Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

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Electromagnetically induced transparency : Optics in coherent media

Publisher Summary This chapter describes the coherent population trapping in laser spectroscopy. Coherent population trapping may be also described as the pumping of the atomic system in a particular state, the coherent superposition of the atomic states, which is a nonabsorbing state. The exciting radiation creates an atomic coherence, such that the atom's evolution is prepared exactly out of phase with the incoming radiation and no absorption takes place. The chapter discusses the basic properties of an atomic system prepared with the coherent population-trapping superposition of states and outlines experimental observations concerned with the establishment of coherent trapping in different discrete systems. The chapter also discusses the theoretical and experimental aspects of trapping that involve states of the continuum and reviews the theoretical and experimental features associated with coherent population trapping in laser cooling, adiabatic transfer, lasing without inversion, pulse matching, and photon statistics. The theoretical aspect of coherent population trapping created by spontaneous emission is also discussed in the chapter.

Coherent Population Trapping in Laser Spectroscopy

We have observed optical phase-conjugate gain (>50) in sodium vapor, using low-intensity pump lasers (1 W/cm2), with a response time of the order of 1 μs. Coherent population trapping is experimentally identified as the phase-conjugate mechanism. A theoretical model is presented that supports these observations by showing that coherent population trapping can write large-amplitude nonlinear-optical gratings at laser intensities well below those needed to saturate the optical transitions.

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Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium.

The efficient and robust manipulation of single spins is an essential requirement for successful quantum devices. The manipulation of a single nitrogen–vacancy spin centre is now demonstrated by means of a mechanical resonator approach.

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Strong mechanical driving of a single electron spin

The internal structure of a particle – an atom or other quantum system in which the excitation energies are discrete – undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes – the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laserpulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a threedimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping “dark” states.

M. A. Lauder

Papers

Atomic interferometers: phase-dependence in multilevel atomic transitions