We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequencyconversion and delay, and requires neither permanent magnets nor microwave control tones, allowing on-chip integration with other superconducting circuits without expensive control hardware. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW (≈103 circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.
We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments.The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dynamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that function as nearly linear, tunable inductors. The connection to familiar ferrite-based circulators is a simple frame boost in the internal dynamics‘ equation of motion. In addition to the general, schematic analysis, we also give an overview of many considerations necessary to achieve a practical design with a tunable center frequency in the 4-8 GHz frequency band, a bandwidth of 240 MHz, reflections at the -20 dB level, and a maximum signal power of approximately order 100 microwave photons per inverse bandwidth.
Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations and quantum information processing. The exchange of real and virtualphotons between atoms gives rise to non-trivial interactions the strength of which decreases rapidly with distance in three dimensions. Here we study much stronger photon mediated interactions using two superconducting qubits in an open onedimensional transmission line. Making use of the unique possibility to tune these qubits by more than a quarter of their transition frequency we observe both coherent exchange interactions at an effective separation of 3λ/4 and the creation of super- and sub-radiant states at a separation of one photon wavelength λ. This system is highly suitable for exploring collective atom/photon interactions and applications in quantum communication technology.
We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional (1D) superconducting transmissionline. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super- and subradiance or to a coherent exchange-type interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A.F. van Loo {\it et al.} (2013)].