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1.2 History using .net touse code128 with web,windows application Reading Data Matrix ECC200 antibunching, and the Code 128B for .NET associated (but inequivalent) sub-Poissonian photon statistics laid the foundation of the study of non-classical light . During the 1970s, several experiments explored the nature of photons: their indivisibility and the build up of interference at the single photon level.

Laser cooling rapidly developed in the 1980s and 1990s and allowed the preparation of states of matter under precise control. Indeed, this has become a major subject in its own right and we have taken the decision here to exclude laser cooling from this text. Following the development of high-intensity pulses of light from lasers, a whole set of nonlinear optical phenomena were investigated, starting with the pioneering work in Ann Arbor by Franken and co-workers.

Harmonic generation, parametric down-conversion and other phenomena were demonstrated. For the most part, none of this early work on nonlinear optics required eld quantization and quantum optics proper for its description. But there were early signs that some could well do so: quantum nonlinear optics was really initiated by the study by Burnham and Weinberg (see 9) of unusual nonclassical correlations in down-conversion.

In the hands of Mandel and many others, these correlations in down-conversion became the fundamental tool used to uncover fundamental insights into quantum optics. Until the 1980s, essentially all light elds investigated had phase-independent noise; this changed with the production of squeezed light sources with phasesensitive noise. These squeezed light sources enabled us to investigate Heisenberg uncertainty relations for light elds.

Again, parametric down-conversion proved to be the most effective tool to generate such unusual light elds. Quantum opticians realized quite early that were atoms to be con ned in resonators, then atomic radiative transition dynamics could be dramatically changed. Purcell, in a remarkable paper in 1946 within the context of magnetic resonance, had already predicted that spontaneous emission rates, previously thought of as pretty immutable were in fact modi ed by enclosing the source atom within a cavity whose mode structure and densities are signi cantly different from those of free space.

Putting atoms within resonators or close to mirrors became possible at the end of the 1960s. By the 1980s the theorists dream of studying single atoms interacting with single modes of the electromagnetic eld became possible. At this point the transition dynamics becomes wholly reversible, as the atom coherently exchanges excitation with the eld, until coherence is eventually lost through a dissipative decoherence process.

This dream is called the Jaynes Cummings model after its proposers and forms a basic building block of quantum optics (and is discussed in detail in this book). New fundamental concepts in information processing, leading to quantum cryptography and quantum computation, have been developed in recent years by Feynman, Benioff, Deutsch, Jozsa, Bennett, Ekert and others. Instead of using classical bits that can represent either the values 0 or 1, the basic unit of a.

Introduction quantum computer is a .net framework Code128 quantum mechanical two-level system (qubit) that can exist in coherent superpositions of the logical values 0 and 1. A set of n qubits can then be in a superposition of up to 2n different states, each representing a binary number.

Were we able to control and manipulate say 1500 qubits, we could access more states than there are particles in the visible universe. Computations are implemented by unitary transformations, which act on all states of a superposition simultaneously. Quantum gates form the basic units from which these unitary transformations are built up.

In related developments, absolutely secure encryption can be guaranteed by using quantum sources of light. The use of the quantum mechanical superpositions and entanglement results in a high degree of parallelism, which can increase the speed of computation exponentially. A number of problems which cannot feasibly be tackled on a classical computer can be solved ef ciently on a quantum computer.

In 1994 a quantum algorithm was discovered by Peter Shor that allows the solution of a practically important problem, namely factorization, with such an exponential increase of speed. Subsequently, possible experimental realizations of a quantum computer have been proposed, for example in linear ion traps and nuclear magnetic resonance schemes. Presently we are at a stage where quantum gates have been demonstrated in these two implementations.

Quantum computation is closely related to quantum cryptography and quantum communication. Basic experiments demonstrating the in-principle possibility of these ideas have been carried out in various laboratories. The linear ion trap is one of the most promising systems for quantum computation and is one we study in this book in detail.

The quantum state preparation (laser cooling and optical pumping) in this system is a well-established technique, as is the state measurement by electron shelving and uorescence. Singly charged ions of an atom such as calcium or beryllium are trapped and laser cooled to micro-Kelvin temperatures, where they form a string lying along the axis of a linear radio-frequency (r.f.

) Paul trap. The internal state of any one ion can be exchanged with the quantum state of motion of the whole string. This can be achieved by illuminating the ion with a pulse of laser radiation at a frequency tuned below the ion s internal resonance by the vibrational frequency of one of the normal modes of oscillation of the string.

This couples single phonons into and out of the vibrational mode. The motional state can then be coupled to the internal state of another ion by directing the laser onto the second ion and applying a similar laser pulse. In this way general transformations of the quantum state of all the ions can be generated.

The ion trap has several features to recommend it. It can achieve processing on quantum bits without the need for any new technological breakthroughs, such as micro-fabrication techniques or new cooling methods. The state of any ion can be measured and re-prepared many times without problem, which is an important feature for implementing quantum error correction protocols.

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