Rare Earth-Doped Crystals for Quantum Information Processing

Philippe Goldner1; Alban Ferrier1,2; Olivier Guillot-Noël1,*    1 Institut de Recherche de Chimie Paris, CNRS-Chimie, ParisTech, Paris, France
2 Sorbonne Universités, UPMC Univ Paris 06, Paris, France
* In memoriam

1 Introduction

Information in digital form is at the heart of nowadays societies, playing a major role in world-scale organizations down to many individual daily activities. Although technology made extraordinary progresses in terms of communication speed and capacity, data storage, or processing power, most of the fundamental concepts of information science were established in the beginning of the twentieth century. In 1984, a quantum algorithm was discovered by Bennett and Brassard for encrypted data exchange (Bennett and Brassard, 1984) and in 1985, Deutsch pioneered quantum computing theory (Deutsch, 1985). This was the start of quantum information processing (QIP), which is currently a major research topic in physics, computer science, mathematics, and material science. Quantum information is a new paradigm, where the classical bits, which can take only discrete values, are replaced by quantum bits, called qubits, which can assume any superposition state. This fundamentally new resource allows data processing, storage, and communication in ways impossible to achieve with classical systems (Kimble, 2008; Nielsen and Chuang, 2000; Stolze and Suter, 2008).

QIP is however very demanding on physical systems and its development has triggered important advances in quantum system control and design. In turn, QIP theory has emerged as a unified way to describe the behavior of these systems, independently of the details of their nature, structure, or interactions. QIP uses superposition states, which exist for a significant duration only in isolated systems. Interactions with a fluctuating environment, with many degrees of freedom, destroy them. Examples of quantum systems suitable for QIP are photons (Gisin and Thew, 2007; Kok et al., 2007) and nuclear spins (Chuang et al., 1998; Morton et al., 2008), which can have very low interactions with surrounding electromagnetic fields and atoms. QIP is also investigated in many other systems (Ladd et al., 2010; Lvovsky et al., 2009) such as trapped ions (Blatt and Roos, 2012), superconductors (Clarke and Wilhelm, 2008), electronic and nuclear spins in insulators and semiconductors (Hanson et al., 2007; Wrachtrup and Jelezko, 2006), and ultracold atoms (Bloch et al., 2012; Chanelière et al., 2005). As light is an excellent carrier of quantum information, as it is of classical one, there is also a need to interface it to material systems to store and process information (Northup and Blatt, 2014). Moreover, progress in lasers has also set them as efficient devices for controlling efficiently and accurately quantum systems. In these respects, rare earth (R)-doped crystals have very favorable spectroscopic properties among solid-state systems. The main one is to exhibit extremely narrow optical transitions, equivalent to long-lived superposition states, at cryogenic temperatures (Macfarlane, 2002). Depending on the R ions considered, these transitions span the entire visible and infrared range, including the telecom window at 1.5 μm. Moreover, many R ions have isotopes with nonzero nuclear spins, which can be therefore optically controlled or interfaced with photonic qubits. Finally, R-doped crystals are generally very robust, photostable materials, which can be readily cooled down to liquid helium temperatures in closed cycle cryostats. Their synthesis and spectroscopy have been widely developed for applications in photoluminescence, lasers, scintillation, etc. In addition, these materials are studied for classical information or signal processing, which shares some requirements and schemes with QIP applications (Le Gouët et al., 2006; Li et al., 2008; Thorpe et al., 2011).

In this chapter, we review the applications of R-doped crystals to two specific QIP applications: optical quantum memories and quantum computing. After a brief introduction to QIP, we describe coherent light-atom interactions, which allow creating and controlling atomic quantum states. The spectroscopic properties of R-doped crystals are discussed afterward, with a focus on the specific features used in QIP. Finally, the concepts and studies related to quantum memories and computing are presented. In the two last sections, we chose to emphasize a few representative experiments, underlining important points, rather than to give extensive lists of results. As this field is relatively new to the rare-earth community, we felt that this approach could be more useful for the reader.

2 Quantum Information Processing

2.1 Qubits and Gates

The reader is referred to Nielsen and Chuang (2000) or Stolze and Suter (2008) for a detailed presentation of QIP. In the following, we only review the basic concepts of the field. The qubit, or quantum bit, is the elementary unit of information in QIP. It is the equivalent of the bit in classical computing and communication. The bit can take two values, 0 or 1, and is implemented as different states...