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arXiv:2606.09759

Suppressing the Motion of Rydberg Atoms in Inhomogeneous Electric Fields via Stark Echo

Dominik Jakab, Manuel Kaiser, Conny Glaser, David Petrosyan, József Fortágh, Andreas Günther

physics.atom-phquant-phSubmitted Jun 8, 2026• Announced Jun 9, 2026• 0 citations
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Abstract

Rydberg atoms possess strong electric dipole transitions and tunable energy levels, making them promising candidates for microwave to optical conversion on integrated superconducting atom chips. Achieving strong coupling of the atoms to e.g. the microwave field of an on-chip resonator requires placing the atoms within tens of micrometers from the chip surface. However, inhomogeneous stray electric fields originating from the surface can induce position-dependent Stark forces, resulting in atomic motion and leading to time-dependent shifts of the Rydberg energy levels. We experimentally investigate these effects using time-of-flight and spectroscopic techniques, observing substantial level shifts and signal loss attributable to field-induced atomic motion. A theoretical model incorporating an exponentially decaying surface field with a superimposed bias accurately reproduces the observed dynamics. To mitigate the level shift, we introduce a Stark echo sequence that dynamically reverses the force. This approach suppresses the atomic motion and maintains the atomic resonance. The method relies solely on global field control and is compatible with atom-resonator coupling architectures, providing a robust strategy for preserving coherence of Rydberg atoms in inhomogeneous electric fields near surfaces.

Comments
9 pages, 7 figures

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Rydberg atoms possess strong electric dipole transitions and tunable energy levels, making them promising candidates for microwave to optical conversion on integrated superconducting atom chips. Achieving strong coupling of the atoms to e.g. the microwave field of an on-chip resonator requires placing the atoms within tens of micrometers from the chip surface. However, inhomogeneous stray electric fields originating from the surface can induce position-dependent Stark forces, resulting in atomic motion and leading to time-dependent shifts of the Rydberg energy levels. We experimentally investigate these effects using time-of-flight and spectroscopic techniques, observing substantial level shifts and signal loss attributable to field-induced atomic motion. A theoretical model incorporating an exponentially decaying surface field with a superimposed bias accurately reproduces the observed dynamics. To mitigate the level shift, we introduce a Stark echo sequence that dynamically reverses the force. This approach suppresses the atomic motion and maintains the atomic resonance. The method relies solely on global field control and is compatible with atom-resonator coupling architectures, providing a robust strategy for preserving coherence of Rydberg atoms in inhomogeneous electric fields near surfaces.
Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave-to-optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric-dipole transitions. Here we report on the experimental realization of coherent coupling of a Rydberg transition of ultracold atoms, trapped on an integrated superconducting atom chip, to the microwave field of an on-chip coplanar waveguide resonator. Close to the chip surface, stray electric fields lead to inhomogeneous Rydberg level shifts, which would hinder coherent interactions of atoms in a cloud with the Rydberg excitation lasers and the microwave cavity field. We, however, use optical excitation of a Rydberg state of atoms in a narrow layer with nearly constant electric field, which allows for resonant coupling of the atoms to the cavity microwave field on an appropriate Rydberg transition. We also achieve state-selective detection of the energetically close Rydberg states. We then observe and characterize cavity-driven Rabi oscillations between a pair of atomic Rydberg states. The residual damping of the oscillations is dominated by the spread of Rabi frequencies of atoms in different positions of the resonant cavity mode, as revealed by our model. Despite the technical challenges, our studies demonstrate the feasibility of coherent-state manipulation of Rydberg atoms interacting with superconducting circuits, paving the way for realization of capable hybrid quantum systems.
Helium atoms in the 1 s 50 s S 1 3 Rydberg level have been resonantly coupled to the 2 π × 11.722 GHz second harmonic mode of a chip-based superconducting coplanar wave-guide microwave resonator. To achieve this, the single-photon electric-dipole-allowed 1 s 50 s S 1 3 → 1 s 50 p P J 3 transition was tuned into resonance with the resonator mode through the ac Stark shift induced by a second strong 2 π × 3.350 GHz microwave dressing field. The effects of this dressing field, and residual uncanceled dc electric fields at the location of the atoms close to the superconducting chip surface were interpreted with support from Floquet calculations of the energy level structure of the Rydberg states. To observe appreciable population transfer in the 1 µ s atom-resonator interaction time using this transition, which had an electric dipole moment of 1500 e a 0 , pulsed microwave fields were injected into the resonator. From the photon occupation number in the resonator mode under these conditions, the single-photon Rabi frequency associated with the coupling of the atoms to the resonator was estimated to be ∼ 2 π × 100 Hz . These results represent an important step toward operation of this Rydberg-atom–superconducting-circuit interface in the single-photon strong-coupling regime.
The experimental realisation of a set of surface-based devices for controlling the positions and velocities of Rydberg atoms initially travelling in pulsed supersonic beams is described. The unique aspect of these devices is that they are based on the geometry of two-dimensional electrical transmission-lines and are therefore suited to integration with chip-based microwave circuits to realise a complete Rydberg laboratory on a chip. Such a chip-based laboratory could be exploited in hybrid approaches to quantum information processing, and for studies of collisions and decay processes of highly excited atoms and molecules. The devices operate through the generation of inhomogeneous electric fields and take advantage of the large electric dipole moments associated with high Rydberg states to exert forces on the atoms. In the experiments, helium atoms in Rydberg-Stark states with principal quantum numbers ranging from 48 to 52 and electric dipole moments of 10000 D are employed. The devices developed include electrostatic guides which permitted control over the transverse motion of beams of atoms. These were used to transport samples, initially travelling at 1950 m/s and deflect them away from their initial axis of propagation. The guided atoms were detected by pulsed electric field ionisation. To control the longitudinal motion of the samples, the transmission-lines were modified to permit the generation of sets of continuously moving electric traps. The resulting transmission-line decelerators were then employed to guide, accelerate and decelerate atoms trapped in three-dimensions. Accelerations up to 2.3 x 10^{7} m/s^{2} were applied to decelerate samples from 2000 m/s to zero-velocity in the laboratory-fixed frame of reference, leading to the removal of 80 meV of kinetic energy, the largest achieved in any Stark decelerator to date. The decelerated atoms were trapped in stationary electric traps and detected in situ. The phase-space acceptances of the decelerators were calculated to characterise the effects of acceleration and deceleration on the trapped atoms. The results of the calculations were employed in the interpretation of the experimental data, and to identify effects of collisions and blackbody transitions.
We demonstrate spatially resolved, coherent excitation of Rydberg atoms on an atom chip. Electromagnetically induced transparency (EIT) is used to investigate the properties of the Rydberg atoms near the gold-coated chip surface. We measure distance-dependent shifts ( ~ 101010 MHz) of the Rydberg energy levels caused by a spatially inhomogeneous electric field. The measured field strength and distance dependence is in agreement with a simple model for the electric field produced by a localized patch of Rb adsorbates deposited on the chip surface during experiments. The EIT resonances remain narrow (<4<4<4 MHz) and the observed widths are independent of atom-surface distance down to  ~ 202020 $\ensuremath{\mu}$m, indicating relatively long lifetime of the Rydberg states. Our results open the way to studies of dipolar physics, collective excitations, quantum metrology, and quantum information processing involving interacting Rydberg excited atoms on atom chips.
Rydberg atoms in dc electric fields acquire static dipole moments. When the atoms are close to a surface producing an inhomogeneous electric field, such as by the adsorbates on an atom chip, depending on the sign of the dipole moment of the Rydberg-Stark eigenstate, the atoms may experience a force toward or away from the surface. We show that by applying a bias electric field and coupling a desired Rydberg state by a microwave field of proper frequency to another Rydberg state with opposite sign of the dipole moment, we can create a trapping potential for the atom at a prescribed distance from the surface. Perfectly overlapping trapping potentials for several Rydberg states can also be created by multicomponent microwave fields. A pair of such trapped Rydberg states of an atom can represent a qubit. Finally, we discuss an optimal realization of the SWAP gate between pairs of such atomic Rydberg qubits separated by a large distance but interacting with a common mode of a planar microwave resonator at finite temperature.
Rydberg atoms in dc electric fields acquire static dipole moments. When the atoms are close to a surface producing an inhomogeneous electric field, such as by the adsorbates on an atom chip, depending on the sign of the dipole moment of the Rydberg-Stark eigenstate, the atoms may experience a force toward or away from the surface. We show that by applying a bias electric field and coupling a desired Rydberg state by a microwave field of proper frequency to another Rydberg state with opposite sign of the dipole moment, we can create a trapping potential for the atom at a prescribed distance from the surface. Perfectly overlapping trapping potentials for several Rydberg states can also be created by multicomponent microwave fields. A pair of such trapped Rydberg states of an atom can represent a qubit. Finally, we discuss an optimal realization of the SWAP gate between pairs of such atomic Rydberg qubits separated by a large distance but interacting with a common mode of a planar microwave resonator at finite temperature.