Motivated by the recent experimental observation of multicomponent spinor condensates via a time-dependent quadrupole-Ioffe-configuration trap, we provide a general framework for the investigation of nonadiabatic Landau-Zener dynamics of a hyperfine spin, e.g., from an atomic magnetic dipole moment coupled to a weak time-dependent magnetic $\left(B\text{−}\right)$ field. The spin flipped population distribution, or the so-called Majorona formula, is expressed in terms of system parameters and experimental observables; thus, the distribution provides much needed insight into the underlying mechanism for the production of spinor condensates due to nonadiabatic level crossings.

The generation of the population oscillation of the multicomponent spinor Bose-Einstein condensate is demonstrated in this paper. We observe and examine the nonsynchronous decreasing processes of the magnetic fields generated between quadrupole coils and Ioffe coils during the switch-off of the quadrupole-Ioffe-configuration trap, which is considered to induce a nonadiabatic transition. Starting from the two-level Schrödinger equation, we have done some numerical fitting and derived an analytical expression identical to the results of Majorana and Zener, of which both results well match the experimental data.

The generalized Thomas-Reiche-Kuhn sum rule is established for any Coulombic system with arbitrary masses and charges of its constituent particles. Numerical examples are given for the hydrogen molecular ions.

The isolated resonance picture (IRP) is tested by comparing calculations on doubly excited autoionizing states of ${\mathrm{H}}_2$ by using two different theoretical approaches: a recent implementation of the exterior complex scaling method and the standard Feshbach method with $B$-spline basis sets. These calculations demonstrate that the IRP can yield poor approximations to autoionization widths when doubly excited states approach the ionization threshold at large internuclear distances, $R$. In contrast, at small $R$ where avoided crossings appear, the IRP produces accurate resonance parameters.

We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant $I\left(t\right)$ they derived does not satisfy the Liouville–Von Neuman equation. (ii) They found that the eigenvalues of $I\left(t\right)$ are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schrödinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.

We demonstrate that two well-established experimental techniques of condensed-matter physics, neutron-diffraction scattering and measurement of magnetic susceptibility, can be used to detect and quantify macroscopic entanglement in solids. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron-scattering experiment from 2000 provides microscopic support for this interpretation and gives the value for the amount of entanglement. We present a quantitative analysis resulting in the critical temperature of 5 K in both, completely independent, experiments below which entanglement exists.

We prove multiplicativity of maximal output $p$ norm of classical noise channels and thermal noise channels of arbitrary modes for all $p>1$ under the assumption that the input signal states are Gaussian states. As a direct consequence, we also show the additivity of the minimal output entropy and that of the energy-constrained Holevo capacity for those Gaussian channels under Gaussian inputs. To the best of our knowledge, newly discovered majorization relation on symplectic eigenvalues, which is also of independent interest, plays a central role in the proof.

Based on quantum entanglement, an all-or-nothing oblivious transfer (OT) protocol is proposed and is proven to be secure. The distinct merit of the present protocol lies in that it is not based on quantum bit commitment. More intriguingly, this OT protocol does not belong to a class of protocols denied by Lo’s no-go theorem of one-sided two-party secure computation, and thus its security can be achieved.

We show how to efficiently exploit decoherence free subspaces (DFSs), which are immune to collective noise, for realizing quantum repeaters with long-lived quantum memories. Our setup consists of an assembly of simple modules and we show how to implement them in systems of cold, neutral atoms in arrays of dipole traps. We develop methods for realizing robust gate operations on qubits encoded in a DFS using collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of all required gate operations and emphasize that all modules can be realized with current or near future experimental technology.

An alternative approach to open-shell molecular calculations using the variational two-electron reduced-density-matrix (2-RDM) theory [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] is presented. The energy and 2-RDM of the open-shell molecule (or radical) are computed from the limit of dissociating one or more hydrogen atoms from a molecule in a singlet state. Because the ground-state energy of an “infinitely” separated hydrogen atom in a given finite basis is known, we can determine the energy of the radical by subtracting the energy of one or more hydrogen atoms from the energy of the total dissociated system. The 2-RDM is constrained to have singlet symmetry in all calculations. Two sets of $N$-representability conditions are employed: (i) two-positivity conditions, and (ii) two-positivity conditions plus the $T_2$ condition, which is a subset of the three-positivity conditions. Optimization of the energy with respect to the 2-RDM is performed with a first-order algorithm for solving the semidefinite program within the variational 2-RDM method. We present calculations of several radicals near equilibrium as well as the dissociation curves of the diatomic radicals CH and OH.

A modified version of the Møller-Plesset approach for obtaining the correlation energy associated with a Hartree-Fock ground state is proposed. The method is tested in a model of interacting fermions that allows for an exact solution. Using up to third order terms improved results are obtained, even in the limit of loosely bound particles. Tested in molecules as well, the modified method appears to give improved results in symmetric systems.

We analyze a four-wave mixing enhancement scheme based on a specific lifetime-broadened four-level atomic configuration. The enhancement can mainly be controlled through the time-dependent propagation dynamics of the applied pulse fields, but it is also found to depend on the sample density and spontaneous emission of the levels involved. A systematic analysis, that illustrates how the applied pulses dynamics, density, and spontaneous emission affect the mixing conversion efficiency, is carried out, anticipating substantially large efficiencies for realistic atomic parameters and short weak laser pulses.

We present a model to realize quantum feedback control of continuous variable entanglement. It consists of two interacting bosonic modes subject to amplitude damping and achieving an entangled Gaussian steady state. The possibility to greatly improve the degree of entanglement by means of Markovian (direct) feedback is then shown.

We discuss the correlations between particles of different momentum in a superfluid Fermi gas, accessible through noise measurements of the absorption images of the expanded gas. We include two elements missing from the simplest treatment, based on the BCS wavefunction: the explicit use of a conserving approximation satisfying particle number conservation and the inclusion of the contribution from Cooper pairs at finite momentum. We expect the latter to be a significant issue in the strongly correlated state emerging in the BCS-Bose-Einstein condensate (BEC) crossover.

In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the U.K. and Innsbruck University respectively. The secular frequencies for ${}^{88}\mathrm{Sr}^{+}$ and ${}^{40}\mathrm{Ca}^{+}$ ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control when no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.

We identify those properties of a quantum channel that are relevant for cryptography. We focus on general key distribution protocols that use prepare and measure schemes and the existing classical reconciliation techniques, as these are the protocols feasible with current technology. Given a channel, we derive an easily computable necessary condition of security for such protocols. In spite of its simplicity, this condition is shown to be tight for the Bennett-Brassard 1984 and six-state protocols. We show that the condition becomes also sufficient in the event of a so-called collective attack.

We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are presented. By unambiguous identification, we mean that we are not allowed to make a mistake but our measurement can produce an inconclusive result. Assuming the two reference states are independently distributed over the whole pure state space in a unitary invariant way, we determine the optimal mean success probability for an arbitrary number of copies of the reference states and a general dimension of the state space. It is explicitly shown that the obtained optimal mean success probability asymptotically approaches that of the unambiguous discrimination as the number of the copies of the reference states increases.

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: (i) the bases are orthonormal, (ii) in each basis, all the states have the same values of entanglement, and (iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many areas related to the quantum information science including quantum cryptography, optimal Bell tests, and the investigation of the enhancement of channel capacity due to entanglement.

In most high-accuracy x-ray experiments, characteristic radiation is used to determine calibration energies or wavelengths. This paper presents experimental results for vanadium $K\alpha$, and component refitting for scandium, titanium, chromium, and manganese, addressing a critical limitation on the current use of this approach. The influence of spectrometer broadening upon the registration of these calibration profiles is quantitatively discussed and determined. The analysis permits such calibration with insignificant loss of accuracy compared to the reference uncertainty, down to a one part per million level. In the process we reveal key empirical structural trends in $K\alpha$ spectral profiles from $Z=21$ to $Z=25$ which originate from detailed physical processes which are neither well understood nor well evaluated theoretically.