A method to optically control a dark transition, for instance, the coupling between different spin states, is proposed. The control is achieved by manipulating the direction, amplitude, and duration of dynamic Stark shifts. Laser-driven spin switches can be prepared by conveniently generalizing different optical techniques, such as $\pi$-pulse schemes and adiabatic passage schemes. The efficiency and robustness of the schemes is analyzed for both two-level and multilevel systems, implying quantum state selective wave packet transfer between states of different multiplicity.

We address the concept of guiding and transporting matter-wave solitons along the channels of optical lattices made by interference patterns of beams containing topological wavefront dislocations. The local lattice distortions that occur around the dislocations cause solitons to move along reconfigurable paths, a phenomenon that may be used for controlled all-optical manipulation of Bose-Einstein condensates. Multiple dislocations form traps that can capture and hold moving solitons. We also show that suitable lattice topologies may be used to explore matter-wave soliton collisions and interactions in a confined reconfigurable environment.

We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.

The interaction of very slow electrons with weak potentials is investigated in an exactly soluble, one-dimensional quantum mechanical model. Slow electrons are produced by a decelerating ramp potential, as in experimental mirror electron microscopy, so the electrons can interact with a weak field as they slow and reverse direction. Our model provides a wave mechanical interpretation of this turning point region and suggests the possibility of imaging optical fields utilizing the phase of electron matter waves.

We present a simple quantum many-body system—a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions—such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.

We calculate the entanglement entropy of strongly correlated low-dimensional fermions in metallic, superfluid, and antiferromagnetic insulating phases. The entanglement entropy reflects the degrees of freedom available in each phase for storing and processing information, but is found not to be a state function in the thermodynamic sense. The role of critical points, smooth crossovers, and Hilbert space restrictions in shaping the dependence of the entanglement entropy on the system parameters is illustrated for metallic, insulating, and superfluid systems. The dependence of the spin susceptibility on entanglement in antiferromagnetic insulators is obtained quantitatively. The opening of spin gaps in antiferromagnetic insulators is associated with enhanced entanglement near quantum critical points.

We report an experimental demonstration of effective entanglement in a prepare-and-measure type of quantum key distribution protocol. Coherent polarization states and heterodyne measurement to characterize the transmitted quantum states are used, thus enabling us to reconstruct directly their $Q$ function. By evaluating the excess noise of the states, we experimentally demonstrate that they fulfill a nonseparability criterion previously presented by Rigas et al. [J. Rigas, O. Gühne, and N. Lütkenhaus, Phys. Rev. A 73, 012341 (2006)]. For a restricted eavesdropping scenario, we predict key rates using postselection of the heterodyne measurement results.

Excitation energies of the $n{s}_{1∕2}$ $(n=7–10)$, $n{p}_j$ $(n=7–9)$, $n{d}_j$ $(n=6–8)$, $n{f}_j$ $(n=5–7)$, and $n{g}_j$ $(n=5,6)$ states in $\mathrm{Th}\mathrm{IV}$ are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 96 possible $n{l}_j\text{−}{n}^{\prime }{l}_{j^{\prime }}^{\prime }$ electric-dipole transitions. Multipole matrix elements ($7s_{1∕2}\text{−}6d_j$, $7s_{1∕2}\text{−}5f_j$, and $5f_{5∕2}\text{−}5f_{7∕2}$) are evaluated to obtain the lifetimes of the $5f_{7∕2}$ and $7s_{1∕2}$ states. Matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and a relativistic all-order method restricted to single and double excitations. Scalar and tensor polarizabilities for the $5f_{5∕2}$ ground state in ${\mathrm{Th}}^{3+}$ are calculated using relativistic third-order and all-order methods. These calculations provide a theoretical benchmark for comparison with experiment and theory.

The determination of the elements of the $S$ matrix within the framework of time-dependent density-functional theory (TDDFT) has remained a widely open question. We explore two different methods to calculate state-to-state transition probabilities. The first method closely follows the extraction of the $S$ matrix from the time-dependent Hartree-Fock approximation. This method suffers from cross-channel correlations resulting in oscillating transition probabilities in the asymptotic channels. An alternative method is proposed, which corresponds to an implicit functional of the time-dependent density. Evaluated with the exact time-dependent density it gives rise to stable and accurate transition probabilities. However, the functional shows an extreme sensitivity with respect to errors in the time-dependent density when evaluated using an approximate density from an actual TDDFT calculation. Two exactly solvable two-electron systems serve as a benchmark for a quantitative test.

It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schrödinger equation with a periodic potential and periodic nonlinearity. In such a system there exist localized modes having peculiar properties. In particular, for some regions of parameters there exists a lower bound for a number of bosons necessary for creation of a mode, while for other domains small amplitude gap solitons are not available in the vicinity of either of the gap edges. We found that the lowest branch of the symmetric solution either does not exist or exists only for a restricted range of energies in a gap, unlike in pure bosonic condensates. The simplest bifurcations of the modes are shown and stability of the modes is verified numerically.

This paper demonstrates switching of a single signal photon by a single gating photon of a different frequency, via a cross-phase-modulation. This effect is mediated by materials exhibiting electromagnetically induced transparency (EIT), which are embedded in photonic crystals (PhCs). An analytical model based on waveguide-cavity QED is constructed for our system, which consists of a PhC waveguide and a PhC microcavity containing a four-level EIT atom. It is solved exactly and analyzed using experimentally accessible parameters. It is found that the strong coupling regime is required for lossless two-photon quantum entanglement.

We calculate correlation function in the Einstein-Podolsky-Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are physically interesting and transform covariantly under the full Lorentz group action—i.e., for pseudoscalar and vector states.

We report on the implementation of Burgers equation as a type-II quantum computation on a NMR quantum-information processor. Since the flow field evolving under the Burgers equation develops sharp features over time, this is a better test of liquid-state NMR implementations of type-II quantum computers than the previous examples using the diffusion equation. In particular, we show that Fourier approximations used in the encoding step are not the dominant error. Small systematic errors in the collision operator accumulate and swamp all other errors. We propose, and demonstrate, that the accumulation of this error can be avoided to a large extent by replacing the single collision operator with a set of operators with random errors and similar fidelities. Experiments have been implemented on 16 two-qubit sites for eight successive time steps for the Burgers equation.

Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and $H$ theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit’s energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory.

We show that $s$ waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of $s$ waves which allows us to perform the calculations analytically. This class includes a Gaussian, a maximally entangled as well as a “shell” state.

We show that, for $N$ parallel input states, an antilinear map with respect to a specific basis is essentially a classical operation. We also consider the information contained in a phase-conjugate pair $\mid \varphi ⟩\mid {\varphi }^{*}⟩$, and prove that there is more information about a quantum state encoded in a phase-conjugate pair than in a parallel pair.

Component instantaneous ionization rate (IIR) is introduced and the approach of its calculation is formulated. The component IIR’s and the overall (time-averaged) component ionization rates are calculated for $\mathrm{H}_2{}^{+}$ at different values of internuclear distance in a linearly polarized laser field with $I=1.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ intensity and $\lambda =1064\mathrm{nm}$ wavelength by direct numerical solution of the fixed-nuclei full dimensional time-dependent Schrödinger equation. The exact overall component ionization rates calculated by time-averaging of the component IIR are compared with those calculated approximately via the virtual detector (VD) method. Details of the time-dependent behavior of the outgoing and incoming electron wave packets of the $\mathrm{H}_2{}^{+}$ system in intense laser field at subfemtosecond time scale are studied based on the calculated component IIR. It is shown clearly that the positive (outgoing electron wave packet) signals of the IIR and its $z$ component are strong and sharp but the negative (returning electron wave packet) signals of the IIR are smooth and weak. The structure of the $\rho$ component of the IIR has smooth structure. Relation between the $R$-dependent ionization rate and duration of the ramp of the laser pulse is studied and it is explicitly shown that for internuclear distance $R<5.6$, when the laser pulse is turned on without a ramp, the first peak of $R$-dependent ionization rates moves towards the peak of the lower time-dependent Floquet quasienergy state (QES).

We consider the photodissociation of ground-state bosonic molecules trapped in an optical lattice potential into a two-component gas of fermionic atoms. The system is assumed to be described by a single-band resonantly coupled Bose-Fermi Hubbard model. We show that in the strong fermion-fermion interaction limit the dissociation dynamics is governed by a spin-boson lattice Hamiltonian. In the framework of a mean-field analysis based on a generalized Gutzwiller ansatz, we then examine the crossover of the dissociation from a regime of independent single-site dynamics to a regime of cooperative dynamics as the molecular tunneling increases. We also show that in the limits of weak and strong intersite tunneling the mean-field solutions agree well with the results from the quantum optical Jaynes-Cummings and Tavis-Cummings models, respectively. Finally, we identify two types of self-trapping transitions, a coherent and an incoherent one, depending on the ratio of the repulsive molecule-molecule interaction strength to molecular tunneling.

We formulate polarization uncertainty relations and polarization squeezing criteria in a SU(2) invariant manner. In this formulation the SU(2) coherent states are the only minimum uncertainty states. We show that polarization squeezing is a nonclassical property. We analyze the relation between polarization squeezing and other nonclassical properties such as entanglement and quadrature squeezing.