Quantum State Engineering

Abstract

The review presents from an historical point of view a number of single-photon sources that have been designed and put into operation in a number of different systems. The use of strongly attenuated thermal or laser sources and the use of entangled states are also discussed.

Introduction

The introduction of quantization of energy to discuss the interaction of electromagnetic radiation with matter was done in 1900 by Planck, 1900a, Planck, 1900b. Einstein (1905) surmised that also free radiation had a granular structure. The name photon was later proposed by Lewis (1926). The quantization of the electromagnetic field was made by Dirac, 1926, Dirac, 1927. A review of some historical papers on the subject has been made by Keller (2007).

What a photon is, exactly nobody can say. It is the quantum representation of a mode of the electromagnetic field and is an exclusively quantum concept. With this definition, photons have associated plane waves of definite wave vector k and definite polarization s. A monochromatic wave implies delocalization in time and space; in practice, a single photon localized to some degree in time and space can be described as superposition of monochromatic photon modes.

When Glauber, 1963a, Glauber, 1963b completed the model of radiation detection, discussing from a quantum point of view the interaction of radiation and matter, and constructed a quantum theory of coherence, a number of interesting states of radiation received a full reconnaissance as useful and possible states: among them coherent and single-photon states are perhaps the most interesting, together with squeezed and entangled ones. Full description of these states may be found in many excellent textbooks, like, e.g., Mandel and Wolf (1995).

The generation of quantum states of the radiation field started to receive great attention from the 1980s. Single-photon states, in particular, are studied because of possible applications in quantum communication, quantum lithography, quantum metrology, information processing, and quantum computing, such as quantum random-number generation, quantum networks, secure quantum communications, and quantum cryptography (see, for example, Beveratos, Brouri, et al., 2002, Cerf and Flurasek, 2006, Dusek et al., 2006, Gisin et al., 2002, Gisin and Thew, 2007, Grangier and Abram, 2003, Kilin, 2001).

For example, the security in some schemes of quantum cryptography is based on the fact that each bit of information is coded on a single photon. The fundamental impossibility of duplicating the complete quantum state of a single particle (no cloning theorem; Cerf and Flurasek, 2006, Diecks, 1982, Ghirardi and Weber, 1983, Wootters and Zurek, 1982) prevents any potential eavesdropper from intercepting the message without the receiver's noticing.

An ideal single-photon source would produce exactly one photon in a definite quantum state, in contrast with a “classical” source, such as attenuated laser pulses, for which the photon number follows a Poisson distribution. A more stringent request would be to have the single-photon generation on demand, that is, at a determined time. Additional requests could be room temperature operation, high repetition frequency, high efficient extraction into free space or fiber, good coherence, and Fourier-transformed linewidth. Much progress has been made in the years toward such devices, especially in suppressing the probability of two photons in the same pulse.

Historically, the first experiment with single photons was made using an atomic cascading process in which an excited atomic level decayed with the emission of two photons of different frequencies (Clauser, 1974). The detection of one of them established the presence of the other; we will describe this experiment later.

In the following, we will give a brief introduction to Fock states, remember the problem of localization of single photons, focus on their antibunching property and photon statistics, and remember the Purcell effect, which allows a control of emission probability. We then discuss the preparation of single-photon states, the so-called quantum engineering, the different kinds of single-photon sources, entangled states, plasmonic sources, and applications to quantum information processing. The problem of detection is deliberately not treated.

A number of review papers already exist on the subject such as Moerner (2004), Lounis and Orrit (2005), Oxborrow and Sinclair (2005), Scheel (2009), and Eisaman, Fan, Mugdall, & Polyakov (2011). Quite recently, a Single-Photon Workshop has been held at Oak Ridge National Laboratory, October 15–18, 2013. The presented papers are available to attendees only. In the following, we will follow an approximate historical presentation enlightening the single contributions and the evolution of the methods to obtain single-photon sources. The survey may not be complete; we apologize for any omission.