We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level.The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsing the frequency detuning between the two resonators. The behavior of the system, which determines how the device can be operated, is analyzed as a function of one key parameter of the system, the damping ratio of the coupled resonators. We show a good agreement between experiments and simulations, realized by solving a set of coupled differential equations.

The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that thisnonlinearity can be used to convert an incoming single microwave photon into an outgoing n-photon Fock state in a different mode. In this process the Coulomb energy released by Cooper-pair tunneling is transferred to the outgoing Fock state, providing energy gain. The conversion can be made reflectionless (impedance-matched) so that all incoming photons are converted to n-photon states. With realistic parameters multiplication ratios n>2 can be reached. By cascading two to three such multiplication stages, the outgoing Fock-states can be sufficiently large to accurately discriminate them from vacuum with linear post-amplification and classical power measurement, implying that our scheme can be used as single-photon detector for itinerant microwave photons without dead time.

We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders ofmagnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially follows a polynomial decay law instead of an exponential one, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. The time delay gives rise to novel features in the reflection, transmission, power spectra, and second-order correlation functions of the system. Furthermore, we find the short-time dynamics of the giant atom for arbitrary drive strength by a numerically exact method for open quantum systems with a finite-time-delay feedback loop.

We propose two different setups to generate single photons on demand using an atom in front of a mirror, along with either a beam-splitter or a tunable coupling. We show that photongeneration efficiency ~ 99% is straightforward to achieve. The proposed schemes are simple and easily tunable in frequency. The operation is relatively insensitive to dephasing and can be easily extended to generate correlated pairs of photons. They can also in principle be used to generate any photonic qubit in arbitrary wave-packets, making them very attractive for quantum communication applications.

It has recently been demonstrated that surface acoustic waves (SAWs) can interact with superconducting qubits at the quantum level. SAW resonators in the GHz frequency range have alsobeen found to have low loss at temperatures compatible with superconducting quantum circuits. These advances open up new possibilities to use the phonon degree of freedom to carry quantum information. In this paper, we give a description of the basic SAW components needed to develop quantum circuits, where propagating or localized SAW-phonons are used both to study basic physics and to manipulate quantum information. Using phonons instead of photons offers new possibilities which make these quantum acoustic circuits very interesting. We discuss general considerations for SAW experiments at the quantum level and describe experiments both with SAW resonators and with interaction between SAWs and a qubit. We also discuss several potential future developments.

Single photon detectors are fundamental tools of investigation in quantum optics and play a central role in measurement theory and quantum informatics. Photodetectors based on differenttechnologies exist at optical frequencies and much effort is currently being spent on pushing their efficiencies to meet the demands coming from the quantum computing and quantum communication proposals. In the microwave regime however, a single photon detector has remained elusive although several theoretical proposals have been put forth. In this article, we review these recent proposals, especially focusing on non-destructive detectors of propagating microwave photons. These detection schemes using superconducting artificial atoms can reach detection efficiencies of 90\% with existing technologies and are ripe for experimental investigations.

We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and showthat its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.

Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwavephoton in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. By performing continuous measurements on the output field of the resonator we theoretically achieve an over-unity signal-to-noise (SNR) for a single shot measurement and 84% distinguishability between zero and one microwave photon with a single transmon and 90% distinguishability with two cascaded transmons. We also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: the higher the measurement efficiency, the greater is the decoherence.

We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconductingcircuits where tunable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.

We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation fieldis established, using a perturbation expansion in the junction’s critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.