| Comparing with the intuitive classical world, quantum mechanics shows us a to-tally different view for understanding the nature. At low temperature or in microscopic area, which is far away from the situations we live, many curious phenomena can be well explained by quantum theory. With being familiar with the quantum mechanics, people are trying to connect it with our daily life. Quantum information process is just a successful application among these attempts. A lot of useful achievements have been realized in many kinds of systems, such as cold atoms and photon cavity. As an important part of quantum information process, quantum communication has a lot of advantages. It is hard to intercept and has an efficient transmission. Because of these, it has attracted amount of people devoting themselves to this subject.Since JILA realized the world first Bose-Einstein condensation in1995, cold atoms have played an important role in researching on quantum field all the time. As a clean and interaction tunable system, it supply an advanced method to study the quantum property of physical matter, which can not be reached before. Our research focus on how to make an entangled state through the coherence of Bose-Einstein Condensation in optical lattice. From this, we can prepare an EPR state, to realize the quantum infor-mation process in cold atoms systems.Photon cavity is an interesting quantum system. Through studying the interactions between atoms and optics field, many quantum characteristics can be found, which is useful in quantum information process. By using photon cavity, lots of theoretical assumptions about quantum phenomena have been verified experimentally. Our work is to realize parity measurement by the coherence of photons leaking from two separated photon cavities.1. Quantum entanglement of many distant Bose-Einstein condensate in an optical latticeWe propose a scheme to generate maximally entangled states of two distant Bose-Einstein condensates, which are trapped in different potential wells of a one-dimensional optical lattice. We show how such a maximally entangled state can be used to test the Bell inequality and realize quantum teleportation of a Bose-Einstein condensate state. The scheme proposed here is based on the interference of Bose-Einstein condensates leaking out from different potential wells of optical lattices. It is briefly pointed out that this scheme can be extended to generate maximally entangled Greenberger-Horne-Zeilinger (GHZ) states of2m (m>1) distant Bose-Einstein condensates.2. Measuring the parity of N distant atoms with linear optics It is known that parity measurement, together with single-qubit rotation, is suffi-cient for implementing scalable quantum computation. In this Brief Report, we propose a scheme for a projective measurement of the parity operator Pz=(?)iN=1σi,z of N distant atoms trapped in spatially separated cavities. Instead of direct interaction between the atoms, quantum interference of polarized photons decaying from the optical cavities is used to realize expected measurement without resorting to a sequence of single-and two-qubit operations. It is shown that parity measurement can be implemented repeat-edly until success without destroying the qubits at any stage of the operation.3. Numerical methods in many body systemsAs an important numerical method in many body systems, The accuracy of den-sity matrix renormalization group (DMRG) has been tested by many experiments. In the strong correlated systems, mean field method will lose its efficacy. To reach the results of this kind of complicated systems, Steven White create DMRG in1992. This method is also able to extend to quasi-one-dimensional systems and time dependence system. DMRG, with Monte Carlo methods together, has been considered a main tools to research many body systems. Our code can be used for the calculation of one dimen-sion fermion system. Now we are trying to extend our codes to quasi-one-dimensional fermion system. |
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