order variations in the dc electric field. Perturbation theory can be used to establish the required dressing field amplitude and frequency. The same perturbative approach may be used to understand removal of the first-order dependence of the transition frequency on electric field about a bias dc electric field [Hyafil et al., Phys. Rev. Lett. 93, 103001 (2004)]. The directional alignment of the dressing and dc fields is critical in determining the electric field sensitivity of the dressed transition frequencies. This sensitivity is significantly larger for circular Rydberg states compared to low-angular momentum Rydberg states of Rb.
A nonresonant microwave dressing field at 38.465GHz38.465\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}38.465GHz was used to eliminate the static electric dipole moment difference between the 49s1/249{s}_{1/2}49s1/2​ and 48s1/248{s}_{1/2}48s1/2​ Rydberg states of 87{}^{87}87Rb in dc fields of $\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\mathrm{V}/\mathrm{cm}$. The reduced susceptibility to electric field fluctuations was measured using two-photon microwave spectroscopy. An anomalous spectral doublet is attributed to polarization ellipticity in the dressing field. The demonstrated ability to inhibit static dipole moment differences, while retaining sensitivity to high frequency fields, is applicable to sensors and/or quantum devices using Rydberg atoms.
Microwave-dressed Rydberg atoms in pairs of states that are optically accessible and engineered so that the frequency of the transition between them is tunable while exhibiting a low sensitivity to stray electric fields have been interfaced with a superconducting coplanar waveguide (CPW) microwave resonator. This was achieved with helium atoms in triplet Rydberg states with principal quantum numbers n = 55 and 56. The atoms were dressed with two strong microwave fields—a control field and a differential polarizability nulling field. The control field allowed the atoms to be coupled to the resonator using the two-color two-photon transition between the equal parity 1 s 55 s S 1 3 ≡ | 55 s 〉 and 1 s 56 s S 1 3 ≡ | 56 s 〉 Rydberg states, with one photon supplied by it and the other provided by the resonator. The nulling field was detuned from the field-free 1 s 55 s S 1 3 → 1 s 55 p P J 3 ≡ | 55 p 〉 transition to admix | 55 p 〉 character into the | 55 s 〉 state and eliminate the differential static electric dipole polarizability of the | 55 s 〉 and | 56 s 〉 states. The experiments were performed with atoms located ∼ 300 µ m above a λ / 4 niobium nitride superconducting CPW resonator operated at temperatures between 3.59 and 3.73 K . The measured ac and dc Stark shifts of the Rydberg states at this atom-circuit interface in the presence of the dressing fields are in good quantitative agreement with the results of Floquet calculations. The differential polarizability nulling fields used in the experiments allowed the difference in the Stark shifts of the | 55 s 〉 and | 56 s 〉 states over the range of dc fields offset from the residual stray field by ± 65 mV/cm to be reduced from 2 π × 2.1 MHz to 2 π × 125 kHz. Published by the American Physical Society 2024
A microwave dressing field was used to induce resonant energy transfer in translationally cold Rydberg atoms. The Rb Rydberg atoms were obtained by laser excitation of cold atoms in a magneto-optical trap. When the amplitude of a 1.356 GHz dressing field was scanned, the two-atom dipole-dipole process 43d5/2 + 43d5/2 → 45p3/2 + 41f5/2,7/2 was enhanced due to the induced degeneracy of the initial and final states. The resulting spectrum had a series of resonant field amplitudes corresponding to different magnetic sublevels possible for the states involved. The scanned field amplitude was calibrated using microwave spectroscopy of the 43d5/2− 41f transition under the influence of non-resonant dressing fields. The calibrated resonant field amplitudes agree well with ac Stark shift calculations performed using the Floquet approach. This method for enhancing interactions is complementary to dc electric field induced resonant energy transfer, but benefits from the ability to shift energy levels in either direction by choice in frequency.