Coherent Frequency Conversion from Microwave to Optical Fields in an Erbium Doped Y2SiO5 Crystal: Towards the Single Photon Regime

Abstract

In the context of quantum information technologies superconducting qubits (SQs) are very attractive devices for the manipulation of quantum states, and present themselves as one of our best candidates to build a quantum processor. They couple naturally to microwave photons, for which suitable quantum memories or a long distance propagation channel don’t exist. A way around these limitations is to turn these microwave photons into optical ones by building a quantum frequency converter: a device by which the frequency of a photon can be changed while preserving its non-classical correlations. Then, optical fibres could be used to link distant SQ-based devices together, facilitating the creation of a network of quantum computers. Moreover, SQs could then be coupled to quantum memories compatible with photons at optical frequencies, which are the most well developed kind of quantum memories at the present time.

This thesis explores the possibility to convert single microwave photons into optical photons using erbium doped in a yttrium orthosilicate crystal (Er3+:Y2SiO5). Er3+:Y2SiO5 is a good candidate because it has a naturally occurring optical transition near 1536 nm close to the point where silica optical fibres show their minimum loss. A microwave transition can be found in two different ways: one way is to use the 167 isotope of erbium, which is the only stable isotope that shows hyperfine splitting as it has non-zero nuclear spin. The hyperfine structure of the ground state of 167Er3+:Y2SiO5 spans over about 5 GHz. The other possibility is to use the other stable isotopes of erbium and Zeeman split their ground state using an external magnetic field. A microwave transition near 5 GHz can be achieved with moderate magnetic fields due to the high 𝑔-factors of Er3+:Y2SiO5.

The physical process of interest is a three wave mixing process involving two fields at optical frequencies and one field at microwave frequencies. In order to boost the efficiency of the frequency conversion process the Er3+:Y2SiO5 crystal is placed inside a microwave and an optical resonator. The problem is first explored from the theoretical point of view, where a nonlinear coefficient Λ(2) is derived (analogous to the 𝜒(2) often used in nonlinear optics), and the interaction between cavity modes and the nonlinear medium is studied. It is predicted that with a sample cooled down to millikelvin temperatures total frequency conversion between microwave and optical fields can be achieved.

A preliminary hole burning spectroscopy experiment is performed with the objective of reconstructing the hyperfine structure of the excited state of 167Er3+:Y2SiO5, but the complexity of the problem makes it too difficult to achieve this goal. Then a series of experiments are shown, aimed at determining whether or not frequency conversion at the single photon level is achievable using the even isotopes of erbium in a magnetic field. These experiments are based in the Raman heterodyne spectroscopy technique, which is used in combination with electron paramagnetic resonance and optical absorption spectroscopy. In all experiments the sample is cooled down to cryogenic temperatures near 4 K. A first experiment shows that the frequency conversion process exists in Er3+:Y2SiO5, in a setup where only a microwave resonator is used, but not an optical one. A second experiment is performed in a similar setup, this time presenting a quantitative study of the properties of the frequency conversion process, and its comparison with the theoretical model previously derived. A third experiment is performed, which incorporates an optical cavity to the system. The interaction between the erbium ions and the optical cavity introduces a whole new range of experimental complications, which are studied and discussed. Then, the frequency conversion signal is studied anew, showing an unexpected highly non-linear scaling behaviour with the input powers. A hypothesis explaining this unexpected behaviour is given, referring to stray optical absorption in the inhomogeneous line of Er3+:Y2SiO5 (and in particular 167Er3+:Y2SiO5), which can be bleached out under certain circumstances due to spectral hole burning effects. The overall maximum frequency conversion efficiency observed is of 3 × 10^−4 per Watt of pump laser power. While this value is still far from the target several ways of improvement are proposed, including cooling down the system to millikelvin temperatures, increasing the dopant concentration and modifying the geometry of the resonators.