In this thesis theoretical studies of hybrid quantum systems composed of solid-state superconducting microwave resonators, mechanical oscillators, and gas-phase Rydberg atoms are described. The thesis begins with an overview of the current state of the field of hybrid quantum in- formation processing. An introduction to the physics of Rydberg atoms and the preparation processes of circular Rydberg states follows, including a review of the associated literature. Three main new research results are then presented. These include (1) numerical studies of static electric dipole interactions in strongly polarized gases of Rydberg atoms. The understanding and characterization of these interactions is essential to maximize the quantum-state preparation procedures required for the hybrid systems studied in the thesis; (2) analytical and numerical studies of quantum-state preparation and cooling in coplanar superconducting microwave resonators using beams of atoms in circular Rydberg states; and (3) studies of coupled Rydberg-atom—mechanical-oscillator systems. The results presented in each of these areas are of interest for hybrid quantum information processing and quantum computation, and optical-to- microwave photon conversion for quantum communication.
In this thesis theoretical studies of hybrid quantum systems composed of solid-state superconducting microwave resonators, mechanical oscillators, and gas-phase Rydberg atoms are described. The thesis begins with an overview of the current state of the field of hybrid quantum in- formation processing. An introduction to the physics of Rydberg atoms and the preparation processes of circular Rydberg states follows, including a review of the associated literature. Three main new research results are then presented. These include (1) numerical studies of static electric dipole interactions in strongly polarized gases of Rydberg atoms. The understanding and characterization of these interactions is essential to maximize the quantum-state preparation procedures required for the hybrid systems studied in the thesis; (2) analytical and numerical studies of quantum-state preparation and cooling in coplanar superconducting microwave resonators using beams of atoms in circular Rydberg states; and (3) studies of coupled Rydberg-atom—mechanical-oscillator systems. The results presented in each of these areas are of interest for hybrid quantum information processing and quantum computation, and optical-to- microwave photon conversion for quantum communication.
A hybrid circuit quantum electro-dynamics (circuit QED) setup consisting of helium atoms in high-n Rydberg states and superconducting co-planar waveguide (CPW) microwave resonators has been developed with the goal of performing hybrid quantum optics experiments with applications in quantum information processing. In this thesis an overview of the field of cavity QED is introduced, and numerical methods to calculate the atomic energy level structure and transition dipole moments in electric and magnetic fields are described. Using this background information, a new method for efficiently preparing high-n circular Rydberg states is presented. This was required to ac- cess circular-state–to–circular-state transition frequencies in experiments which are compatible with superconducting CPW microwave resonators. Experimental and numerical results demonstrating the implementation of this method for the preparation of the |n = 70, l = 69, ml = +69⟩ circular state in helium are reported. The design and fabrication of λ/4 superconducting CPW microwave resonators, compatible with these high-n circular Rydberg states of helium is then described. The effects of microwave driving power, temperature and magnetic field on the characteristics of these resonators are presented. Finally, experiments in which helium Rydberg atoms have been coherently coupled to the microwave field of a superconducting co-planar waveguide resonator are reported.
Hybrid quantum systems provide a promising route toward combining the complementary strengths of distinct physical platforms for quantum information processing. In this context, highly excited Rydberg atoms are particularly attractive due to their strong electric dipole moments, long lifetimes, and compatibility with both optical and microwave frequency regimes. Mechanical resonators, on the other hand, offer long coherence times and the ability to store quantum information in macroscopic degrees of freedom. In this thesis, the development of a novel hybrid platform interfacing ultracold Rydberg atoms with high-overtone bulk acoustic wave resonators (HBARs) in a cryogenic environment is presented. The core components of the experimental apparatus have been designed, assembled, and characterized, including a room-temperature realization featuring the complete cold-atom preparation chain. A first-generation superconducting atom chip for trapping ultracold atoms in a cryogenic environment has been designed and fabricated, establishing the foundation for future experiments under cryogenic conditions. The full experimental realization of the hybrid system, including the integration of the mechanical resonator, was delayed by the delivery of a custom-built cryostat. Nevertheless, the preparation of the cryogenic experiment has been completed, enabling rapid progress toward first experiments once cryogenic operation becomes available. At an operating temperature of 4 K, thermal phonon occupation of HBAR modes is significantly reduced compared to room temperature but remains above the quantum ground state, motivating the development of active cooling strategies. Complementing the experimental work, the feasibility of cooling a mechanical mode toward its quantum mechanical ground state using a cloud of Rydberg atoms is investigated theoretically. In this approach, Rydberg atoms act as a dissipative resource that extracts phononic excitations from the mechanical resonator and removes them via radiative decay. Furthermore, the potential of Rydberg atom-mediated interactions to generate entanglement between spatially separated mechanical oscillators is analyzed. Together, these results establish a foundation for future experimental investigations of Rydberg atom–mechanical oscillator hybrid systems.
Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s ^{3}S_{1} Rydberg level by two-color two-photon laser excitation from the metastable 1s2s ^{3}S_{1} level. Two-photon microwave transitions between the 1s55s ^{3}S_{1} and 1s56s ^{3}S_{1} levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the atom-resonator coupling was studied by time-domain measurements of Rabi oscillations.
This thesis intends to give a concise yet meaningful overview about the progress in the physical realization of quantum information processing using hybrid systems of ultracold atoms and superconducting microwave resonators, describing our own theoretical and experimental contributions to advancing. Ultracold atoms in their ground states are well-isolated quantum systems offering long coherence times, and therefore are prime candidates for quantum memory applications. Their performance is limited by their sensitivity on external magnetic-field noises and inhomogeneous Zeeman shifts inherently present in magnetic traps. We have developed an efficient method to eliminate the magnetic-field dependence of the differential Zeeman shift between the magnetically trappable clock-states up to second order around an arbitrarily chosen offset field, hence rendering atom-based quantum memory insensitive to magnetic noises. We describe two protocols to mediate long-range interactions between Rydberg atoms using a thermally populated microwave cavity, realizing universal 2-bit quantum gates. This is of great practical interest, since in existing hybrid atom-superconducting resonator experiments the attainable temperature is not low enough to reach the vacuum state of the cavity mode. The first method relies on active mode cooling using an auxiliary reservoir of atoms. The second method makes use of a destructive quantum interference between different excitation paths, making the scheme insensitive to the actual photon state of the cavity. We also report on a new laboratory for optical lattice clocks that we have established in parallel with this work. We present a novel concept for continuously operated atomic clocks, along with the steps we have taken towards its experimental realization.
Abstract Hybrid quantum systems that integrate complementary advantages of different physical platforms provide a new pathway toward large-scale, fault-tolerant quantum information processing. In this work, we theoretically investigate a hybrid system consisting of a Rydberg atom, a piezoelectric nanomechanical resonator, and a superconducting qubit, aiming to achieve high-fidelity steady-state entanglement. In this scheme, the nanomechanical resonator acts as a quantum bus, resonantly coupling to the superconducting qubit via the piezoelectric effect and to the Rydberg atom via the electric dipole interaction. Under the strong-coupling condition, we introduce a dressed-state transformation to analyze the eigenenergy structure of the system. By properly controlling the laser driving fields, the otherwise detrimental dissipation processes are turned into a crucial resource for entanglement preparation. Numerical simulations show that under optimal parameters the fidelity of the target state can reach above 98 % , and the scheme exhibits strong robustness against fluctuations in the driving field strengths and against spontaneous emission noise. This study provides a feasible theoretical approach and technical reference for cross-platform quantum interfaces, distributed quantum computing, and dissipation-assisted quantum state engineering.
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis reports the first observation of the resonant electric dipole-dipole interaction between cold Rydberg atoms using microwave spectroscopy, the observation of the magnetic field suppression of resonant interactions, and the development of a unique technique for precise magnetic field measurements. ARydbergstate(46d 5/2) of laser cooled 85 Rb atoms has been optically excited. A fraction of these atoms has been transferred to another Rydberg state (47p 3/2 or 45f 5/2,7/2) to introduce resonant electric dipole-dipole interactions. The line broadening of the two-photon 46d 5/2 − 47d 5/2 microwave transition due to the interaction of 46d 5/2 with 47p 3/2 or 45f 5/2,7/2 atoms has been used as a probe of the interatomic interactions. This experiment has been repeated with a DC magnetic field applied. The application of a weak magnetic field ( ≤ 0.6 G) has reduced