Investigations On Quantum Optical Phenomena In Solid-state Superconducting Quantum Circuits

Quantum optics, which is an elegant combination of quantum field theory and physical optics, aims at exploring interesting phenomena in the field of light-matter interaction. And its basic theoretical frame consists of semiclassical theory involving only the quantization of medium and full quantum theory based on the quantization of both field and medium. From the date of birth, quantum optics has always attracted a great deal of attention from many outstanding physicists. Meanwhile, the considered systems are developed from initial natural atoms to various new-type systems, such as quantum dots, nitrogen-vacancy color centers, optomechanical systems, and superconducting quantum circuits. Here superconducting quantum systems with Josephson junctions have been used to demonstrate numerous quantum optical phenomena, which indicates the advent of circuit quantum electrodynamics (QED). Superconducting qubits, which are the key components of superconducting circuits and behave as artificial multi-level atoms, can be tuned and controlled unprecedentedly by external gate voltage and magnetic flux. Compared with the conventional cavity QED, circuit QED architecture possesses exceptional tunability and controllability, which can lead to flexible quantum optics.In this doctoral thesis, we study several interesting quantum optical issues using superconducting circuits and obtain some original results. To be specific,1. We present a theoretical study of the quantum Zeno effect in a driven superconducting charge qubit strongly and ultrastrongly coupled to a transmission line resonator. Using the dressed-state approach, we predict the different dynamics behaviors of the dressed qubit subjected to two opposite projection measurements. We show that, for very frequent measurements, the survival probability of the initial state is of exponential form and the Zeno time of the dressed qubit can be several orders of magnitude longer than that of the bare qubit. For slowly repeated measurements, the detuning of the driving field has significant impact on the measurement dynamics, and by choosing appropriate parameters for the dressed qubit, the Zeno effect can occur in nonresonant coupling case. Such a Zeno effect is excluded from a usual two-level system.2. We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in a driven three-level superconducting artificial system which is a dressed-state system resulting from the coupling of a superconducting charge qubit and a transmission line resonator. In the frame of the dressed-state approach and steady-state approximation, we study the linear absorption of the dressed artificial system to a weak probe signal in depth. In light of the spectrum-decomposition method and some other restrictions, we obtain the explicit conditions for the dressed-state realization of EIT and ATS and present a corresponding "phase diagram". In contrast to usual bare systems, these conditions given in the dressed system have an extra dependency on the qubit-resonator parameters. And by varying the qubit's Josephson coupling energy we demonstrate a transition from EIT to ATS. Our study exhibits the superiority of tunability of superconducting circuits again.3. We investigate electromagnetically induced transparency and Autler-Townes splitting in a superconducting quantum circuit with a four-level V-type energy spectrum constructed by two coupled superconducting charge qubits. For the two-qubit system, we obtain the general solutions to its eigenvalues and eigenstates. We show that it is possible for this four-level superconducting system to exhibit multiple dips in the absorption spectrum of a probe field, with at most three dips, which indicates the breakdown of the traditional correspondence between a (N+1)-level system and N-1 dips. By decomposing the four-level system into two three-level subsystems, we give a reasonable explanation for the novel phenomenon. It is also shown that the role between the peak and the dip at the zero detuning point is exchangeable by changing the system's parameters.4. We present a theoretical study of multi-wave mixing in a driven superconducting quantum qubit with a cyclic A-type three-level structure. We first show that three-wave mixing (3WM), four-wave mixing (4WM) and five-wave mixing (5WM) processes can coexist in the microwave regime in such an artificial system due to the absence of selection rules. We also show that 4WM efficiency can be as high as 0.1%for only a single artificial atom, which is comparable to or even larger than that of many previous schemes in atomic systems. Moreover, Autler-Townes splitting occurs in the 3WM and 5WM spectra and quantum interference has a significant impact on the total signal intensity being a coherent superposition of these two signals.5. We present a new type of phase-and frequency-sensitive amplification and attenuation in a cyclically driven three-level superconducting Josephson system. Different from the previous linear theory of pure phase-sensitive amplification, a new physical mechanism——combined action of nonlinear wave mixing and wave interference——is developed and leads to not only amplification but also attenuation. This is referred to as interference nonlinear optics. Our results show the sudden output signal transition from large gain to deep suppression by tuning the relative phase and in this case the system can act as a phase-controlled amplitude modulator. We also show the continuous change from output enhancement to attenuation by adjusting the driving-field frequency and in this situation the system behave as a frequency-controlled amplitude modulator. Our study opens up a new perspective for its widespread applications in quantum information science.