Ebook: Nanoscale Quantum Optics

More than 60 people from all over the world, including students, researchers and lecturers, gathered in Varenna for the 204 Course of the International School of Physics “E. Fermi” dedicated to Nanoscale Quantum Optics. The course was organized in collaboration with the COST Action MP1403 “Nanoscale Quantum Optics”, a network that involved 28 European countries and more than 500 researchers.

Recent developments aiming at the realization of new technologies based on quantum physics have been recognized by the European Commission as priorities, with the launch of the Quantum Technology Flagship Programme. These are, for example, new cryptographic techniques for security in telecommunications, new computing hardware that can solve problems so far inaccessible even to the latest generation of supercomputers, and new precision standards and sensors capable of measuring for instance extremely weak magnetic fields, with applications ranging from materials science to medical diagnostics. Nanoscale quantum optics combines these themes with nanophotonics, which addresses the control of light and its coupling with matter on a nanometer scale, a miniaturization comparable to the transition from valve-based electronics to integrated circuits. Structured materials provide confinement much beyond the wavelength scale, the interaction of light with nanoscale object offers novel means for interfacing light with different degrees of freedom, and quantum optics experiments are being upgraded in miniaturized nanophotonic platforms.

Based on such advances, the Course was therefore an opportunity to train new gener- ations of scientists, who will have the privilege of doing research on topics that promise great innovations in science and technology.

This proceedings book contains the following lecture and seminars held during the school:

– “Basic concepts for quantum optics and quantum technologies”, by I. D’Amico, introduces the background concepts.

– “Materials for quantum nanophotonics”, by N. P. de Leon, outlines the requirements for a range of quantum nanophotonics applications, and describes the key material characteristics that affect physical properties related to these requirements.

– “Quantum optics and nonclassical light generation”, by J. Vuckovic et al., discusses the theoretical underpinnings of the seminal experiments in solid-state quantum optics.

– “Creating quantum correlations between quantum-dot spins”, by M. Atatüre, describes how to generate nonlocal quantum correlations between electron spins in semiconductor quantum dots.

– “Platforms for telecom entangled photon sources”, by F. Sciarrino et al., reviews different platforms used to generate telecom-entangled photon pairs, focusing in particular on an integrated source realized by the femtosecond laser writing technique.

– “Quantum optics with single spins”, by L. C. Bassett, describes the quantum-mechanical coupling between atom-like spin states and light, using the diamond nitrogen-vacancy (NV) center as a paradigm. Moreover, it explains various methods that serve as the basis for advanced protocols at the heart of many emerging quantum technologies.

– “Nanoscale sensing and quantum coherence”, by F. Reinhard, summarizes concepts and techniques about single-qubit sensors, including an outlook to the major trends of the field.

– “ Many-body physics and quantum simulations with strongly interacting photons”, by D. G. Angelakis and Jirawat Tangpanitanon, focuses on interacting photons in superconducting circuits for quantum simulation of both in and out-of-equilibrium quantum many-body systems.

– “Nano-optomechanics”, by E. Verhagen, introduces the basic physical description of optomechanical interactions at a tutorial level, and highlight several directions of current research.

In addition, among all poster contributions the following were selected for this book:

– “Photostable molecules on chip: a scalable approach to photonic quantum technologies”, by M. Colaiutti et al., presents the design and characterization of the evanescent coupling between dibenzoterrylene molecules and a ridge waveguide made of silicon nitride.

– “Environment spectroscopy with an NV center in diamond”, by S. Hernández-Gómez et al., describes in detail a method to spectroscopically characterize the spin bath around an NV center and identify the coherent coupling with the nearest nuclear spins.

– “Ultrafast photonic quantum correlations mediated by individual phonons”, by S. Tarragó Vélez and C. Galland, outlines a new technique to prepare and measure the lifetime of the first phonon Fock state in diamond using single photon time-correlated Raman spectroscopy.

In this collection of chapters we hope the readers will find a valuable overview of the state-of-the-art and current trends in nanoscale quantum optics.

Mario Agio, Irene D’Amico, Costanza Toninelli and Rashid Zia

This introductory paper aims to provide a brief review of some basic concepts in quantum optics and quantum information, such as quantization of the electro-magnetic field, Fock and coherent states, quadrature operators, qubits and quantum gates, entanglement, Bell states and Bell inequality, mixed states and the density operator.

Engineering coherent systems is a central goal of quantum science, quantum optics, and quantum information processing. For quantum nanophotonics applications, it is particularly important to design and control systems that exhibit coherent optical transitions and long spin coherence times. This review outlines the requirements for a variety of quantum nanophotonics applications, and describes the key material properties that affect physical properties related to these requirements.

This paper will focus on the theoretical and experimental study of light-matter interaction in photonic structures. We will therefore start by describing quantum optical models of optical cavities and waveguides. Then we will describe the basic physics behind light matter interactions, and provide a theoretical analysis of the phenomena that result from it. Finally, we will describe single-photon sources, their characterization and introduce solid-state platforms that can be employed for their implementation. Throughout this paper, we have tried to provide a sound and complete description of the theoretical underpinnings of the seminal experiments in quantum optics. Detailed derivations of some of the results employed in the main text have been provided in the appendices.

This paper focuses on generating nonlocal quantum correlations between electron spins in semiconductor quantum dots located far from each other. Some of the key prerequisite concepts are covered in other contributions to these proceedings and we focus on applying some of the concepts for creating correlated spins. We start by describing how nonlocal correlations can be generated between quantum systems that have no prior connection, by utilising a particular type of measurement known as quantum erasure. We will focus on self-assembled semiconductor quantum dots and contrast the observed results to other systems.

Entanglement represents a fundamental resource for quantum technologies, including quantum communication tasks. In this context, photons are the ideal physical systems due to their capability of carrying information over long distances. Hence, it is fundamental to design reliable sources of entangled photons in the telecom wavelength regime (around 1.55 μm), where optical fiber losses are low. In this paper we review different platforms used to generate telecom entangled photon pairs, and we focus in particular on an integrated source realized by the femtosecond laser writing (FLW) technique, which allows to devise stable and compact optical circuits in glass. We show how this technique can be employed to inscribe waveguides in nonlinear crystals for generation of telecom entangled photon pairs on a chip.

Defects in solids are in many ways analogous to trapped atoms or molecules. They can serve as long-lived quantum memories and efficient light-matter interfaces. As such, they are leading building blocks for long-distance quantum networks and distributed quantum computers. This paper describes the quantum-mechanical coupling between atom-like spin states and light, using the diamond nitrogen-vacancy (NV) center as a paradigm. We present an overview of the NV center’s electronic structure, derive a general picture of coherent light-matter interactions, and describe several methods that can be used to achieve all-optical initialization, quantum-coherent control, and readout of solid-state spins. These techniques can be readily generalized to other defect systems, and they serve as the basis for advanced protocols at the heart of many emerging quantum technologies.

Small solid-state qubits, most prominently single spins in solids, can be remarkable sensors for various physical quantities ranging from magnetic fields to temperature. They package the performance of their bulk semiconductor counterparts into a nanoscale device, sometimes as small as a single atom. This review is a minimalist introduction into this concept. It gives a brief summary of quantum coherence, Ramsey spectroscopy and a derivation of the “standard quantum limit” of the sensitivity that a single-qubit sensor can reach. It goes on to discuss the surprising improvement that dynamical decoupling has brought about and concludes with an outlook to the major frontiers of the field.

Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponentially with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-T_c superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. State-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.

This tutorial presents a brief introduction to the physical principles of cavity optomechanics. When light and mechanical motion are both confined in nanoscale structures, they can effectively couple through radiation pressure. This lecture discusses the quantum limits to optical measurement of mechanical motion and the basic physics of optomechanical interactions between photons and phonons. It reviews several recent developments in the field that exploit state transfer, breaking of time-reversal symmetry, and nonlinearities to develop new ways to control both light and motion in the classical and quantum domains.

In this manuscript we demonstrate the potential of a hybrid technology which combines single organic molecules as quantum light sources and dielectric chips. In particular, we discuss our approach based on evanescent coupling of dibenzoterrylene molecules to silicon nitride waveguides and show a coupling efficiency of up to 42 ± 2% over both propagation directions. Our results open a novel path towards a fully integrated and scalable photon processing platform.

Nitrogen-vacancy (NV) centers in diamond have emerged in the last decade as a prominent platform for quantum technologies. As for any qubit system, a good understanding of their local environment is crucial to build quantum devices protected from detrimental noise. Here, we describe in detail a method to spectroscopically characterize the spin bath around an NV center, even when the NV coherence time is short, and identify the coherent coupling with the nearest nuclear spins. In the regime of weak qubit-bath coupling, the acquired knowledge of the bath reliably predicts the qubit dynamics under different controls.

This contribution to the proceedings describes a new technique to prepare and measure the lifetime of the first phonon Fock state in diamond using single-photon time-correlated Raman spectroscopy. By using a pair of ultrafast laser pulses of two different colors we can spectrally distinguish the Stokes photons created during the first pulse from the anti-Stokes photons created during the second pulse. Single-photon detection on the Stokes signal acts as a projective measurement preparing the phonon in an energy eigenstate. During the lifetime of the phonon, the second pulse, which arrives after a controllable delay, has a higher probability of emitting an anti-Stokes photon than allowed by classical mechanics. Two-photon quantum correlations between Stokes and anti-Stokes can therefore be used to map the phonon decay.