Quantum controlled-NOT (CNOT) gates with single trapped cold ions have been experimentally demonstrated [C. Monroe et al., Phys. Rev. Lett. 75, 4714 (1995)] by using auxiliary atomic levels (besides the qubit ones) and under the usual Lamb-Dicke (LD) limit (wherein the so-called LD parameter, which represents the interaction strength between the internal and external degrees of freedom of the driven ion, is required to be sufficiently small). It has been shown [C. Monroe et al., Phys. Rev. A 55, R2489 (1997); L. F. Wei et al., 65, 062316 (2002)] that, beyond the LD limit, these gates could also be implemented for certain specific LD parameters. Here, we further show that, without any auxiliary atomic level, the desirable quantum logic gates could still be realized with sufficiently high fidelities for arbitrary LD parameters, as long as the durations of the applied laser pulses are accurately set within the decoherence times of the ions.

We investigate effects of the adiabatic ramp-up of optical lattices to the temperatures of Bose gases. Applying the mean-field approximation to the three-dimensional Bose-Hubbard model at finite temperatures, we calculate the isentropic curves in the phase diagram against the temperatures and the lattice height. The adiabatic cooling or heating through superfluid-normal phase transition is clearly understood. It is found that the cooling occurs in superfluid phase while the heating occurs in normal phase and the efficiency of adiabatic cooling or heating is higher at higher temperatures. This behavior can be understood from the lattice-height dependence of dispersion relation in each phase. Furthermore, the connection of the adiabatic cooling or heating between the cases with and without the trap potential is addressed.

Decoherence in Markovian systems can result indirectly from the action of a system Hamiltonian which is usually fixed and unavoidable. Here, we show that in general in Markovian systems, because of the system Hamiltonian, quantum information decoheres. We give conditions for the system Hamiltonian that must be satisfied if coherence is to be preserved. Finally, we show how to construct robust subspaces for quantum-information processing.

We observe high-resolution diffraction patterns of a thermal-energy helium atom beam reflected from a microstructured surface grating at grazing incidence. The grating consists of $10\text{−}\mu \mathrm{m}$-wide Cr strips patterned on a quartz substrate and has a periodicity of $20\mu \mathrm{m}$. Fully resolved diffraction peaks up to the seventh order are observed at grazing angles up to $20\mathrm{mrad}$. With changes in de Broglie wavelength or grazing angle the relative diffraction intensities show significant variations which shed light on the nature of the atom-surface interaction potential. The observations are explained in terms of quantum reflection at the long-range attractive Casimir–van der Waals potential.

The quasilinear development of the modulational instability of a partially coherent wave in a dispersive and nonlinear medium is analyzed. It is found that the quasilinear diffusion process tends to further stabilize the instability growth in addition to the stabilizing effect which is due to the partial coherence. In an unstable situation, the growth of the perturbation causes a slow change of the coherence spectrum such as to increase the degree of incoherence and eventually saturate the instability. On the other hand, in a stable situation the decay of the perturbation may cause a reversed quasilinear diffusion of the background distribution, which leads to an increasing degree of coherence of the background.

We propose a thought technique for detecting gravitational waves (GWs) using Einstein-Podolsky-Rosen photon entangled states. GWs decohere the entangled photon pairs, introduce a relative rotation, and desynchronize Alice’s and Bob’s reference frames, thus reducing the measured nonlocality of correlated quanta described by Bell’s inequalities. Gravitational waves, distorting quantum encryption key statistics away from a pure white noise, act then as shadow eavesdroppers. The deviation from the intrinsic white-noise randomness of a quantum key distribution process can reveal the presence of a gravitational wave by analysis of the emerging color distortions in the key. Photon entangled states provide the key advantage of revealing the polarization rotation introduced by GWs without the need of previously fixed reference frames.

The Casimir energy is computed in the geometry of interest for the most precise experiments, a plane and a sphere in electromagnetic vacuum. The scattering formula is developed on adapted plane waves and multipole basis, leading to an expression valid for arbitrary relative values of the sphere radius and interplate distance. In the limiting case of perfect reflection, the electromagnetic result is found to depart from the commonly used proximity-force approximation (PFA) significantly more rapidly than expected from scalar computations.

We study dynamical decoupling in a multiqubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the computation. We derive a rigorous error bound on the trace distance or fidelity between the desired computational state and the actual time-evolved state, for a system subject to coupling to a bounded-strength bath. The bound is expressed in terms of the operator norm of the effective Hamiltonian generating the evolution in the presence of decoupling and logic operations. We apply the bound to the case of periodic pulse sequences and find that in order to maintain a constant trace distance or fidelity, the number of cycles—at fixed pulse interval and width—should scale in inverse proportion to the square of the number of qubits. This sets a scalability limit on the protection of quantum computation using periodic dynamical decoupling.

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that “generates” an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.

We study the evolution of a system of two qubits, each of which interacts locally with a spin chain with nontrivial internal Hamiltonian. We present an exact solution to this problem and analyze the dependence of decoherence on the distance between the interaction sites. In the strong coupling regime we find that decoherence increases with increasing distance. In the weak coupling regime the dependence of decoherence with distance is not generic (i.e., it varies according to the initial state). Decoherence becomes independent of distance when the latter is over a saturation length $l$. Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\xi$. For strong coupling we display evidence of the existence of non-Markovian effects (such as environment-induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of “sudden deaths and revivals” of entanglement, with a time scale related to the distance between qubits.

We present a general state-independent optimal control strategy for weakly dissipative quantum systems which allows the identification of Hamilton operators which approximately perform a specified unitary operation and minimize the adverse effects of the dissipative environment. Compared to traditional approaches, it avoids the need for Lagrange multipliers and the repeated solving of the full kinetic equations of the quantum subsystem. This direct method is outlined for a single qubit raealization, such as the spin of an excess electron in a quantum dot or a Josephson qubit. We show that for this system formulated within the Lindblad equation, optimal solutions for arbitrary unitary single-qubit operations may be found analytically provided there is full control over the system Hamiltonian. Absolute bounds for controllability are derived analytically. Numerical implementations of this approach confirm these results and allow an efficient determination of optimal solutions for various dissipators, starting from various initial guesses, both for limited and full control over the Hamiltonian of the quantum system.

We investigate localization of entanglement of multipartite mixed Gaussian states into a pair of modes by local Gaussian measurements on the remaining modes and classical communication. We provide a detailed proof that for arbitrary symmetric Gaussian state maximum entanglement can be localized by homodyne detection of either the amplitude or phase quadrature on each mode. We then consider arbitrary mixed three-mode Gaussian states and show that the optimal Gaussian measurement on one mode yielding maximum entanglement among the other two modes can be determined by calculating roots of a high-order polynomial. Finally, we discuss localization of entanglement with single-photon detection.

A large-scale relativistic configuration-interaction (CI) calculation is performed for the magnetic-dipole and the electric-quadrupole hyperfine structure splitting in ${}^{7,6}\mathrm{Li}$ and ${}^9\mathrm{Be}^{+}$. Numerical results for the $2{}^{2}S$, $3{}^{2}S$, $2{}^{2}P_{1∕2}$, and $2{}^{2}P_{3∕2}$ states are reported. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with separate treatments of the QED, nuclear-magnetization distribution, recoil, and negative-continuum effects.

We determine the cyclotron frequency ratio of $\text{H}_2{}^{+}$ and ${\text{D}}^{+}$, applying the two-pulse Ramsey-excitation technique in the Penning-trap mass spectrometer SMILETRAP. The final result, based on probing more than 100 000 ions, is a frequency ratio of 0.999 231 659 33(17). Using a value of the ${\text{D}}^{+}$ mass recently measured by the Seattle group, we obtain so far the most precise experimental $\text{H}_2{}^{+}$ mass value of 2.015 101 497 16(34) u. From this value a proton mass value of 1.007 276 466 95(18) u (0.18 ppb relative uncertainty) could be derived, in good agreement with the value of 1.007 276 466 89(14) u published by Van Dyck et al. [R. S. Van Dyck, Jr., D. L. Farnham, S. L. Zafonte, and P. B. Schwinberg, in Trapped Charged Particles and Fundamental Physics, edited by D. E. Dubin and D. Schneider, AIP Conf. Proc. No. 457 (AIP, Woodbury, NY, 1999)].

We report on a technique to determine the van der Waals coefficients of lithium (Li) atoms based on relativistic coupled-cluster theory. These quantities are determined using the imaginary parts of the scalar dipole and quadrupole polarizabilities, which are evaluated using an approach that we have proposed earlier [B. K. Sahoo, Chem. Phys. Lett. 448, 144 (2007)]. Our procedure is fully ab initio, and avoids the sum-over-the-states approach. We present the dipole and quadrupole polarizabilities of many of the low-lying excited states of Li. Also, the off-diagonal dipole and quadrupole polarizabilites between some of the low-lying states of Li have been calculated.

A method to generate low-energy phase shifts for elastic scattering using bound-state calculations is applied to the problem of $e^{+}\text{−}\text{Mg}$ and $e^{+}\text{−}\text{Zn}$ scattering after an initial validation on the $e^{+}\text{−}\text{Cu}$ system. The energy shift between a small reference calculation and the largest possible configuration interaction calculation of the lowest-energy pseudostate is used to tune a semiempirical optical potential. The potential was further fine-tuned by utilizing the energy of the second lowest pseudostate. The $s$- and $p$-wave phase shifts for positron scattering from Mg and Zn are given from threshold to the first excitation threshold. The $e^{+}\text{−}\text{Mg}$ cross section has a prominent $p$-wave shape resonance at an energy of about 0.096 eV with a width of 0.106 eV. The peak cross section for $e^{+}\text{−}\text{Mg}$ scattering is about $4800a_0^2$, while $Z_{\text{eff}}$ achieves a value of 1310 at an energy of 0.109 eV.

We show that there exists a sum rule for the local mode density that is associated with radiative spontaneous decay of an atom in an absorbing dielectric material. The existence of such a sum rule in particular means that dielectric surroundings merely redistribute the local density of states along the real frequency axis. This result supercedes a previously obtained sum rule [S. M. Barnett and R. Loudon, Phys. Rev. Lett. 77, 2444 (1996)] that is valid only for strictly nonabsorbing dielectric materials. The new sum rule also provides a way of computing the integrated density of states associated with nonradiative decay channels.

A unified homogenization procedure for split-ring metamaterials taking into account time and spatial dispersion is introduced. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.

As a companion work to our previous study [F. Xu, et al., Phys. Rev. E. 75, 026613 (2007)] on radiation force prediction for a homogeneous spheroid, we provide in this paper the analytical solution to the radiation torque exerted by an arbitrarily shaped beam on a spheroid, which can be prolate or oblate, transparent or absorbing. Calculations based upon this theoretical development are performed for both linearly and circularly polarized incident beams, and the results are compared to those of a sphere. Stable orientations of spheroids inside a linearly and a circularly polarized Gaussian beam are predicted. We analyze two physical mechanisms, the polarization torque and the reaction force torque, which do not exist or have no contribution to the torque on a sphere but cause rotation of a spheroid. As verification, the dipole method is also developed for the torque calculation for spheroids of size much less than the wavelength, and geometrical optics is developed to qualitatively analyze the torque exerted on spheroids of large size.

We present an experimental characterization of a heralded single-photon source based on spontaneous four-wave mixing in a single-mode microstructure fiber. We measure the second-order correlation function $g^{\left(2\right)}\left(0\right)$ to be far below the classical, Poissonian limit of 1 over a broad spectral range. With single-spatial-mode output, such a spectrally bright and broad fiber-based heralded single-photon source is suitable for a variety of quantum-information applications.