Superconducting planar-transmission-line resonators play an increasingly important role in applications such as astronomical detection and circuit quantum electrodynamics. When measuring the transmission response of an array of resonators, however, one often observes some spurious resonances besides the intrinsic ones. In this letter, the effect of the cavity accommodating a half-wavelength superconducting microstrip resonator is investigated. An attenuation pole associated with the intrinsic resonance of the half-wavelength resonator is clearly observed and found to be resulted from the mutual coupling between the microstrip resonator and the cavity. In addition, it is demonstrated that adding a superconducting ground layer for such a microstrip resonator can avoid the frequency shift owing to an ever-present thin air gap between the microstrip resonator and the cavity and can also improve the Q factor of the microstrip resonator.
One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.
We present a device demonstrating a lithographically patterned transmon integrated with a micromachined cavity resonator. Our two-cavity, one-qubit device is a multilayer microwave integrated quantum circuit (MMIQC), comprising a basic unit capable of performing circuit-QED (cQED) operations. We describe the qubit-cavity coupling mechanism of a specialized geometry using an electric field picture and a circuit model, and finally obtain specific system parameters using simulations. Fabrication of the MMIQC includes lithography, etching, and metallic bonding of silicon wafers. Superconducting wafer bonding is a critical capability that is demonstrated by a micromachined storage cavity lifetime
34.3 μs, corresponding to a quality factor of 2 million at single-photon energies. The transmon coherence times are
T1=6.4 μs, and
T2Echo=11.7 μs. We measure qubit-cavity dispersive coupling with rate
χqμ/2π=−1.17 MHz, constituting a Jaynes-Cummings system with an interaction strength
g/2π=49 MHz. With these parameters we are able to demonstrate cQED operations in the strong dispersive regime with ease. Finally, we highlight several improvements and anticipated extensions of the technology to complex MMIQCs.