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From Quantum Optics to Quantum Technologies From Quantum Optics to Quantum Technologies Dan Browne,1 Sougato Bose,1 Florian Mintert,2 and M. S. Kim2 1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK 2QOLS, Blackett Laboratory, Imperial College London, SW7 2AZ, UK Quantum optics is the study of the intrinsically quantum properties of light. During the second part of the 20th century experimental and theoretical progress developed together; nowadays quan- tum optics provides a testbed of many fundamental aspects of quantum mechanics such as coherence and quantum entanglement. Quantum optics helped trigger, both directly and indirectly, the birth of quantum technologies, whose aim is to harness non-classical quantum effects in applications from quantum key distribution to quantum computing. Quantum light remains at the heart of many of the most promising and potentially transformative quantum technologies. In this review, we cele- brate the work of Sir Peter Knight and present an overview of the development of quantum optics and its impact on quantum technologies research. We describe the core theoretical tools developed to express and study the quantum properties of light, the key experimental approaches used to control, manipulate and measure such properties and their application in quantum simulation, and quantum computing. I. INTRODUCTION the quantisation of the field was the collapses and re- vivals of Rabi oscillations [13] which was tested in a cav- In 1900, Max Planck postulated that the energy of the ity quantum electrodynamics (QED) setup [14, 15]. An light field was quantised, triggering the birth of quan- information-theoretic approach [17] for the JCM found tum mechanics which become one of the central pillars that the cavity field which was initially prepared in a of modern physics. The development of the laser in 1960 large amplitude coherent state will become a coherent provided a precise new tool for the generation of coher- superposition state at a certain interaction time [18, 19]. ent monochromatic light, and the field of quantum optics While quantum optics focusses on the physics of light flourished through close alignment of experimental and and atoms, quantum information focusses on the proper- theoretical research. ties and applications of the qubit. A qubit, or quantum In this review, we celebrate the works of Sir Peter bit, is the quantum-mechanical extension of a conven- Knight, who is known for many pioneering works, in- tional bit f0; 1g. As a quantum state, the state of a fluential reviews and textbooks [1, 2] in quantum optics. qubit j i can be in a superposition of 0 and 1: Quantum optics was instrumental in the development of j i = αj0i + βj1i quantum technology and quantum information and Peter Knight is one of the founding fathers in this development. where α and β are complex numbers satisfying jαj2 + Quantum optics provided the tools to study the foun- jβj2 = 1. The number of complex numbers needed to dations of quantum mechanics with exquisite precision. describe the state of a quantum system grows exponen- The interaction of an isolated atom and a light field pro- tially with its complexity (for example, the numbers of its vided the ideal testbed for controversial ideas. For exam- constituents) which soon makes it prohibitively difficult ple, \quantum jumps" are a manifestation of the discon- to perform exact calculations of its behaviour, particu- tinuity inherent in the quantum measurement process, larly those emergent properties which cannot be easily [3, 4] which can be directly observed [5]. One of the approximated or guessed by human ingenuity. This fact key concepts of quantum optics is the coherent state, lead Feynman [22] to suggest, in the early 1980s, that introduced by Schr¨odinger,and used by Glauber and Su- the properties of complex quantum systems should ide- darshan to study high-order coherences of light [6, 7]. ally be studied with collections of controllable and pro- Squeezed light, [8] in which the quantum noise is re- grammable quantum entities which interact with each duced in one quadrature at the expense of the increased other to \mimic" the behaviour of the system being stud- noise in the other quadrature, has also played a central ied. role in quantum optics as it developed. From the begin- The counterpart to coherence in quantum optics is ning, quantum optics combined the study of fundamen- the quantum mechanical superposition of the qubit. Ex- tal physics with applications to technology. Squeezed tended across multiple qubits, superposition leads to en- light, for example, enables a new kind of precision mea- tanglement, and information can be represented and pro- surement, with application, for instance, in gravitational cessed in an intrinsically non-classical way. Thus a quan- wave detection [9] and for noiseless communications [10]. tum computer [20] would be able to compute in an in- The Jaynes-Cummings model (JCM) [11, 12], which trinsically different way to standard classical computers. describes the interaction between a two-level atom and Quantum computing became the subject of intense study a single mode of the electromagnetic field, provided a after Shor invented an efficient quantum algorithm for lens for studying the nonclassical properties of the atom- factoring, a problem for which no efficient classical algo- field interaction. One of the important consequences of rithm is known despite centuries of study [21]. 2 Another application of quantum mechanics in infor- weakly entangled pairs [30, 31]. A simple but powerful mation processing is found in sending secret messages. distillation protocol [32] was developed using entangle- It is well-known that a one-time pad (a string of random ment swapping [33, 34]. Entanglement can be described numbers shared by two people) is the most secure way by using the Schmidt decomposition [35]. Finding a mea- to send a secret message. In 1984, Bennett and Brassard sure of entanglement was one of the issues to characterise [23] invented a scheme to create a one-time pad between quantum entanglement, Peter Knight and his colleagues distant partners using non-classical light fields prepared pioneered to find useful quantification of quantum entan- in superposition states (I). glement [36{38]. The current development of quantum technology and Atom optics, which is an effort to use quantum coher- quantum information processing is based on our ability ences of atomic motion, is another branch of quantum to control coherences of a large quantum system. In do- optics. Indeed, a very early form of atom interferometry ing this one of the main obstacles is the system's uncon- is the Ramsey interferometry based on the quantum co- trollable interaction with its environment. There have herences in atomic internal states. Atomic clocks have been extensive studies of decoherence mechanisms in the been developed and precision sensors and accelerometers framework of Markovian and non-Markovian open quan- have been investigated based on atom optics. tum systems and quantum trajectories. Knight worked In this review, we survey how quantum optics has de- on the sources and characteristics of quantum decoher- veloped into quantum technology highlighting the roles ence using a quantum jump approach [16] with his col- and characteristics of photons, ions, atoms and mechan- league Martin Plenio. He also worked on various ways ical oscillators. In Section II, we review the quantum to protect a quantum state from decoherence using the properties of light itself, focussing on photons and coher- phase control of the system [24] and the concept of ent states. In Section III, we see how the JCM provides a decoherence-free subspace [25]. A key to overcome the powerful tool for the study of the interaction of quantum decoherence in quantum computation came from quan- light and atoms. In Section IV, we review trapped ions, tum error correction which requires a large number of an important test-bed for these theoretical ideas and a entangled resources [26]. The theory of quantum er- platform for the development of quantum technologies. ror correction was further developed with the concept In Section V, we introduce mechanical oscillators, repre- of fault-tolerant quantum computation [27]. senting an analogue of quantum light in meso-scopic mat- Quantum entanglement is one of the most important ter. Finally, in Section VI we review how the application non-classical ingredients in quantum technology. We say of these ideas and tools for the precise manipulation of two quantum systems are entangled when the density op- quantum systems is giving rise to new technologies. erator of the total system cannot be written as a weighted sum of the product states: X II. PHOTONS ρ^ 6= Pnρ^1;n ⊗ ρ^2;n (1) n=0 The study of photons is at the heart of quantum op- tics. The concept of \particles of light" has gone through where Pn is a probability function andρ ^i;n is a density op- erator of system i = 1; 2. Entanglement can be thought various stages. While the quantisation of energy was of as a special kind of correlation where it is possible suggested to explain the blackbody radiation at the ini- for the states of local systems to carry more uncertainty tial stage of quantum mechanics, it was not clear which than the state of the global system, something impossi- energy was really quantised as well as its consequences. ble in classical statistics. Entanglement, which is closely Glauber [6] defined the coherent state of photons as an connected to nonlocality in the Einstein-Podolsky-Rosen eigenstate of the annihilation operator and found that (EPR) paradox [28], has had a number of direct applica- the coherent state is represented as a displaced vacuum tions. Ekert [29] proposed a scheme to share a one-time in phase space. The coherent state is known to describe pad between the two users of a secret message, using the photon number statistics and the coherence proper- the entangled nonlocal state of light fields.
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