Entangling two distant non-interacting microwave modes

We propose a protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto-electro-mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may represent a fundamental tool for the realization of quantum networks connecting distant solid-state and superconducting qubits, which are typically manipulated with microwave fields. The certifying measurements on the optical modes guarantee the success of entanglement swapping without the need of performing explicit measurements on the distant microwave fields.Comment: 7 pages, 3 figures; to appear in the special issue "Quantum and Hybrid Mechanical Systems - From Fundamentals to Applications" in Annalen der Physi

Entangling a nanomechanical resonator with a microwave field

We show how the coherent oscillations of a nanomechanical resonator can be entangled with a microwave cavity in the form of a superconducting coplanar resonator. Dissipation is included and realistic values for experimental parameters are estimated.Comment: submitted to J. Mod. Op

Entangling optical and microwave cavity modes by means of a nanomechanical resonator

We propose a scheme that is able to generate stationary continuous-variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a nanomechanical resonator. We show that when both cavities are intensely driven, one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and optomechanical entanglement

Stationary Entangled Radiation from Micromechanical Motion

Mechanical systems facilitate the development of a new generation of hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom. Entanglement is the essential resource that defines this new paradigm of quantum enabled devices. Continuous variable (CV) entangled fields, known as Einstein-Podolsky-Rosen (EPR) states, are spatially separated two-mode squeezed states that can be used to implement quantum teleportation and quantum communication. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers and at microwave frequencies Josephson circuits can serve as a nonlinear medium. It is an outstanding goal to deterministically generate and distribute entangled states with a mechanical oscillator. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30 micrometer long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40(37) dB below the vacuum level. This mechanical system correlates up to 50 photons/s/Hz giving rise to a quantum discord that is robust with respect to microwave noise. Such generalized quantum correlations of separable states are important for quantum enhanced detection and provide direct evidence for the non-classical nature of the mechanical oscillator without directly measuring its state. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects with potential implications in sensing, open system dynamics and fundamental tests of quantum gravity. In the near future, similar on-chip devices can be used to entangle subsystems on vastly different energy scales such as microwave and optical photons.Comment: 13 pages, 5 figure