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

A modified back-projection approach deduced from an exact reconstruction solution was applied to our photoacoustic tomography of the optical absorption in biological tissues. Pulses from a Ti:sapphire laser (4.7 ns FWHM at 789.2 nm) were employed to generate a distribution of photoacoustic sources in a sample. The sources were detected by a wide-band nonfocused ultrasonic transducer at different positions around the imaging cross section perpendicular to the axis of the laser irradiation. Reconstructed images of phantoms made from chicken breast tissue agreed well with the structures of the samples. The resolution in the imaging cross section was experimentally demonstrated to be better than 60 μm when a 10 MHz transducer (140% bandwidth at −60 dB) was employed, which was nearly diffraction limited by the detectable photoacoustic waves of the highest frequency.

Photoacoustic tomography of biological tissues with high cross-section resolution: Reconstruction and experiment

Although there are sixteen elements of the Stokes matrix, they are constructed from basically four amplitudes and three phase differences. This of course implies that there exist nine independent relationships connecting the elements. These relationships are equalities for scattering by a single particle in a fixed orientation and in a fixed direction. When Stokes matrices from an ensemble of particles differing in size, orientation, morphology, or optical properties are added incoherently, only six equalities become one-way inequalities. These relations will prove to be very useful for providing consistency checks on experimental measurements of all sixteen elements.

Relationships between elements of the Stokes matrix.

A proposal for an experimental realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment is described. Two $^{199}\mathrm{Hg}$ atoms, each with nuclear spin 1/2, are produced in an entangled state with total nuclear spin zero. Such a state is obtained by dissociation of dimers of the $^{199}\mathrm{Hg}_{2}$ isotopomer using a spectroscopically selective stimulated Raman process. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two-photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition.

Proposal for a loophole-free test of the Bell inequalities

A new technique for maintaining single-frequency output from injection-seeded Nd:YAG lasers is described. It involves quickly sweeping the slave-cavity longitudinal-mode spectrum when the flash lamps have created a maximum population inversion. An interference signal is detected by fast electronics, and the Q switch is opened when the slave cavity is resonant with the injected field.

Fast resonance-detection technique for single-frequency operation of injection-seeded Nd:YAG lasers.

When ground-state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The reason is a strong nonadiabatic effect at cavity boundaries and its interplay with the standard Unruh effect. The cavity field at steady state is still described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, squeezed radiation can be produced.

https://arxiv.org/pdf/quant-ph/0305178.pdf

Edward S. Fry

Papers

Photoacoustic tomography of biological tissues with high cross-section resolution: Reconstruction and experiment

Relationships between elements of the Stokes matrix.

Proposal for a loophole-free test of the Bell inequalities

Fast resonance-detection technique for single-frequency operation of injection-seeded Nd:YAG lasers.

Enhancing acceleration radiation from ground-state atoms via cavity quantum electrodynamics.