Phases of Bose or Fermi atoms in optical lattices confined in harmonic traps are studied within the Thomas-Fermi approximation. Critical radii and particle numbers for the onset of Mott insulator states are calculated and phase diagrams are shown in one dimension, and estimated for two and three dimensions. Methods to observe these and phases such as $d$-wave superconductivity are discussed. Specifically, the collective modes are calculated.

The Gross-Pitaevskii gain equation is used to model atom laser and Bose-Einstein condensation (BEC) fed by the surrounding thermal cloud. It is shown that the number of atoms continuously injected into BEC from the reservoir can be controlled by applying the external magnetic field via Feshbach resonance.

A Mach-Zehnder-type atom interferometer with a Bose-Einstein condensate has been investigated on an atom chip by using optical Bragg diffraction. A phase shift and a contrast degradation, which depend on the atomic density and the trapping frequency of the magnetic-guide potential, have been observed. Also, the output wave packets were found to exhibit a spatial interference pattern. The atom-atom interaction and the guide potential induce the spatially inhomogeneous phase evolution of the wave packets in each arm of the interferometer. The observed contrast degradation can be quantitatively explained as a dephasing due to this inhomogeneous phase evolution.

We study a continuous-variable entangled state composed of two states which are squeezed in two opposite quadratures in phase space. Various entanglement conditions are tested for the entangled squeezed state and we study decoherence models for noise, producing a mixed entangled squeezed state. We briefly describe a probabilistic protocol for entanglement swapping based on the use of this class of entangled states and the main features of a general generation scheme.

When considering an application of quantum-information technology, we should consider realistic conditions first. From this point of view, we propose using antisqueezed light as a resource for optical communication because antisqueezing maintains its nature even after loss and amplification. Applying antisqueezed light to cipher communication using randomized sender bases, we can increase, by high order of magnitude, the bit-error rate of eavesdroppers who do not have the basis information. Even at macroscopic optical intensity, an ordinary level of optical communication, we can cause the bit-error rate of eavesdroppers to be as high as it would be at low intensity, through increased antisqueezing depending on optical intensity, leading to more secure optical communication.

Reduced-period optical lattices based on Raman transitions allow for sub-Doppler laser cooling. An important parameter of this Raman optical lattice is the frequency difference ${\Delta }_{\mathrm{d}}$ between two virtual energy levels involved in the atom-field interaction scheme. In this work, we use experimental time-of-flight data and quantum simulations to characterize laser cooling in the Raman lattice as a function of ${\Delta }_{\mathrm{d}}$. Two different domains of laser cooling are identified. For small ${\Delta }_{\mathrm{d}}$, atoms are cooled due to a well-known mechanism that also occurs in standard optical lattices. For large ${\Delta }_{\mathrm{d}}$, atoms are cooled based on Raman transitions. We study the transition between the two domains of laser cooling in detail.

We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.

In this paper, we study the entanglement between two neighboring sites and the rest of the system in a simple quantum phase transition of a one-dimensional transverse field Ising model. We find that the entanglement shows interesting scaling and singular behaviors around the critical point, and thus can be used as a convenient marker for the transition point.

We propose a scheme for preparing a stationary microwave single-photon state of a transmission line resonator via off-resonant interaction with a single superconducting Cooper-pair Box (CPB). It is shown that with the help of an auxiliary microwave field, single-photon state can be persistently produced with high efficiency by using the CPB and cavity loss. The scheme is feasible with the current experimental technology and can be extended to prepare a multiphoton Fock state in a transmission line cavity.

We analyze quantum teleportation for composite systems, specifically for concatenated teleporation (decomposing a large composite state into smaller states of dimension commensurate with the channel) and partial teleportation (teleporting one component of a larger quantum state). We obtain an exact expression for teleportation fidelity that depends solely on the dimension and singlet fraction for the entanglement channel and entanglement (measures by $I$ concurrence) for the state; in fact quantum teleportation for composite systems provides an operational interpretation for $I$ concurrence. In addition we obtain tight bounds on teleportation fidelity and prove that the average fidelity approaches the lower bound of teleportation fidelity in the high-dimension limit.

The combination of a vortex line in a one-dimensional optical lattice with fermions bound to the vortex core makes up an ultracold superstring. We give a detailed derivation of the way to make this supersymmetric string in the laboratory. In particular, we discuss the presence of a fermionic bound state in the vortex core and the tuning of the laser beams needed to achieve supersymmetry. Moreover, we discuss experimental consequences of supersymmetry and identify the precise supersymmetry in the problem. Finally, we make the mathematical connection with string theory.

We theoretically study the effects of elastic collisions on the determination of frequency standards via Ramsey-fringe spectroscopy in optical-lattice atom clocks. Interparticle interactions of bosonic atoms in multiply occupied lattice sites can cause a linear frequency shift, as well as generate asymmetric Ramsey-fringe patterns and reduce fringe visibility due to interparticle entanglement. We propose a method of reducing these collisional effects in an optical lattice by introducing a phase difference of $\pi$ between the Ramsey driving fields in adjacent sites. This configuration suppresses site-to-site hopping due to interference of two tunneling pathways, without degrading fringe visibility. Consequently, the probability of double occupancy is reduced, leading to cancellation of collisional shifts.

In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.

We present what is to our knowledge the most complete one-dimensional numerical analysis of the evolution and the propagation dynamics of an ultrashort laser pulse in a Ti:sapphire laser oscillator. This study confirms the dispersion managed model of mode locking, and emphasizes the role of the Kerr nonlinearity in generating mode-locked spectra with a smooth and well-behaved spectral phase. A very good agreement with experimental measurements of pulse energy, spectrum, and temporal width of extracavity compressed pulses is found.

We consider the recently measured case of $730\mathrm{eV}$ electron-impact ionization of the ground state of helium with 205 and $500\mathrm{eV}$ coplanar outgoing electrons by Catoire et al. [J. Phys. B 39, 2827 (2006)]. These measurements, which are on a relative scale, show some unexpected structure and variation from the second-order distorted-wave Born approximation $R$-matrix and Brauner-Briggs-Klar theories. Using the convergent close-coupling method we provide an improved agreement with experiment, but some discrepancies still remain.

Relativistic corrections to a previously established generalized sum rule are obtained using the Foldy-Wouthysen transformation. This sum rule derived previously by Wang [Phys. Rev. A 60, 262 (1999)] for a nonrelativistic system contains both the well-known Thomas-Reiche-Kuhn and Bethe sum rules, for which relativistic corrections have been obtained in the literature. Our results for the generalized formula will be applied to recover several results obtained previously in the literature, as well as to another sum rule whose relativistic corrections will be obtained.

A Michelson interferometer using Bose-Einstein condensates is demonstrated with coherence times of up to $44\mathrm{ms}$ and arm separations up to $180\mathrm{\mu }\mathrm{m}$. This arm separation is larger than that observed for any previous atom interferometer. The device uses atoms weakly confined in a magnetic guide and the atomic motion is controlled using Bragg interactions with an off-resonant standing-wave laser beam.

We investigate the anti-Zeno phenomenon as well as the quantum Zeno effect for the irreversible quantum tunneling from a quantum dot to a ring array of quantum dots. By modeling the total system with the Anderson-Fano-Lee model, it is found that the transition from the quantum Zeno to the quantum anti-Zeno effect can happen by adjusting magnetic flux and gate voltage.

We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of $n$ to $m$ cloning of mixed Gaussian states.

We explore the relation between entanglement entropy of quantum many-body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that, in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, $XY$ spin chain, and chains with strong randomness.