Directional amplifiers are an important resource in quantum information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of
phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise. In the reverse direction, they emit thermal noise stemming from the mechanical resonators and we discuss how this noise can be suppressed, a crucial aspect for technological applications. The isolation bandwidth in both is of the order of the mechanical linewidth divided by the amplitude gain. We derive the bandwidth and gain-bandwidth product for both and find that the phase-sensitive amplifier has an unlimited gain-bandwidth product. Our study represents an important step toward flexible, on-chip integrated nonreciprocal amplifiers of microwave signals.
We propose a device architecture capable of direct quantum electro-optical conversion of microwave to optical photons. The hybrid system consists of a planar superconducting microwave
circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that electro-optical (vacuum) coupling rates g0 as large as∼2π(10−100) kHz are achievable with currently available technology, due to the small mode volume of the planar microwave resonator. Operating at millikelvin temperatures, such a converter would enable high-efficiency conversion of microwave to optical photons. We analyze the added noise, and show that maximum conversion efficiency is achieved for a multi-photon cooperativity of unity which can be reached with optical power as low as (1)mW.
and circuit quantum electrodynamics (cQED) . Coupled to
artificial atoms in the form of superconducting"]qubits [3, 4], they now provide
a technologically promising and scalable platform for quantum information
processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum
systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots 
or mechanical oscillators [14, 15] has been explored to realize hybrid systems
with extended functionality. Here, we couple a superconducting coplanar
waveguide resonator to a nano-coshmechanical oscillator, and demonstrate
all-microwave field controlled slowing, advancing and switching of microwave
signals. This is enabled by utilizing electromechanically induced transparency
[16-18], an effect analogous to electromagnetically induced transparency (EIT)
in atomic physics . The exquisite temporal control gained over this
phenomenon provides a route towards realizing advanced protocols for storage of
both classical and quantum microwave signals [20-22], extending the toolbox of
control techniques of the microwave field.