Nonreciprocal microwave devices are ubiquitous in radar and radio communication and indispensable in the readout chains of superconducting quantum circuits. Since they commonly rely on ferrite materials requiring large magnetic fields that make them bulky and lossy, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using the Josephson nonlinearity. Here, we realize reconfigurable nonreciprocal transmission between two microwave modes using purely optomechanical interactions in a superconducting electromechanical circuit. The scheme relies on the interference in two mechanical modes that mediate coupling between the microwave cavities and requires no magnetic field. We analyse the isolation, transmission and the noise properties of this nonreciprocal circuit. Finally, we show how quantum-limited circulators can be realized with the same principle. All-optomechanically mediated nonreciprocity demonstrated here can also be extended to directional amplifiers, and it forms the basis towards realizing topological states of light and sound.

Nonreciprocal microwave devices are ubiquitous in radar and radio communication and indispensable in the readout chains of superconducting quantum circuits. Since they commonly rely on ferrite materials requiring large magnetic fields that make them bulky and lossy, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using the Josephson nonlinearity. Here, we realize reconfigurable nonreciprocal transmission between two microwave modes using purely optomechanical interactions in a superconducting electromechanical circuit. The scheme relies on the interference in two mechanical modes that mediate coupling between the microwave cavities and requires no magnetic field. We analyse the isolation, transmission and the noise properties of this nonreciprocal circuit. Finally, we show how quantum-limited circulators can be realized with the same principle. All-optomechanically mediated nonreciprocity demonstrated here can also be extended to directional amplifiers, and it forms the basis towards realizing topological states of light and sound.

Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride, respectively, as the electrodes and the insulating dielectric, a strongly nonlinear behavior at zero bias and small voltages is obtained. When the temperature is sufficiently low, the strong nonlinear interaction emerging from the quantum capacitance exhibits a diverse range of phenomena. The proposed structure could take over the functionalities of nonlinear elements in many cryogenic quantum systems, and in particular, quantum electrooptics. It is shown that ultrastrong coupling is easily reached with small number of pump photons at temperatures around 1 K and capacitor areas of the order of 1 μm 2 . A measure of anharmonicity is defined and as potential applications, a qubit design as well as schemes for non-reciprocal devices such as an electromagnetic frequency circulator are discussed. 20 Josephson junctions, despite their strong nonlinearity, normally operate at very small currents, which limits their maximum total photon occupation number. Moreover, they occasionally need to be biased by either a direct current (DC) magnetic field or electric current. As for the nonlinear capacitors, Graphene has been used in optomechanics as the mechanical element in the form of a drum capacitor.

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