In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.Comment: Review article, 170 pages (main text 101 pages), 35 figures, 5 tables, 1362 references; v2: a few more references added, typos corrected; Physics Reports (in press

Exceptional points (EPs) correspond to degeneracies of open systems. These are attracting much interest in optics, optoelectronics, plasmonics, and condensed matter physics. In the classical and semiclassical approaches, Hamiltonian EPs (HEPs) are usually defined as degeneracies of non-Hermitian Hamiltonians such that at least two eigenfrequencies are identical and the corresponding eigenstates coalesce. HEPs result from continuous, mostly slow, nonunitary evolution without quantum jumps. Clearly, quantum jumps should be included in a fully quantum approach to make it equivalent to, e.g., the Lindblad master equation approach. Thus, we suggest to define EPs via degeneracies of a Liouvillian superoperator (including the full Lindbladian term, LEPs), and we clarify the relations between HEPs and LEPs. We prove two main theorems: Theorem 1 proves that, in the quantum limit, LEPs and HEPs must have essentially different properties. Theorem 2 dictates a condition under which, in the “semiclassical” limit, LEPs and HEPs recover the same properties. In particular, we show the validity of Theorem 1 studying systems which have (1) an LEP but no HEPs and (2) both LEPs and HEPs but for shifted parameters. As for Theorem 2, (3) we show that these two types of EPs become essentially equivalent in the semiclassical limit. We introduce a series of mathematical techniques to unveil analogies and differences between the HEPs and LEPs. We analytically compare LEPs and HEPs for some quantum and semiclassical prototype models with loss and gain.

We propose how to create and manipulate one-way nonclassical light via photon blockade in rotating nonlinear devices. We refer to this effect as nonreciprocal photon blockade (PB). Specifically, we show that in a spinning Kerr resonator, PB happens when the resonator is driven in one direction but not the other. This occurs because of the Fizeau drag, leading to a full split of the resonance frequencies of the countercirculating modes. Different types of purely quantum correlations, such as single- and two-photon blockades, can emerge in different directions in a well-controlled manner, and the transition from PB to photon-induced tunneling is revealed as well. Our work opens up a new route to achieve quantum nonreciprocal devices, which are crucial elements in chiral quantum technologies or topological photonics.

We propose an experimentally feasible method for enhancing the atom-field coupling as well as the ratio between this coupling and dissipation (i.e., cooperativity) in an optical cavity. It exploits optical parametric amplification to exponentially enhance the atom-cavity interaction and, hence, the cooperativity of the system, with the squeezing-induced noise being completely eliminated. Consequently, the atom-cavity system can be driven from the weak-coupling regime to the strong-coupling regime for modest squeezing parameters, and even can achieve an effective cooperativity much larger than 100. Based on this, we further demonstrate the generation of steady-state nearly maximal quantum entanglement. The resulting entanglement infidelity (which quantifies the deviation of the actual state from a maximally entangled state) is exponentially smaller than the lower bound on the infidelities obtained in other dissipative entanglement preparations without applying squeezing. In principle, we can make an arbitrarily small infidelity. Our generic method for enhancing atom-cavity interaction and cooperativities can be implemented in a wide range of physical systems, and it can provide diverse applications for quantum information processing.

We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to protect and engineer quantum resources by utilizing diverse nonreciprocal devices, for building noise-tolerant quantum processors, realizing chiral networks, and backaction-immune quantum sensors.