Spontaneous parametric downconversion (SPDC) has been a key enabling technology in exploring quantum phenomena and their applications for decades. For instance, traditional SPDC, whichsplits a high energy pump photon into two lower energy photons, is a common way to produce entangled photon pairs. Since the early realizations of SPDC, researchers have thought to generalize it to higher order, e.g., to produce entangled photon triplets. However, directly generating photon triplets through a single SPDC process has remained elusive. Here, using a flux-pumped superconducting parametric cavity, we demonstrate direct three-photon SPDC, with photon triplets generated in a single cavity mode or split between multiple modes. With strong pumping, the states can be quite bright, with flux densities exceeding 60 photon/s/Hz. The observed states are strongly non-Gaussian, which has important implications for potential applications. In the single-mode case, we observe a triangular star-shaped distribution of quadrature voltages, indicative of the long-predicted „star state“. The observed star state shows strong third-order correlations, as expected for a state generated by a cubic Hamiltonian. By pumping at the sum frequency of multiple modes, we observe strong three-body correlations between multiple modes, strikingly, in the absence of second-order correlations. We further analyze the third-order correlations under mode transformations by the symplectic symmetry group, showing that the observed transformation properties serve to „fingerprint“ the specific cubic Hamiltonian that generates them. The observed non-Gaussian, third-order correlations represent an important step forward in quantum optics and may have a strong impact on quantum communication with microwave fields as well as continuous-variable quantum computation.

In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconductingcavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a variety of entanglement measures, we demonstrate both full inseparability and genuine tripartite entanglement of the states. Our method is easily extensible to more modes.

We propose a generalization of the superconducting circuit simulation of the dynamical Casimir effect where we consider relativistically moving boundary conditions following differenttrajectories. We study the feasibility of the setup used in the past to simulate the dynamical Casimir effect to reproduce richer relativistic trajectories differing from purely sinusoidal ones. We show how different relativistic oscillatory trajectories of the boundaries of the same period and similar shape produce a rather different spectrum of particles characteristic of their respective motions.

We address the recent advances on microwave quantum optics with artificial
atoms. This field relies on the fact that the coupling between a
superconducting artificial atom and propagatingmicrowave photons in a 1D open
transmission line can be made strong enough to observe quantum coherent
effects, without using any cavity to confine the microwave photons. We
investigate the scattering properties in such a system with resonant coherent
microwaves. We observe the strong nonlinearity of the artificial atom and under
strong driving we observe the Mollow triplet. By applying two resonant tones,
we also observe the Autler-Townes splitting. By exploiting these effects, we
demonstrate two quantum devices at the single-photon level in the microwave
regime: the single-photon router and the photon-number filter. These devices
provide essential steps towards the realization of an on-chip quantum network.

In this work we theoretically analyze a circuit QED design where propagating
quantum microwaves interact with a single artificial atom, a single Cooper pair
box. In particular, we derivea master equation in the so-called transmon
regime, including coherent drives. Inspired by recent experiments, we then
apply the master equation to describe the dynamics in both a two-level and a
three-level approximation of the atom. In the two-level case, we also discuss
how to measure photon antibunching in the reflected field and how it is
affected by finite temperature and finite detection bandwidth.