An exact Gaussian solution with initial phase-front curvature for the Snyder-Mitchell linear model is presented. It is found that the propagation of the beam in strongly nonlocal media is deeply affected by the initial phase-front curvature, which can cause pulsating behavior of the Gaussian beam and lead to the occurrence of a periodic interference pattern during the interaction of two Gaussian beams. Also, we show that these properties are still valid for the nonlocal nonlinear Schrödinger equation provided that the characteristic response length of the nonlocal media is much broader than the width of the optical beam. It is useful for further understanding the properties of optical beams in strongly nonlocal media and may be applied to precision measurements.

We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with ${\widehat{\sigma }}^z$-dependent forces for trapped ion quantum computing. The force is exerted by two laser beams in a Raman configuration. Qubit-state dependency is achieved by a small frequency detuning from the virtually excited state. Ion species with excited states of long radiative lifetimes are used to reduce the chance of a spontaneous photon emission to less than ${10}^{-8}\mathrm{per}$ gate run. This eliminates the main source of gate infidelity in previous implementations. With this scheme it seems possible to reach the fault-tolerant threshold.

We model the predissociation of ${\mathrm{H}}_3$ in the electronic state corresponding to the upper sheet of the conically intersecting $1{{}^{2}A}^{\prime }$ and $2{{}^{2}A}^{\prime }$ states, and we show that product-state rovibrational distributions are strongly influenced by the geometric phase. Similarly, the differences in the product-state energy distributions in recent three-body dissociation experiments for the $2s,{}^{2}A_1^{\prime }$ and $2p,{}^{2}A_2^{″}$ states of ${\mathrm{H}}_3$ are shown to result from the presence of the geometric phase in this system, and thus provide experimental evidence of the influence of this phase in a molecular dynamical process.

We examine antiferromagnetic and $d$-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases, antiferromagnetism induces superfluidity by charge redistributions. We furthermore demonstrate how these shell structures can be detected as distinct antibunching dips and pairing peaks in the density-density correlation function probed in expansion experiments.

We study the disentanglement evolution of two spin qubits which interact with a general $XY$ spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of a quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two spin qubits may be greatly enhanced by the quantum critical behavior of the environmental spin chain. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the coherence factor. Furthermore, the scaling behavior in the disentanglement dynamics is also revealed and analyzed.

We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the nonexistence of any other copy with better fidelity. The effect of the initially distributed maximally entangled state on the process is presented; the concurrence and the fully entangled fraction of the shared states are discussed. We intend to show that prior information on the dissipative channel and the range of qubit states to be teleported is helpful for the evaluation of the success of teleportation, where success is defined as surpassing the fidelity limit imposed by the fidelity of the 1-to-2 optimal cloning machine for the specific range of qubits.

We show that a general linear transformation from one single photon qudit to another, the dimension of which can be either equal or unequal to that of the first one, can be implemented by linear optics. As an application of the scheme we elaborate a method to deterministically realize any finite-element positive operator-valued measure on single photon signals, which is also generalizable to any quantum system in principle.

Using a quantum-mechanical three-step model, we present numerical calculations of the high-order harmonic generation from four polyatomic molecules. Ethylene $\left({\text{C}}_2{\text{H}}_4\right)$ serves as an example where orbital symmetry directly affects the harmonic yield. We treat the case of methane $\left({\text{CH}}_4\right)$ to address the high-order harmonic generation resulting from a molecule with degenerate orbitals. To this end we illustrate how the single-orbital contributions show up in the total high-order harmonic signal. This example illustrates the importance of adding coherently the amplitude contributions from the individual degenerate orbitals. Finally, we study the high-order harmonic generation from propane $\left({\text{C}}_3{\text{H}}_8\right)$ and butane $\left({\text{C}}_4{\text{H}}_{10}\right)$. These two molecules, being extended and far from spherical in structure, produce harmonics with nontrivial orientational dependencies. In particular, propane can be oriented so that very high-frequency harmonics are favored, and thus the molecule contains prospects for the generation of uv attosecond pulses.

Spin squeezing of a nonlinear interaction model with Josephson-like coupling is studied to obtain the time scale of maximal squeezing. Based upon two exactly solvable cases for two and three particles, we find that the maximal-squeezing time depends on the level spacing between the ground state and its next-neighbor eigenstate.

We investigate the effect of an external periodic driving on the self-trapping transitions of two weakly coupled Bose-Einstein condensates in a double-well potential. Exact nonlinear Floquet solutions are obtained when the driving parameters satisfy certain conditions. These solutions can give an analytic demonstration of the ac control of self-trapping transitions.

Models of two-dimensional (2D) traps, with double-well structure in the third direction, for Bose-Einstein condensates are introduced with attractive or repulsive interactions between atoms. The models are based on systems of linearly coupled 2D Gross-Pitaevskii equations, where the coupling accounts for tunneling between the wells. Each well carries an optical lattice (OL) (stable 2D solitons cannot exist without OLs). The linear coupling splits each finite band gap in the spectrum of the single-component model into two subgaps. The main subject of the work is spontaneous symmetry breaking (SSB) in two-component 2D solitons and localized vortices (SSB was not considered before in 2D settings). Using variational approximation (VA) and numerical methods, we demonstrate that, in a system with attraction or repulsion, SSB occurs in families of symmetric or antisymmetric solitons (or vortices), respectively. The corresponding bifurcation destabilizes the original solution branch and gives rise to a stable branch of asymmetric solitons or vortices. The VA provides for an accurate description of the emerging branch of asymmetric solitons. In the model with attraction, all stable branches eventually terminate due to the onset of collapse. Stable asymmetric solitons in higher finite band gaps and vortices with a multiple topological charge are found too. The models also give rise to first examples of embedded solitons and embedded vortices (the states located inside Bloch bands) in two dimensions. In the linearly coupled system with opposite signs of the nonlinearity in the two cores, two distinct types of stable solitons and vortices are found, dominated by either the self-attractive component or the self-repulsive one. In the system with a mismatch between the two OLs, a pseudobifurcation is found: when the mismatch attains its largest value $\left(\pi \right)$, the bifurcation does not happen, as branches of different solutions asymptotically approach each other, but fail to merge.

The first detailed comparison between ab initio calculations of finite fermionic superfluid systems, performed recently by Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] and by von Stecher, Grange, and Blume [e-print arXiv:0705.0671v1] and the extension of the density-functional theory superfluid local-density approximation (SLDA) is presented. It is shown that SLDA reproduces the total energies, number density distributions in inhomogeneous systems along with the energy of the normal state in homogeneous systems. Unlike the Kohn-Sham LDA, in SLDA the effective fermion mass differs from the bare fermion mass and the spectrum of elementary excitations is also reproduced.

We suggest a type of scanning fluorescence microscope that is capable of resolving nanometer-size objects in the far field. The key idea is to use the spatial sensitivity of the dark state of electromagnetically induced transparency and localize an atomic excitation to a spot much smaller than the wavelength of light.

$1s\text{−}2p$ Lyman $\alpha$ transitions in hydrogenic iron ${\mathrm{Fe}}^{25+}$ have been observed from a beam-foil source in fourth-order diffraction off ADP 101 and PET 002 crystals, simultaneously with the $n=2$ to $n=4$ Balmer $\beta$ transitions diffracted in first order. Calibration of the local dispersion relation of the spectrometer using Balmer $\beta$ lines provides measurements of Lyman $\alpha$ wavelengths. The approach of fitting the full two-dimensional dispersion relation, including other members of Balmer and Lyman series, limits random and systematic correlation of parameters, and reveals a major systematic due to dynamical diffraction depth penetration into a curved crystal. The development of a theory of x-ray diffraction from mosaic crystals was necessary for the accurate interpretation of the experimental data. Photographic theory was also developed in the process of this research. Several systematics are discussed and quantified for the first time for these medium-$Z$ QED comparisons. $2s\text{−}1s$ and $4f\text{−}2p$ satellites are explicitly investigated, and a dominant systematic is uncovered, which is due to the variable location of spectral emission downstream of the beam-foil target. $1s\text{−}2p_{3∕2}$, $1s\text{−}2p_{1∕2}$ iron Lamb shifts are measured to be $35376\pm 1900{\mathrm{cm}}^{-1}$ and $35953\pm 1800{\mathrm{cm}}^{-1}$. These agree with but lie higher than theory. This represents a 5.7% measurement of the hydrogenic $1s\text{−}2p_{1∕2}$ Lamb shift in iron. The technique also reports the iron $2p_{3∕2}\text{−}2p_{1∕2}$ fine structure as $171108{\mathrm{cm}}^{-1}\pm 180{\mathrm{cm}}^{-1}$, which represents a 51% measurement of the hydrogenic iron fine-structure Lamb shift, and reports measurements of secondary lines.

Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum system whose state is to be determined is first coupled to a second quantum system (the “assistant”) in such a way that part of the information in the quantum state is transferred to the assistant. The actual measurement is then performed on the enlarged system including the original system and the assistant. We discuss in detail the requirements of this procedure and experimentally implement it on a simple quantum system consisting of nuclear spins.

We consider the optimal measurement procedures for estimating an unknown maximally entangled state with local operations and classical communications (LOCC). By the “optimal,” we mean that there is no other LOCC measurements that can provide a higher estimation fidelity. In fact, we first use the positive partial transpose constraint to obtain an upper bound of the fidelity; then, we show there exists a kind of LOCC measurement that can attain such a bound. The estimation fidelity of the optimal LOCC estimation procedures is $\frac{D+2}{(D+1)D^2}$ with $D$ denoting the dimension of the relevant quantum system.

We show that braiding transformation is a natural approach to describe quantum entanglement by using the unitary braiding operators to realize entanglement swapping and generate the Greenberger-Horne-Zeilinger states as well as the linear cluster states. A Hamiltonian is constructed from the unitary ${\check{R}}_{i,i+1}(\theta ,\phi )$ matrix, where $\phi =\omega t$ is time-dependent while $\theta$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.

Charge-transfer processes in collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{O}}^{+}$ ions with ${\mathrm{C}}_2{\mathrm{H}}_4$ molecules have been studied in joint theoretical and experimental approaches for collision energies below $10\mathrm{keV}∕\mathrm{u}$. Since H and O atoms possess nearly identical ionization potentials, these two ions are expected to share similar dynamics and hence to have similar cross-section values for charge transfer, at least for the energy region above $100\mathrm{eV}$. In the present experiments, these cross sections of ${\mathrm{H}}^{+}$ and ${\mathrm{O}}^{+}$ ions have been derived by the initial growth rate method in the energy range of $0.20\text{to}3.6\mathrm{keV}$, while the present theoretical study has been carried out for ${\mathrm{H}}^{+}$ impact only. We have examined the vibrational effect on charge transfer, especially the “temperature effect” of the initial vibrational states of the ${\mathrm{C}}_2{\mathrm{H}}_4$ molecule as well as the final vibrational states of the product ${\mathrm{C}}_2{\mathrm{H}}_4^{+}$ molecular ion. Indeed, a strong influence of the initial vibrational states on charge transfer has been observed since these vibrationally excited initial and final states force the process to be more nearly resonant, thus making charge transfer more efficient. This vibrational effect, and perhaps rotational effect as well, that makes the collision process more nearly resonant has not been well investigated previously, and thus the present study is expected to shed much light on this effect in general.

We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on it by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena of early collapse and superslow collapse of the mixture.