Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air

Abstract

Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a cryostat, where they are created, to an environment dominated by thermal noise. Indeed, the states carrying such quantum resources are generated in a cryostat characterized by a temperature Tin≃50 mK and an intrinsic impedance Zin=50Ω. Then, an antenna-like device is required to transfer them with minimal losses into open air, characterized by an intrinsic impedance of Zout=377Ω and a temperature Tout≃300 K. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure, we find the optimal shape of the impedance, and we propose a functional ansatz to qualitatively describe this shape. Additionally, this study reveals that the reflectivity of the antenna is very sensitive to this shape, so that small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work is relevant in the fields of microwave quantum sensing and quantum metrology with special application to the development of the quantum radar, as well as any open-air microwave quantum communication protocol.

Bi‐Frequency Illumination: A Quantum‐Enhanced Protocol

“…This information can be related to the electromagnetic response of a reflective object to changes in frequency, and, consequently, the protocol can be applied to a wide spectrum of situations. Although the results are general, we suggest two applications within quantum microwave technology: radar physics, motivated by the atmospheric transparency window in the microwaves regime, together with the naturally noisy character of open‐air; [ 71,98,100–103 ] and quantum‐enhanced microwave medical contrast‐imaging of low penetration depth tissues, motivated not only by the non‐ionizing nature of these frequencies, but also because resorting to methods that increase the precision and/or resolution without increasing the intensity of radiation is crucial in order not to heat the sample.…”

Open-Air Microwave Entanglement Distribution for Quantum Teleportation

“…When considering a lossy antenna, we observe higher entanglement degradation in the symmetric state due to the fact that both modes of the state are output by an antenna, whereas only one mode of the asymmetric state goes through it. Although √ η ant can theoretically be reduced below 10 −9 [86], this leads to a slightly lower fidelity in the case of the symmetric state. In the figures appearing in this section, however, we consider η ant = 0 for simplicity.…”

“…2) for open-air entanglement distribution relies on a variety of things: first, generation of two-mode squeezed thermal (TMST) states with thermal photons n < e −r sinh(r), given squeezing r, which will take place in a cryostat at T ∼ 50 mK temperatures; second, efficient transmission of states out of the cryostat and into open air, targeting optimal entanglement preservation; for this task, we rely on an antenna based on the design proposed in Ref. [86] with special attention given to the shape of the impedance function, which greatly affects entanglement preservation; third, estimation of losses in open air that describe the attenuation of the signal caused by the presence of thermal noise in the environment, with the objective of setting bounds on effective transmission distances. This protocol will prepare the foundation for an open-air microwave quantum teleportation protocol, whose fidelity will depend on the entanglement of the resource shared by the parties involved.…”

“…Such an antenna can be modeled by a finite transmission line with variable characteristic impedance and designed to match the impedances of the cryostat and of open air at its ends. This approach was discussed in a previous study [86], where the transmissivity of the antenna was optimized for the task of entanglement distribution with TMST states of 5 GHz in an antenna of 3 cm. With an exponential profile of the impedance inside the antenna, reflectivity can be reduced down to √ η < 10 −9 , qualitatively matching the classical result of a horn antenna.…”

“…An infinite array of beam splitters that reproduce these features (see Ref. [86]) can be replaced by a single beam splitter with an effective reflectivity and number of thermal photons given by…”