Quantum State Preparation And Quantum Information Processing In Cavity QED

Quantum information science is a new field of science and technology, combining and drawing on the disciplines of physical science, mathematics, computer science, and engineering. Owing to the difference between quantum mechanics and classical mechanics, quantum information science takes on a new look and is completely different from its classical counterpart. It manifests distinct advantages in many aspects. For example, the quantum superposition allows that quantum information evolves in a parallel way. Based on this feature, scientists developed some skillful quantum parallelism arithmetic to resolve some problems that cannot be resolved by classical computers, such as factorization of large numbers. In addition, perfect cloning of quantum states is forbidden, which leads to the birth of quantum cryptography and security communication. What's more, quantum entanglement can act as a quantum channel connecting different locations, thus enabling quantum teleportation. In a word, quantum information science brings new features to information science and technology. Advances in quantum information science will become increasingly critical to the national competitiveness in information technology during the 21st century.The exciting scientific opportunities offered by quantum information science are attracting the interest of a growing community of scientists and technologists worldwide, and are promoting unprecedented interactions across traditional disciplinary boundaries. In the research of quantum information, we need deal with the information, then the hardware is absolutely necessarily. At present cavity quantum elec-trodynamics(QED) is studied earlier, developed faster and promises well.In this Dissertation, we make some systematic theoretical studies about cavity QED. The problems covered are as follows:I. Preparation of entangled state in cavity QED systemQuantum entanglement is one of the most important problems in quantum information science, because dealing with quantum information can not depart from the evolvement of quantum states and quantum entangled state is one of the most important states in quantum information science. Quantum entanglement has many extensive applications in quantum communication and computation, so investigation of preparation and manipulation of quantum entangled states is very important. The preparation of quantum entangled states has been realized in many systems, such as ion trap, atom-cavity and spontaneous parameter down-conversation etc. In this Dissertation, we use the adiabatical state evolution under large detuning to generate entangled photon pairs in cavity QED system. One of distinct advantages of our proposal is that the excited states can be effectively eliminated and the atomic spontaneous emission does not play an important role. Moreover, our scheme can generate arbitrary four-mode multi-photon entangled states by passing N identical atoms through two high-Q cavities in turn. In the case of N=l, the scheme can deterministically generate Einstein-Podolsky-Rosen (EPR) entangled photon pairs.II. Teleporting an arbitrary superposition of atomic Dicke states via multi-fold coincidence detection in cavity QED systemQuantum teleportation is not only a fundamental phenomenon of quantum world, but also one of the key procedure in the area of quantum information processing. By teleportation, an unknown quantum state can be transported from one place to another without moving through the intervening space. Since the pioneering contribution of Bennett et al, quantum teleportation was first demonstrated experimentally by using spontaneous parametric down-conversions. More recently, teleportation of single atomic state was reported in trapped-ion system. However, in realizing quantum information processing, it is expected to use atoms as stationary qubits to store quantum information in long-lived internal states, and the photons as flying qubits to transport quantum information over long distance. Cavity QED provides a promising candidate for such a scheme. We propose an alternative scheme for teleporting an arbitrary superposition of atomic Dicke states from one cavity to another. Our scheme is based on multi-photon coincidence detection and has the following advantages: The fidelity is unity for any superposition of Dicke states, and scheme is insensitive to the imperfection of the photon detectors, i.e. the scheme does not require distinguishing between zero, one and two photons. Imperfection of the photon detectors decreases the success probability, but has no influence on the fidelity of the teleportation.III. Quantum phase gate of photonic qubits in cavity QED systemThe existence of quantum algorithms for specific problems shows that a quantum computer can in principle provide a tremendous speed up compared to classical computers. This discovery motivated an intensive research into this mathematical concept which is based on quantum logic operations on multi-qubit systems. It is well known that two-qubit controlled phase gate and one-qubit gate are universal for constructing quantum computer, i.e. any unitary transformation can be decomposed into these elementary gates. Here we present a scheme to realize the quantum phase gate of two polarization modes by using a A-type three-level atom as data bus. Our scheme has the following characters: 1) The two qubits are represented by the zero- and single-photon states of two different polarization modes of the radiation field inside the cavity because experimental realization of typical quantum algorithms may require the two qubits to be treated on equal footing. 2)We use atoms as stationary qubits to store quantum information in long-lived internal states, and the photons as flying qubits to transport quantum information over long distance. 3)The quantum phase gate operation can be performed successfully by requiring the two-photon resonance condition. A precise control of the interaction time between the three-level atom and the cavity modes will yield the conditional evolution needed to implement the quantum phase gate. 4)We also discuss the influence of the atomic spontaneous emission, cavity decay and deviation of coupling strength on fidelity of the quantum phase gate.