There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.

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Circuit quantum electrodynamics

A bandwidth enhanced method of a low-profile substrate integrated waveguide (SIW) cavity-backed slot antenna is presented in this paper. Bandwidth enhancement is achieved by simultaneously exciting two hybrid modes in the SIW-backed cavity and merging them within the required frequency range. These two hybrid modes, whose dominant fields are located in different half parts of the SIW cavity, are two different combinations of the and resonances. This design method has been validated by experiments. Compared with those of a previously presented SIW cavity-backed slot antenna, fractional impedance bandwidth of the proposed antenna is enhanced from 1.4% to 6.3%, its gain and radiation efficiency are also slightly improved to 6.0 dBi and 90%, and its SIW cavity size is reduced about 30%. The proposed antenna exhibits low cross polarization level and high front to back ratio. It still retains advantages of low-profile, low fabrication cost, and easy integration with planar circuits.

Bandwidth-Enhanced Low-Profile Cavity-Backed Slot Antenna by Using Hybrid SIW Cavity Modes

Cavity-backed patch antenna arrays with full corporate substrate integrated waveguide (SIW) feed networks are demonstrated at V-band for applications with the needs of high-gain antennas. A prototype of $16 \times 16$ radiating elements with a waveguide transition is fabricated by applying standard printed circuit board (PCB) facilities. A gain up to 30.1 dBi with a 3-dB gain bandwidth of 16.1%, an impedance bandwidth of 15.3% for $\mathrm{SWR} \,{ , and symmetrically broadside radiation patterns with $-40\,\mathrm{dB}$ cross-polarizations are achieved. The performance of the proposed antenna array is also systematically evaluated. The result serves as a reference for designing large antenna arrays operating at millimeter-wave frequencies.

60-GHz Substrate Integrated Waveguide Fed Cavity-Backed Aperture-Coupled Microstrip Patch Antenna Arrays

A low side-lobe substrate-integrated-waveguide (SIW) antenna array is presented at the 28-GHz band using broadband unequal feeding network for millimeter-wave (mm-wave) handset devices. The ground-plane size of the proposed antenna is fixed to half of the size of the Samsung Galaxy Note 4. The antenna array has been implemented with a multilayer structure created by stacking three substrates and a copper plate. An 8-way SIW feeding network with broadband 4-stage T-junction dividers and a cavity-backed antenna are investigated to obtain broadband performance. The proposed unequal T-junction dividers with phase compensation are introduced and designed for various output ratios. Applying Taylor beam-pattern synthesis in the 8-way SIW feeding network, low side-lobe performance is achieved. The measured result of the fabricated antenna has 2.3 GHz bandwidth within $\text{S}_11\,{ . The fabricated antenna can be performed with a gain up to 13.97 dBi with a low cross-polarization and symmetrical fan beam radiation patterns with low side-lobe levels. Most of the measured results are validated with the simulated results. The proposed antenna array provides low cost, broadband performance, and good radiation performances with low side-lobe levels for mm-wave handset devices.

Low Side-Lobe Substrate-Integrated-Waveguide Antenna Array Using Broadband Unequal Feeding Network for Millimeter-Wave Handset Device

Very-high-quality-factor superconducting radio-frequency cavities developed for accelerators can enable fundamental physics searches with orders of magnitude higher sensitivity, and they can also offer a path to a 1000-fold increase in the achievable coherence times for cavity-stored quantum states in three-dimensional circuit QED architecture. Here we report measurements of multiple accelerator cavities of resonant frequencies of ${f}_{0}=1.3$, 2.6, 5 GHz down to temperatures of about 10 mK and field levels down to a few photons, which reveal very long photon lifetimes up to 2 s, while also further exposing the role of the two-level systems (TLS) in niobium oxide. We also demonstrate how the TLS contribution can be greatly suppressed by vacuum heat treatments at 340--450 ${}^{\ensuremath{\circ}}\mathrm{C}$.

Three-Dimensional Superconducting Resonators at T <20 mK with Photon Lifetimes up to τ =2 s

The substrate-integrated waveguide (SIW) technology is utilized as an alternative low-cost approach in fabricating cavity-backed patch antennas. The proposed antenna arrays combine the attractive features of the conventional metalized cavity-backed patch arrays like surface wave suppression, high radiation efficiency, and enhanced bandwidth, yet provide a low manufacturing cost. A previously developed design of a 2×2 SIW cavity-backed microstrip patch sub-array is extended here and used as a basic building block to attain larger arrays of 2 × 4, 4 × 4, and 8 × 8 elements. The fabricated arrays have been measured and demonstrate good agreement with their simulated performance. The design and performance of these arrays are compared to other conventional bandwidth enhancement techniques, which prove SIW as a viable alternative.

Substrate-Integrated Cavity-Backed Patch Arrays: A Low-Cost Approach for Bandwidth Enhancement

A class of wide-scan angle wide-band microstrip patch phased arrays is proposed. The proposed phased arrays are composed of probe-fed microstrip patches backed by substrate-integrated cavities. First, a simplified 2-D numerical analysis based on Floquet's theorem is presented to qualitatively demonstrate the E-plane scan performance of the cavity-backed structure compared to that of the conventional microstrip patch phased array. Second, the 3-D scan performance of the proposed phased arrays is thoroughly investigated varying both the substrate thickness and dielectric constant using commercially available EM simulation tools, which is followed by presenting simple design guidelines for the cavity, patch and substrate. A 7 × 7 prototype phased array of the proposed SIW cavity-backed patch structure was fabricated and its measured results agree well with our theoretical prediction and indicate a relatively wide-scan performance when compared to the corresponding microstrip patch phased array without cavities.

Analysis and Design of Wide-Scan Angle Wide-Band Phased Arrays of Substrate-Integrated Cavity-Backed Patches

A set of substrate-integrated cavity-backed patch antennas of alternative topologies is proposed. Using the substrate-integrated waveguide (SIW) technology, the cavity backing the patch is emulated using array of plated through via holes. The proposed topologies have the potential to widen the inherent limited bandwidth of the conventional patch from typically 2% to about 15% depending on the height of the backing cavity. Additionally, the cavity enhances the antenna gain by about 2 dB, as the cavity is very effective in suppressing the unwanted surface waves, thus improving the radiation efficiency. Meanwhile, the proposed SIW topology has a low fabrication cost, as the whole structure could be attained using conventional printed circuit board processing. Design parameters of the SIW cavities are thoroughly investigated in this study, demonstrating their leakage characteristics. Four different structures are investigated corresponding to the different combinations of rectangular or circular patches backed by rectangular or circular SIW cavities. Detailed design guidelines are presented for the SIW cavities to ensure minimum leakage losses and for the radiating elements to achieve a desired fractional bandwidth. Based on experimental prototypes, a thorough comparative study between the four different topologies is presented demonstrating the attractive characteristics of each topology as far as gain, bandwidth, cross-pol level and mutual coupling.

Design guidelines of substrate-integrated cavity backed patch antennas

A new family of compact rat-race hybrid couplers is proposed. The novelty of the new structures stems from the idea of utilizing the vacant space inside the conventional rat-race coupler in increasing the rat-race ring path. The couplers have been designed to operate at 1.8 GHz. The size of the new structures is 70% less than conventional rat-race hybrid coupler at the same center frequency. The measurements are in good agreement with the designed values. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 606–609, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21421

Mohamed H. Awida

Papers

Three-Dimensional Superconducting Resonators at T <20 mK with Photon Lifetimes up to τ =2 s

Substrate-Integrated Cavity-Backed Patch Arrays: A Low-Cost Approach for Bandwidth Enhancement

Analysis and Design of Wide-Scan Angle Wide-Band Phased Arrays of Substrate-Integrated Cavity-Backed Patches

Design guidelines of substrate-integrated cavity backed patch antennas

Compact rat-race hybrid coupler using meander space-filling curves