We propose a promising hybrid quantum system, where a highly-excited atom strongly interacts with a superconducting LC oscillator via the electric field of capacitor. An external electrostatic field is applied to tune the energy spectrum of atom. The atomic qubit is implemented by two eigenstates near an avoided-level crossing in the DC Stark map of Rydberg atom. Varying the electrostatic field brings the atomic-qubit transition on-or off-resonance to the microwave resonator, leading to a strong atom-resonator coupling with an extremely large cooperativity. Like the nonlinearity induced by Josephson junctions in superconducting circuits, the large atom-resonator interface disturbs the harmonic potential of resonator, resulting in an artificial two-level particle. Different universal twoqubit logic gates can also be performed on our hybrid system within the space where an atomic qubit couples to a single photon with an interaction strength much larger than any relaxation rates, opening the door to the cavity-mediated state transmission. Introduction. Superconducting (SC) circuits and neutral atoms define coherent systems of key importance in quantum technology. Besides the features of flexibility, tunability, and scalability, SC devices manipulate quantum states rapidly owing to the strong coupling to external fields. Nevertheless, this sensitivity of SC circuits leads to short decoherence times caused by environmental noise [1]. In contrast, atoms can maintain the quantum coherence exceeding one second [2], but processing quantum information as fast as SC devices is impractical.Hybridizing SC circuits and atoms bears great potential to overcome the bottlenecks of above quantum technologies [3][4][5][6][7]. In this context, one competitive candidate is the SC resonator-atom system, where a coherent microwave photon strongly drives an atomic transition between two long-lived states [8,9]. The SC resonators, such as coplanar waveguide (CPW) cavity and LC resonator, can maintain the quantum coherence of microwave photons of the order of 1 µs -1 ms [10]. The strong hybrid coupling requires the microscopic particles possess large dipole moments and long-lifetime qubit states, for which atoms in highly-excited Rydberg states are usually employed as intermediate qubits to interact with the resonator [11]. After gate operations, the quantum information encoded in Rydberg states can be mapped onto two hyperfine ground states for long-time storage [12]. Moreover, the energy spectrum of highlyexcited states can be controlled by the external electrostatic field, making the hybrid system more tunable.In analogy with the SC qubits [13] relying on Josephson junctions (JJ), the anharmonicity coming from the atom-

We propose a superconducting circuit-atom hybrid, where the Rabi oscillation of single excess Cooper pair in the island is stabilized via the common atomic clock technique. The noise in the superconducting circuit is mapped onto the voltage source which biases the Cooper-pair box via an inductor and a gate capacitor. The fast fluctuations of the gate charge are significantly suppressed by an inductor-capacitor resonator, leading to a long-relaxation-time Rabi oscillation. More importantly, the residual low-frequency fluctuations are further reduced by using the general feedback-control method, in which the voltage bias is stabilized via continuously measuring the dc-Stark-shift-induced atomic Ramsey signal. The stability and coherence time of the resulting charge-qubit Rabi oscillation are both enhanced. The principal structure of this Cooper-pair-box oscillator is studied in detail.

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