Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is guaranteed to have the same polarization as the original photon. But is it possible by this or any other process to amplify a quantum state, that is, to produce several copies of a quantum system (the polarized photon in the present case) each having the same state as the original? If it were, the amplifying process could be used to ascertain the exact state of a quantum system: in the case of a photon, one could determine its polarization by first producing a beam of identically polarized copies and then measuring the Stokes parameters1. We show here that the linearity of quantum mechanics forbids such replication and that this conclusion holds for all quantum systems.

A single quantum cannot be cloned

Quantum teleportation — the transmission and reconstruction over arbitrary distances of the state of a quantum system — is demonstrated experimentally. During teleportation, an initial photon which carries the polarization that is to be transferred and one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon. This latter photon can be arbitrarily far away from the initial one. Quantum teleportation will be a critical ingredient for quantum computation networks.

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Experimental quantum teleportation

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

Structural polymers are susceptible to damage in the form of cracks, which form deep within the structure where detection is difficult and repair is almost impossible. Cracking leads to mechanical degradation of fibre-reinforced polymer composites; in microelectronic polymeric components it can also lead to electrical failure. Microcracking induced by thermal and mechanical fatigue is also a long-standing problem in polymer adhesives. Regardless of the application, once cracks have formed within polymeric materials, the integrity of the structure is significantly compromised. Experiments exploring the concept of self-repair have been previously reported, but the only successful crack-healing methods that have been reported so far require some form of manual intervention. Here we report a structural polymeric material with the ability to autonomically heal cracks. The material incorporates a microencapsulated healing agent that is released upon crack intrusion. Polymerization of the healing agent is then triggered by contact with an embedded catalyst, bonding the crack faces. Our fracture experiments yield as much as 75% recovery in toughness, and we expect that our approach will be applicable to other brittle materials systems (including ceramics and glasses).

Autonomic healing of polymer composites

Definitive data on the absorption spectrum of pure water from 380 to 700 nm have been obtained with an integrating cavity technique. The results are in good agreement with those recently obtained by our group with a completely independent photothermal technique. As before, we find that the absorption in the blue is significantly lower than had previously been generally believed and that the absorption minimum is at a significantly shorter wavelength, i.e., 0.0044 ? 0.0006 m(-1) at 418 nm. Several spectroscopic features have been identified in the visible spectrum to our knowledge for the first time.

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Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements

We report the observation of small group velocities of order 90 m/s and large group delays of greater than 0.26 ms, in an optically dense hot rubidium gas ( $\ensuremath{\approx}360\mathrm{K}$). Media of this kind yield strong nonlinear interactions between very weak optical fields and very sharp spectral features. The result is in agreement with previous studies on nonlinear spectroscopy of dense coherent media.

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Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas

We have measured the linear polarization correlation between the two photons from the $7^{3}S_{1}\ensuremath{\rightarrow}6^{3}P_{1}\ensuremath{\rightarrow}6^{1}S_{0}$ cascade of ${\mathrm{Hg}}^{200}$. The results were used to evaluate Freedman's version of the Bell inequality, $\ensuremath{\delta}l~0$. Our result is ${\ensuremath{\delta}}_{\mathrm{exp}}=+0.046\ifmmode\pm\else\textpm\fi{}0.014$, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, ${\ensuremath{\delta}}_{\mathrm{QM}}=+0.044\ifmmode\pm\else\textpm\fi{}0.007$. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.

Experimental Test of Local Hidden-Variable Theories

We have determined an empirical equation for the index of refraction of water as a function of temperature, salinity, and wavelength at atmospheric pressure. The experimental data selected by Austin and Halikas ["The index of refraction of seawater," SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976)] were fitted to power series in the variables. A ten-parameter empirical equation that reproduces the original data to within its experimental errors was obtained.

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Empirical equation for the index of refraction of seawater

A collection of $N$ static atoms is fixed in a crystal at a low temperature and prepared by a pulse of incident radiation of wave vector ${\stackrel{\ensuremath{\rightarrow}}{k}}_{0}$. The $N$ atoms are well described by an entangled Dicke-like state, in which each atom carries a characteristic phase factor $\mathrm{exp}﻿(i{\stackrel{\ensuremath{\rightarrow}}{k}}_{0}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{r}}_{j})$, where ${\stackrel{\ensuremath{\rightarrow}}{r}}_{j}$ is the atomic position in the crystal. It is shown that a single photon absorbed by the $N$ atoms will be followed by spontaneous emission in the same direction. Furthermore, phase matched emission is found when one photon is absorbed by $N$ atoms followed by two-photon down-conversion.

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Edward S. Fry

Papers

Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements

Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas

Experimental Test of Local Hidden-Variable Theories

Empirical equation for the index of refraction of seawater

Directed spontaneous emission from an extended ensemble of N atoms: timing is everything.