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Trapping potentials and quantum gates for microwave-dressed Rydberg atoms on an atom chip

Iason Tsiamis, Georgios Doultsinos, Andreas F. Tzortzakakis, Manuel Kaiser, Dominik Jakab, Andreas Günther, József Fortágh, David Petrosyan

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.17169/refubium-51599

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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.
Trapped Rydberg ions are a promising new platform for quantum computation and simulation. They combine the exquisite control of trapped ion systems with the strong dipole-dipole interactions available in Rydberg atom systems. In order to realize strong interactions between Rydberg ions, microwave dressing is required to induce strong oscillating dipoles. Additionally, microwave dressing of Rydberg states with polarizabilities of opposite sign allows for the realization of Rydberg states with vanishing polarizability. Such states are insensitive to external electric fields and can be trapped independently of their state. Vanishing-polarizability Rydberg states allow for implementing Rydberg entangling gates in large ion crystals.
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.
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.
Combining the strong and long-range interaction of cold Rydberg atoms with the controllability of trapped ions, ultracold trapped Rydberg ions provide a promising platform for scalable quantum computing. We demonstrate how microwave-dressed Rydberg states result in rotating permanent dipole moments causing strong dipole-dipole interaction between ions in highly excited Rydberg states. Due to the large difference in time scales, the fast electronic dynamics of the Rydberg ions decouple from the slower oscillator modes in the linear Coulomb crystal. These properties allow us to realize a submicrosecond two-qubit gate between two Rydberg ions confined in a Paul trap reaching fidelities of > 99% under consideration of the finite lifetime of the Rydberg states at room temperature.