The dynamics of entanglement and fidelity for a subsystem of two separate spin-$1∕2$ qubits prepared in Bell states is investigated. One of the subsystem qubit labeled $A$ is under the influence of a Heisenberg $XY$ spin bath, while another one labeled $B$ is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\to \infty$, and (ii) $N$ is finite, $N=40$. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit $A$. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.

Many efforts are currently underway to build a device capable of large scale quantum information processing (QIP). Whereas QIP has been demonstrated for a few qubits in several systems, many technical difficulties must be overcome in order to construct a large-scale device. In one proposal for large-scale QIP, trapped ions are manipulated by precisely controlled light pulses and moved through and stored in multizone trap arrays. The technical overhead necessary to precisely control both the ion geometrical configurations and the laser interactions is demanding. Here we propose methods that significantly reduce the overhead on laser-beam control for performing single- and multiple-qubit operations on trapped ions. We show how a universal set of operations can be implemented by controlled transport of ions through stationary laser beams. At the same time, each laser beam can be used to perform many operations in parallel, potentially reducing the total laser power necessary to carry out QIP tasks. The overall setup necessary for implementing transport gates is simpler than for gates executed on stationary ions. We also suggest a transport-based two-qubit gate scheme utilizing microfabricated permanent magnets that can be executed without laser light.

Negative ion mass spectrometry and pulsed discharge electron capture detector data for thermal electron attachment to $\mathrm{S}{\mathrm{F}}_6$ are reported. Electron affinities and activation energies for $\mathrm{S}{\mathrm{F}}_6$ and $\mathrm{S}{\mathrm{F}}_5$ are obtained from these data and literature magnetron, swarm, beam, and collisional ionization data. The thermodynamic and kinetic data cover temperatures from $50\text{to}7500\mathrm{K}$. The largest electron affinity of $\mathrm{S}{\mathrm{F}}_6$, $2.60\left(10\right)\mathrm{eV}$ is assigned to the adiabatic electron affinity. The numbers in parentheses indicate uncertainties. Excited state values are (in eV) 2.45(3), 2.20(3), 2.00(3), 1.80(3), 1.60(3), 1.20(3), 1.04(3), 0.80(3), 0.65(3), 0.45(3), 0.35(3), 0.25(3), and 0.10(10). The activation energies range from near zero to $0.65\left(2\right)\mathrm{eV}$. The adiabatic electron affinity of $\mathrm{S}{\mathrm{F}}_5$, $3.85\left(2\right)\mathrm{eV}$ and an excited state value, $2.77\left(5\right)\mathrm{eV}$ are obtained from a kinetic analysis of published magnetron data. The energies for dissociative electron attachment to give $\mathrm{S}{\mathrm{F}}_5(-)$, $\mathrm{F}(-)$, and excited state $\mathrm{S}{\mathrm{F}}_5(-)$ are $0.20\left(11\right)\mathrm{eV}$, $0.65\left(10\right)\mathrm{eV}$, and $1.28\left(11\right)\mathrm{eV}$ from the $\mathrm{S}{\mathrm{F}}_5\text{−}\mathrm{F}$ dissociation energy, the electron affinity of the fluorine atom, and these values. The average relative anion bond orders for the bonding curves is 0.63(2) and for the antibonding curves is 0.30(2). Fourteen Herschbach ionic Morse Person empirical curves are calculated from these data. Six bonding and six antibonding curves are pseudo-two-dimensional cuts through the multidimensional surface. Representative long-range anionic curves are calculated in reaction coordinates analogous to Marcus parabolas.

Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermion ground state are further developed through a medium-dependent potential in terms of the Bethe-Peierls contact interaction model. The methods are exact in the unitary limit regime and they lead to self-consistent equations analogous to the Hartree ones. The single particle energy spectrum rearrangement effects on the thermodynamics due to the Hugenholtz–van Hove theorem constraint are addressed. These effects lead to an additional instantaneous correlation potential contribution to the system physical chemical potential and pressure, i.e., equation of state, in order to enforce the classical thermodynamic consistency. The Dyson-Schwinger equations represent implicitly the various Bethe-Goldstone expansion ones. In a thermodynamically self-consistent way, the universal dimensionless factor is analytically calculated to be $\xi =\frac{4}{9}$, which defines the ratio of the unitary fermions energy density to that of the ideal noninteracting ones at $T=0$.

We investigate theoretically the magnetic spin-flip transitions of neutral atoms trapped near a superconducting slab. Our calculations are based on a quantum-theoretical treatment of electromagnetic radiation near dielectric and metallic bodies. Specific results are given for rubidium atoms near a niobium superconductor. At the low frequencies typical of atomic transitions, we find that BCS theory greatly overestimates coherence effects, which are much less pronounced when quasiparticle lifetime effects are included through Eliashberg theory. At $4.2\mathrm{K}$, the typical atomic spin lifetime is found to be larger than $1000\mathrm{s}$, even for atom-superconductor distances of one $1\mathrm{\mu }\mathrm{m}$. This constitutes a large enhancement in comparison with normal metals.

Here we present a problem related to the local Hamiltonian problem (identifying whether the ground-state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for Hamiltonians with a fixed local dimension and $O\mathbf{\left(}\log \left(N\right)\mathbf{\right)}$-body local terms, or local dimension $N$ and two-body terms, there are instances where finding the ground-state energy is quantum-Merlin-Arthur-complete and simulating the dynamics is BQP-complete (BQP denotes “bounded error, quantum polynomial time”). We discuss the implications for the computational complexity of finding ground states of these systems and hence for any classical approximation techniques that one could apply including density-matrix renormalization group, matrix product states, and multiscale entanglement renormalization ansatz. One important example is a one-dimensional lattice of bosons with nearest-neighbor hopping at constant filling fraction—i.e., a generalization of the Bose-Hubbard model.

A fast ion beam stored in an ion storage ring will suffer from collisional interaction with the residual gas even in extreme ultrahigh vacuum. Normally these effects are negligible or easy to correct for. For measurements of extremely long radiative lifetimes of metastable levels we have found that correction for collisional effects is very important and usually limits the accuracy. We now suggest that by monitoring the process of collisional excitation of the metastable level of interest the lifetime value could be determined directly with improved accuracy. The method is applied to available data from our recent measurement of the $5d{}^{2}D_{5∕2}$ level in ${\mathrm{Ba}}^{+}$, yielding a value of $32.0\pm 2.9\mathrm{s}$, thus squeezing the error bar by 35%.

In this paper we present a quantization of cellular automata. Our formalism is based on a lattice of qudits and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains, and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.

A series of x-ray emission spectra of xenon in the region of $L_3{M}_{5,4}\left(L{\alpha }_{1,2}\right)$ and $L_3{N}_{5,4}\left(L{\beta }_{2,15}\right)$ lines were recorded along the polarization direction of the incoming photons with energies ranging from 4779.4 to $4804.4\mathrm{eV}$. A combination of monochromatic photon beam and high resolution x-ray spectrometer resulted in the experimental broadening of $1\mathrm{eV}$ allowing the observation of resonantly enhanced and narrowed emission lines from the decay of $\left[2p_{3∕2}\right]nd,ns$ states. The measured spectra are decomposed into the continuum and resonant contributions to determine their relative emission strengths and the energies of the lowest resonant excitations converging to the $L_3$ edge. The calculated differential cross section for inelastically scattered photons is compared to the measured data. Each of the resonant states is described by a single relativistic configuration in the frame of the Dirac-Fock model, and the continuum contribution to the scattered light is evaluated within the Caldwell-Zare approach, which neglects anisotropic interaction of the ejected electron with the ion.

Previously proposed schemes of coupling short-range density-functional-based with long-range wave-function-based methods are tested for the notoriously difficult case of correctly describing the charge distribution in compounds containing late transition elements. We show that for the dipole moments of the group-11 transition metal hydrides and halides the recently developed Coulomb-attenuated Becke three-parameter Lee-Yang-Parr hybrid functional already leads to a substantial improvement compared to other density functionals. Further improvement is achieved by combining a gradient-corrected short-range functional of the Perdew-Burke-Ernzerhof type with coupled-cluster theory. The results clearly demonstrate that mixing of long-range ab initio Hartree-Fock and post-Hartree-Fock methods helps to remove deficiencies of current density functionals.

$K$-shell photodetachment of ${\mathrm{B}}^{-}$ has been measured using the collinear photon-ion beamline at the Advanced Light Source, Lawrence Berkeley National Laboratory, as well as calculated using two separate $R$-matrix methods. The measurement of the absolute photodetachment cross section, as a function of photon energy, exhibits three near-threshold shape resonances due to the ${}^{3}S$, ${}^{3}P$, and ${}^{3}D$ final partial waves. A fit to the measured data using three resonance profiles shows good overall qualitative agreement with the three partial wave cross sections calculated using either $R$-matrix method. However, certain significant and unresolved quantitative discrepancies exist between the experimentally inferred and the calculated resonance profiles.

We describe a technique based upon the principles of two-pathway coherent control that allows one to amplify the magnitude of a weak atomic or molecular transition. In our initial demonstrations, we amplify a weak Stark-induced transition (the $6s{{}^{2}S}_{1∕2}\to 8s{{}^{2}S}_{1∕2}$ transition in atomic cesium) by coherently beating it with a stronger two-photon transition. We describe the measurements in detail, provide a quantitative discussion of the effects of beam overlap and alignment on the depth of modulation, and discuss the enhancement in the signal-to-noise ratio for this measurement technique over that of direct detection of the weak transition rate.

We investigate the geometric phase of an atom inside an adiabatic radio-frequency (rf) potential created from a static magnetic field ($B$ field) and a time-dependent rf field. The spatial motion of the atomic center of mass is shown to give rise to a geometric phase, or Berry’s phase, in the adiabatically evolving atomic hyperfine spin along the local $B$ field. This phase is found to depend on both the static $B$ field along the semiclassical trajectory of the atomic center of mass and an effective magnetic field consisting of the total $B$ field, including the oscillating rf field. Specific calculations are provided for several recent atom interferometry experiments and proposals utilizing adiabatic rf potentials.

Analog models of gravity have been motivated by the possibility of investigating phenomena not readily accessible in their cosmological counterparts. In this paper, we investigate the analog of cosmological particle creation in a Friedmann-Robertson-Walker universe by numerically simulating a Bose-Einstein condensate with a time-dependent scattering length. In particular, we focus on a two-dimensional homogeneous condensate using the classical field method via the truncated Wigner approximation. We show that for various forms of the scaling function the particle production is consistent with the underlying theory in the long wavelength limit. In this context, we further discuss the implications of modified dispersion relations that arise from the microscopic theory of a weakly interacting Bose gas.

We study the spatiotemporal coherence properties of superfluorescence radiation generated in optical parametric amplification of quantum noise. We show that the angular dispersion properties of the spatiotemporal spectra, measured in different phase-matching conditions, lead to a clear $X$-shaped structure of the mutual correlation function of the radiation. Within a statistical picture, we interpret the generated superfluorescence as a stochastic “gas” of quasistationary modes characterized by a skewed correlation in the spatiotemporal domain, with characteristics similar to linear and nonlinear $X$ waves not describable within a separable approach in space and time.

We examine the possibility of measuring the emission linewidth $2\hslash {\Gamma }_2$ of a single-photon source by Michelson interferometry. Such an emitter is characterized by a limited fluorescence intensity and, when embedded in a solid matrix, a large spectral diffusion. We show that fast spectral diffusion renders standard Fourier spectroscopy irrelevant. We then calculate the correlations of the intensities detected at the two interferometer outputs, point out the existence of two-photon interferences (coalescence) even for a non-single-mode emission, and show that the correlations are not affected by spectral diffusion at correlation times shorter than spectral dynamics. This yields two ways to measure the decoherence rate ${\Gamma }_2$: the recently proposed photon-correlation Fourier spectroscopy, and the study of the coalescence dip. We examine the feasibility and spectral resolution of each method, depending on spectral-diffusion characteristics, and show that both methods could be applied to typical nanometer-sized emitters such as colloidal quantum dots.

Group-velocity mismatch between the pump and Stokes pulses and the inertia of optical nonlinearity are shown to modify scenarios of slow-light evolution of laser pulses accompanying stimulated Raman and Brillouin scattering (SRS and SBS) of light. In the transient regime of SRS and SBS, the inertia of nonlinear polarization of a medium shifts the peak of an amplified Stokes field envelope relative to the input Stokes pulse. This shift is sensitive to the shape of input laser pulses and is controlled by the SRS and/or SBS gain, the damping time of the optical phonon wave, and the delay time between the input pump and Stokes pulses. In the regime where both the inertia of nonlinear polarization of an SRS medium and group-delay effects are significant, stationary modes of the Stokes field may exist in the frame of reference propagating with the group velocity of the pump field. The maximum group delay attainable for such modes of the Stokes field is limited, similar to the steady-state regime, by the ratio of the steady-state SRS gain to the Raman gain bandwidth.

We discuss the implementation of an iterative quantum phase estimation algorithm with a single ancillary qubit. We suggest using this algorithm as a benchmark for multiqubit implementations. Furthermore, we describe in detail the smallest possible realization, using only two qubits, and exemplify with a superconducting circuit. We discuss the robustness of the algorithm in the presence of gate errors, and show that seven bits of precision is obtainable, even with very limited gate accuracies.