Efficient quantum memory is of paramount importance for long-distance quantum communications, as well as for complex large-scale computing architectures. We investigate the capability of Er$^{3+}$:Y$_2$SiO$_5$ crystal to serve as a quantum memory for the travelling microwave photons by employing techniques developed for dense optical ensembles. In our efforts to do so, we have performed high-resolution microwave spectroscopy of Er$^{3+}$:Y$_2$SiO$_5$, where we identified electronic spin as well as hyperfine transitions. Furthermore, we have explored spectral hole burning technique and studied the spin relaxation process at millikelvin temperatures, determined the main relaxation mechanisms, which lay the groundwork for further studies of the topic.
Microwave cavity-free hole burning spectroscopy of Er3+:Y2SiO5 at millikelvin temperatures
Efficient quantum memory is of paramount importance for long-distance quantum communications, as well as for complex large-scale computing architectures. We investigate the capability of Er3+:Y2SiO5 crystal to serve as a quantum memory for the travelling microwave photons by employing techniques developed for dense optical ensembles. In our efforts to do so, we have performed high-resolution microwave spectroscopy of Er3+:Y2SiO5, where we identified electronic spin as well as hyperfine transitions. Furthermore, we have explored spectral hole burning technique and studied the spin relaxation process at millikelvin temperatures, determined the main relaxation mechanisms, which lay the groundwork for further studies of the topic.
Rare-earth-ions (REI) doped crystals have remarkable optical and spin properties characterized by narrow homogeneous linewidths, which can be studied despite the large inhomogeneous broadening of the ensemble line through spectral hole burning (SHB). Here, we report SHB spectroscopic measurements in a scheelite crystal of CaWO4 by pumping the spin transition of a paramagnetic REI (Er3+) at microwave frequency and millikelvin temperatures, with nuclear spin states of neighboring 183W atoms serving as the auxiliary levels. The repeated application of pairs of microwave pulses generates a periodic modulation of the Er3+ density profile, which we observe spectrally and in the time-domain as an accumulated echo. The lifetime of the holes and accumulated echoes rises steeply as the sample temperature is decreased, exceeding a week at 10mK. Our results demonstrate that millikelvin temperatures can be beneficial for signal processing applications requiring long spectral hole lifetimes. The authors report spectral hole burning with a record hole lifetime in a Er3+ doped scheelite crystal CaWO4 at mK temperatures. This can benefit applications in classical and quantum information processing.
Enhancement of optical coherence in 167Er:Y2SiO5 crystal at sub-Kelvin temperatures
Er3+:Y2SiO5 crystal is a promising candidate with a great variety of its potential applications in quantum information processing and quantum communications ranging from optical/microwave quantum memories to circuit QED and microwave-to-optics frequency converters. Some of the above listed applications require ultra-low temperature environment, i.e., temperatures T≲0.1K. Most of the experiments with erbium doped crystals have been so far carried out at temperatures above 1.5~K. Therefore, only little information is known about Er3+:Y2SiO5 coherence properties at millikelvins. Here, we investigate optical decoherence of 167Er:Y2SiO5 crystal by performing 2- and 3-pulse echo experiments at millikelvin temperature range and at weak and moderate magnetic fields. We show that the deep freezing of the crystal results in an increase of optical coherence time by one order of magnitude compared to temperature of 1.5 Kelvin and magnetic field of $\sim$0.2~T, taken as a reference point. We further describe the detailed investigation of the decoherence mechanisms in this regime.
Rare-earth-ion (REI) ensembles in crystals have remarkable optical and spin properties characterized by narrow homogeneous linewidths relative to the inhomogeneous ensemble broadening. This makes it possible to precisely tailor the ensemble spectral density and therefore the absorption profile by applying narrow-linewidth radiation to transfer population into auxiliary levels, a process broadly known as spectral hole burning (SHB). REI-doped crystals find applications in information processing, both classical (pattern recognition, filtering, spectral analysis) and quantum (photon storage), all protocols requiring suitable ensemble preparation by SHB as a first step. In Er3+-doped materials, the longest reported hole lifetime is one minute, and longer lifetimes are desirable. Here, we report SHB and accumulated echo measurements in a scheelite crystal of CaWO4 by pumping the electron spin transition of Er3+ ions at microwave frequencies and millikelvin temperatures, with nuclear spin states of neighboring 183W atoms serving as the auxiliary levels. The lifetime of the holes and accumulated echoes rises steeply as the sample temperature is decreased, exceeding a month at 10 mK. Our results demonstrate that millikelvin temperatures can be beneficial for signal processing applications requiring long spectral hole lifetimes.
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.
This thesis investigates the potential of Er:YSO and Er:Si for quantum communication and computation applications. Erbium uniquely possess optical transitions in the 1.5 um region, making it suitable for both fibre telecommunication and silicon photonics. The properties of the I15/2↔I13/2 optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in Er3+ dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial (C3) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.
The realization of scalable quantum networks for distribution of entanglement over long distances hinges on quantum repeaters. To outperform the exponential transmission loss in optical fibers, quantum repeaters must employ multiplexing schemes in the temporal, spectral, or spatial domain. The performance of such a multiplexed scheme is contingent on efficient quantum memories offering both extended storage times and large multimode capacities. Towards this goal, we experimentally demonstrate a memory platform operating at telecom wavelength using an Er3+:Y2SiO5 crystal. We record on-demand storage and recall of weak coherent pulses for up to 1 ms, exceeding by an order of magnitude that of previously reported demonstrations based on Er3+. The memory exhibits an efficiency of 10.36 % at 300 μs storage time with a signal-to-noise ratio of 10.9, mainly limited by spontaneous emission noise. We also store two spectral modes representing a frequency-bin encoding and retrieve the state with an overlap of 81.8 %. Furthermore, we demonstrate multimode capacity by simultaneously storing 20 temporal and 3 spectral modes with on-demand and selective recall capabilities, serving as a promising step toward a scalable quantum repeater architecture.