We study the behavior of ultracold bosonic atoms held in an optical lattice. We first show how a self-trapping transition can be induced in the system either by increasing the number of atoms occupying a lattice site or by raising the interaction strength above a critical value. We then investigate how applying a periodic driving potential to the self-trapped state can be used to coherently control the emission of a precise number of correlated bosons from the trapping site. This allows the preparation and transport of entangled bosonic states, which are of great relevance to novel technologies such as quantum-information processing.

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency using the two-mode approach. Starting from Bloch states, we succeed in obtaining analytical solutions for the TD Schrödinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differ by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one-species condensate in a double-well potential (external Josephson effect).

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error-correcting code that takes advantage of this asymmetry and shows good performance at a relatively small cost in redundancy, requiring less than a doubling of the number of physical qubits for error correction. This code is particularly adapted for building an efficient quantum memory.

A nonlinear ${\chi }^{\left(2\right)}$ Mach-Zehnder interferometer is proposed as a simple device for conditional preparation of a two-photon maximally entangled state. Successful generation is unambiguously heralded by detection of a single photon in one of the routes of the nonlinear ${\chi }^{\left(2\right)}$ Mach-Zehnder interferometer. The mechanism of the conditional preparation is based on interference of the pumping modes. The scheme works without photon-number-resolving detection with a high fidelity.

Based on superconducting quantum interference devices (SQUID’s) coupled to a cavity, we propose a scheme for implementing a quantum phase-shift gate and generating a $W$ state by an adiabatic evolution of dark eigenstates, without any contributions from dynamical and geometric gates. The Sole requirement is of adiabatically increasing or decreasing Rabi frequencies of classical microwave pluses. Thus, the manipulation is robust against certain types of errors. We also analyze the experimental possibility that identical coupling can be achieved between SQUID qubits and cavity fields, and the cavity decay can be ignored in certain conditions. Based on a simple operation, our scheme may be realized in this solid-state system.

The dynamic scalar and tensor polarizabilities of the rare-earth-metal atoms are calculated with time-dependent density functional theory. The frequency-dependent polarizabilities at imaginary frequencies are used to determine the isotropic and orientation-dependent van der Waals coefficients for the interactions of the rare-earth-metal atoms with helium atoms. The static polarizabilities are compared with other theoretical values and with experimental results. The agreement is satisfactory in most cases but there are some exceptions where the discrepancy between theory and experiment is significant. The derived isotropic van der Waals coefficients range between 37 and 50 $E_H{a}_0^6$ and the orientation-dependent coefficients between 2 and $-1$ $E_H{a}_0^6$. Thus the ratio of elastic to inelastic scattering cross sections is expected to be substantial and any one of the rare-earth-metal atoms is an excellent candidate for trapping and cooling in a He gas.

In this paper we carry out a stability analysis of the Bloch states of a two-component Bose-Einstein condensate confined to a one-dimensional optical lattice. We consider two concrete systems: a mixture of two hyperfine states of rubidium-87 and a mixture of sodium-23 and rubidium-87. The former is seen to exhibit similar phenomena to a single component condensate while the latter also suffers an instability to phase separation at small Bloch wave vectors. It is shown that sufficiently deep optical lattices can remove this latter instability, potentially allowing immiscible cold atoms species to be held in intimate contact and transported within an experimental system.

We study the quantum dynamics of a single mode (particle) interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space, where the dynamics takes place. Two relevant examples are given: the inhomogeneous Tavis-Cummings model (e.g., $N$ atomic qubits coupled to a single cavity mode, or to a motional mode in trapped ions) and the inhomogeneous coupling of an electron spin to $N$ nuclear spins in a quantum dot.

An astigmatic optical resonator consists of two astigmatic mirrors facing each other. The resonator is twisted when the symmetry axes of the mirrors are nonparallel. We present an algebraic method to obtain the complete set of the paraxial eigenmodes of such a resonator. Basic ingredients are the complex eigenvectors of the four-dimensional transfer matrix that describes the transformation of a ray of light over a roundtrip of the resonator. The relation between the fundamental mode and the higher-order modes is expressed in terms of raising operators in the spirit of the ladder operators of the quantum harmonic oscillator.

We propose linear optical schemes for generating entangled states of two ququarts (four-dimensional quantum systems) in which the single-ququart state is constructed with frequency-nondegenerate biphoton polarization states of spontaneous parametric down-conversion. We show explicitly that it is possible to generate various two-ququart entangled states by interfering two ququarts at a linear optical beam splitter (an ordinary 50-50 beam splitter, a polarizing beam splitter, or a dichroic beam splitter).

The effect of the detector electronic noise in an optical homodyne tomography experiment is shown to be equivalent to optical loss if the detector is calibrated by measuring the quadrature noise of the vacuum state. An explicit relation between the electronic noise level and the equivalent optical efficiency is obtained and confirmed in an experiment with a narrow-band squeezed vacuum source operating at an atomic rubidium wavelength.

We discuss the transition from a fully decoherent to a (quasi)condensate regime in a harmonically trapped weakly interacting one-dimensional (1D) Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an ideal trapped 1D gas.

We introduce a picture of quantum dynamics in which the representation basis vectors are the quantities that evolve, instead of state vectors or operators. These vectors allow us to pick the parts of a probability density that correspond to some values of energy or time, providing us with energy and time representations. The properties of these representations are analyzed and an application to the free particle is presented.

We study the role of discrete rotational symmetry in the quantum key distribution by generalizing the well-known Bennett-Brassard 1984 and Scarani-Acin-Ribordy-Gisin 2004 protocols. We observe that discrete rotational symmetry results in the protocol’s invariance to continuous rotations, thus leading to a simplified relation between bit and phase error rates and consequently a straightforward security proof.

We present a probabilistic (ideally 50%) nondestructive interaction-free atom-photon controlled-NOT gate, where nondestructive means that all four outgoing target photon modes of the gate are available and feed-forwardable. Individual atoms are controlled by a simulated Raman adiabatic passage transition and photons by a ring resonator with two outgoing ports. Realistic estimates we obtain for ions confined in a Paul trap around which the resonator is mounted show that a strong atom-photon coupling can be achieved. It is also shown how the resonator can be used for controlling superposition of atom states.

We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement whose outcomes are associated with product states. We develop analytically the upper bound $0.7935\text{bits}$ to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value $0.8664\text{bits}$ attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.

Consider a function where its entries are distributed among many parties. Suppose each party is allowed to send only a limited amount of information to a referee. The referee can use a classical protocol to compute the value of the global function. Is there a quantum protocol improving the results of all classical protocols? In a recent work Brukner et al. showed the deep connection between such problems and the theory of Bell inequalities. Here we generalize the theory to trits. There, the best classical protocol fails whereas the quantum protocol yields the correct answer.

We estimate the nuclear polarizability correction to atomic transition frequencies in various helium isotopes. This effect is non-negligible for high precision tests of quantum electrodynamics or accurate determination of the nuclear charge radius from spectroscopic measurements in helium atoms and ions; in particular it amounts to $28\left(3\right)\mathrm{kHz}$ for $1S\text{−}2S$ transition in ${}^4\mathrm{He}^{+}$.

Although the outer shapes of molecular orbitals (MO’s) are of great importance in many phenomena, they have been difficult to be probed by experiments. Here we show that metastable helium $\left({\mathrm{He}}^{*}\right)$ atoms can sensitively probe the outer properties of molecules and that an electron spectroscopic technique using velocity-selected ${\mathrm{He}}^{*}$ atoms in combination with classical trajectory simulations leads to a consistent determination of MO functions and the molecular surface. MO functions composed of linear combinations of atomic orbital functions were fitted to the observed collision energy dependences of partial ionization cross sections (CEDPICS). The obtained CEDPICS MO functions were compared with conventionally available Hartree-Fock, Kohn-Sham, and Dyson orbitals.