Theoretical Research On Quantum Computation And Quantum Simulation Via Quantum Optics

In the past twenty years, quantum computation has being more and more attractivefor its promising power of parallelism computation and simulating quantum dynamicseffectively, which is incompetent for classical computers. In the research field ofquantum computation, quantum logic gate is one of the basic operations. Meanwhile,quantum state transfer is a necessary means to conduct distributed quantum computation.On the other hand, the quantum simulation, which plays important role in the researchof condensed matter physics and in finding the new physics of the microscale material,is a direct application of quantum computers.In this thesis, first, we will focus on how to achieve scalable quantum logic gates andhow to realize quantum state transfer between different nodes in cavity QED. Second,by using the principle and technology of quantum computing, we propose the schemesof simulating effective spin systems with trapped ions and trapped cold polar molecules,respectively. The main results and innovation are summarized as follows:1. We propose a scheme to achieve a parallelized controlled-NOT (C-NOT) gatebased on electromagnetically induced transparency (EIT) and cavity-assisted photonscattering. By using the flying photon as the control bit, we can implement a conditionaltransfer between two logical states of an atom trapped in the cavity with high fidelityand on a microsecond time scale. Thanks to the fact that the photon is well suited forscalable quantum computation, a quantum C-NOT gate between the single-photonpulses and the nonlocal gate on remote atoms are obtained by reflecting the photonpulse from an optical cavity with a single-trapped atom. Our protocol is robust forspontaneous emission and works quite well in the bad-cavity limit, which makes it moreapplicable in the laboratory with current experimental techniques.2. A scheme is presented to realize transfer of a three-dimensional quantum statebetween two atoms trapped in distant cavities connected by an optical fiber, whosemode is resonant with the polarization cavity mode. Performing an adiabatic passagealong dark states, the fiber mode remains in the vacuum state and the population of thecavities being excited can be negligible under certain conditions. In addition, atomictransitions in our scheme are largely detuned from cavity modes. As a consequence, theatomic spontaneous emission and the fiber decay can be effectively eliminated.Furthermore, we give some discussions about the fidelity of our scheme.3. We simulate an effective spin system with trapped ions via the exchange of virtualphonons. By tuning the parameters of the external lasers, an long-range Heisenbergmodel is induced between effective spins which behavior rich variety of quantum phasetransition. The competing interactions would lead to frustrated magnetic network.Thanks for the population of phonon state is strongly suppressed, our model is insensitive to the temperature of the ion system. Furthermore, our model requires noindividual addressing by lasers.4. We describe a simple scheme for the implementation and control of effectivespin-spin interactions in selfassembled crystals of cold polar molecules. In our scheme,spin states are encoded in two long-lived rotational states of the molecules and coupledvia state-dependent dipole-dipole forces to the lattice vibrations. We show that, bychoosing an appropriate time-dependent modulation of the induced dipole moments, theresulting phonon-mediated interactions compete with the direct dipole-dipole couplingand lead to long-range and tunable spin-spin interaction patterns. We illustrate how thistechnique can be used for the generation of multiparticle entangled spin states and theimplementation of spin models with long-range and frustrated interactions, whichexhibit nontrivial phases of magnetic ordering.