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

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.

💡 Research Summary

The paper presents a novel method for trapping Rydberg atoms near an atom‑chip surface and for implementing quantum gates using microwave‑dressed states. Rydberg atoms placed in the inhomogeneous static electric field generated by adsorbates on a chip acquire Stark‑shifted energy levels that depend on their static electric dipole moments. By selecting a pair of Rydberg‑Stark eigenstates |r⟩ and |a⟩ whose dipole moments are equal in magnitude but opposite in sign, the authors show that a microwave field resonant with the |r⟩↔|a⟩ transition can create an avoided crossing in the rotating frame. The position of the crossing, z₀, is set by the condition ℏΔ+(d_r−d_a)|F(z₀)|=0, where Δ is the microwave detuning and F(z) is the total electric field (adsorbate field plus a homogeneous bias field). When the microwave Rabi frequency Ω is turned on, the upper dressed eigenenergy E₊(z) develops a potential well around z₀. The curvature of this well, k≈