Preparation Of Quantum Optical States And Properties Of Quantum States Of Ultra-cold Atoms In Optical Traps

As it is well known photons, ultra-cold atoms and their interacting systems havebeen the most efficient carriers of the newly developed techniques of quantum manipulation, quantum computation and quantum information. The preparation ofquantum states of optical field has drawn great interests since the optical field has many special advantages in carrying quantum information. On the other hand, the techniques of laser cooling and trapping cold atoms provide an opportunity to manipulate cold atoms including Bose-Einstein condensates (BEC). The research on the properties of quantum states of BEC modulated by lasers is becoming the focused problem recently. Our present study focuses on the preparation and the properties of quantum states, including the optical preparation of some non-classical quantum states and entangled state and the properties of the quantum states of ultra-cold atoms. The main contents are as follows:1) The experimental realization of single-photon-added coherent state (SPACS) provides a tool to take a closer look at the evolution of the quantum-to-classical transition and as a starting point for the investigation of the fuzzy border that separates the quantum and classical regimes of light behavior. We proposed a simple scheme to generate a special non-classical quantum state: photon-added coherent state (PACS). When SPACS is observed in the output signal channel, we can simultaneously obtain the generalized N-qubit discrete variable entangled state. Therefore, we give a simple optical scheme to further enhance the success probability of the SPACS generation, which can also be used in the preparation of the hybrid entangled state.2) Based on the Mach-Zehnder interferometer, we proposed a feasible scheme to generate the entangled SPACS, and then lead to generation of the novel hybrid entangled state(type II hybrid entangled state). Type II hybrid entangled state is different from any other hybrid entangled state, it realizes the entanglement of continuous-variable and discrete-variable quantum state. This hybrid entangled state can not be interpreted as the spin or the parity qubit. We can view the new hybrid entangled state as the entangled schr?dinger's cat state if we define the classical-world continuous variable and the quantum-world discrete variable as the living-cat and dead-cat states, respectively.3) We theoretically considered the Josephson effect of BEC with a weak link created by superposing a far-off-resonant red-detuned laser beam on a double-well potential. Thenumerical simulations of the density distribution and the population oscillation show that there is clear Josephson effect for this sort of three-well system when the intensity of the laser beam is modulated. Our present work gives a feasible scheme to study a new type ofweak link which is crucial to investigate experimentally the Josephson effect.4) For ultra-cold Bose gases in a combined potential of a harmonic trap and an optical lattice, we considered the evolution of the density-density correlation after switching off the optical lattice alone. Our studies show that the density-density correlation exhibits a periodic evolution behavior because of the modulation of the harmonic trap. A simple analytical expression for the motion of the interference peaks in the density-density correlation is given, which agrees well with our numerical results. This analytical expression gives potential application of the measurement of the harmonic frequency based on spatial quantum noise interferometry.