The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell’s original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.

We investigate the possibility of trapping ultracold ${}^{87}\mathrm{Rb}$ atoms near the outside of a metallic carbon nanotube, which we imagine using as a miniaturized current-carrying wire. We calculate atomic spin-flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism, and we compute the minimum distance to the carbon nanotube at which the atoms can be trapped to be larger than $100\mathrm{nm}$.

A single ${}^{88}\mathrm{Sr}^{+}$ ion has been cooled to the zero point of its axial motion in a radio frequency endcap trap. A ground-state occupation probability of 98.6(8)% was achieved using resolved sideband laser cooling on the $674\mathrm{nm}$ ${}^{2}S_{1∕2}\text{−}{}^{2}D_{5∕2}$ quadrupole transition. The ion’s heating rate was measured to be 0.054(4) quanta/ms, implying a spectral density of electric field noise comparable to the other reported values, summarized in the paper by Deslauriers et al. [Phys. Rev. A 70, 043048 (2004)]. Low heating rates were only observed using a trap that had minimal exposure to atomic flux.

We present a method for spectral (bound and continuum) and partial-wave analysis of a three-dimensional time-dependent wave function, defined on a grid, without projecting onto the field-free eigenstates of the system. The method consists of propagating the time-dependent Schrödinger equation to obtain its autocorrelation function $C\left(t\right)=⟨\psi (\mathbf{r},T)\mid \psi (\mathbf{r},T+t)⟩$ after the end of the interaction, at time $T$, of the system with an external time-dependent field. The Fourier spectrum of this correlation function is directly related to the expansion coefficients of the wave function on the field-free bound and continuum energy eigenstates of the system. By expanding on a spherical harmonics basis we show how to calculate the contribution of the various partial waves to the total photoelectron energy spectrum.

We present a very efficient technique for solving the three-dimensional time-dependent Schrödinger equation. Our method is applicable to a wide range of problems where a fullly three-dimensional solution is required, i.e., to cases where no symmetries exist that reduce the dimensionality of the problem. Examples include arbitrarily oriented molecules in external fields and atoms interacting with elliptically polarized light. We demonstrate that, even in such cases, the three-dimensional problem can be decomposed exactly into two two-dimensional problems at the cost of introducing a trivial rotation transformation. We supplement the theoretical framework with numerical results on strong-field ionization of arbitrarily oriented $\mathrm{H}_2{}^{+}$ molecules.

We present here a finite slab of triangular checkerboard of negative refractive index material that exhibits a form of extraordinary transmission. We show that such a checkerboard can be used to confine light and can act as an open resonator. Effectively even a single point of intersection between three triangular wedges of negative refractive index may act as a resonator that confines light in the limit when $n$ tends toward $-1$. We find that the quality of the confinement improves by adding more triangular wedges around the initial point in a checkerboard fashion. The confinement effect is also demonstrated by using a photonic crystal that shows the negative refraction effect.

A method of preparing a single photon in temporally delocalized entangled modes is proposed and analyzed. We show that two single-photon pulses propagating in a driven nonabsorbing medium with different group velocities are temporally split under parametric interaction into well-separated pulses. As a consequence, the single-photon “time-bin-entangled” states are generated with a programmable entanglement, which is easily controlled by driving field intensity. The experimental study of nonclassical features and nonlocality in generated states by means of balanced homodyne tomography is discussed.

We analyze the optical gain property of a probe pulse in a four-level system of ultracold ${}^{87}\mathrm{Rb}$ atoms prepared via a stimulated Raman adiabatic passage type process. During the process of preparation, most population is transferred from the ground state to the highest excited state by two driving pulses in the counterintuitive order. Thus population inversion can be achieved between the highest state and a lower-lying state in a suitable period of time, which then allows very large gain for the probe pulse applied after the driving pulses. In particular, we investigate in detail the influence of several interaction parameters of interest on the probe gain via numerical simulation and qualitative analysis.

We theoretically study a parallel optical configuration which includes $N$ periodically coupled whispering-gallery-mode resonators. The model shows an obvious effect which has a direct analogy with the phenomenon of multiple electromagnetically induced transparency in quantum systems. The numerical simulations illuminate that the frequency transparency windows are sharp and highly transparent. We also briefly discuss the experimental feasibility of the current scheme in two practical systems, microrings and microdisks.

We investigate how Bose-Einstein condensates, whose initial state is either irrotational or contains a single vortex, scatter off a one-dimensional Gaussian tunnel barrier. We find that for low atom densities the vortex structure within the condensate is maintained during scattering, whereas at medium and high densities, multiple additional vortices can be created by the scattering process, resulting in complex dynamics and disruption of the atom cloud. This disruption originates from two different mechanisms associated, respectively, with the initial rotation of the atom cloud and the interference between the incident and reflected matter waves.

We present a theoretical treatment of electromagnetically induced transparency and light storage using standing-wave coupling fields in a medium comprised of stationary atoms, such as an ultracold atomic gas or a solid state medium. We show that it is possible to create stationary pulses of light which have a qualitatively different behavior than in the case of a thermal gas medium, offering greater potential for quantum-information-processing applications.

It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using only linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of freedom, has been shown to assist the complete Bell analysis of the four Bell states (given a fixed state of the other degrees of freedom). Yet introducing other degrees of freedom also enlarges the total number of Bell-like states. We investigate the limits for unambiguously distinguishing these Bell-like states. In particular, when the additional degree of freedom is qubitlike, we find that the optimal one-shot discrimination schemes are to group the 16 states into seven distinguishable classes, and that an unambiguous discrimination is possible with two identical copies.

A discrete-time quantum walk on a graph $\Gamma$ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup $H$ of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup $H$ used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup $H$ from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup.

We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. [Phys. Rev. A 61, 013410 (2000)], by introducing the possibility of nonlinear self-phase modulation on the wave function during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau-Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of nondispersive pulses in the field distribution (solitonlike structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, nonelastic collisions, and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.

A combined experimental and theoretical investigation of the role of electronic and nuclear spins in molecular photoionization is reported. Photoionization spectra of autoionizing $p$ Rydberg states belonging to series converging on the $X$ ${}^2\Sigma _g^{+}(v^{+}=0,N^{+}=3)$ level of ortho-${\mathrm{H}}_2^{+}$ have been measured in the range of principal quantum number $n=50–200$ from the long-lived $H$ ${}^1\Sigma _g^{+}(v=0,J=3)$ level. The use of a pulsed near-Fourier-transform-limited laser with a bandwidth of less than $10\mathrm{MHz}$ resulted in a Doppler-limited linewidth of $25\mathrm{MHz}$ which sufficed to partially resolve the hyperfine structure of the Rydberg states. Below $n\approx 70$, the exchange interaction between the ion core and Rydberg electrons is larger than the hyperfine interactions in the ion core and the observed levels can be understood in terms of Hund’s angular momentum coupling case (d). With increasing value of $n$, the hyperfine interactions in the core lead to a mixing of singlet and triplet characters of the Rydberg states and eventually to a complete decoupling of the Rydberg electron spin from the core spins that results in distinct series converging on the hyperfine components of the ion. Several intermediate coupling cases have been identified and two of them completely characterized. Most interestingly, the total spin angular momentum has been found to be a good quantum number up to $n\approx 150$ at least, i.e., far beyond the region where the ionic hyperfine structure starts dominating the coupling hierarchy. Multichannel quantum defect theory including nuclear and electron spins has been extended to treat autoionization and predict spectral intensities. The comparison with the experimental spectra has revealed a satisfactory agreement between calculated and measured line positions, linewidths, and intensities and has enabled us to extract, by extrapolation, a more accurate term value for the $H$ ${}^1\Sigma _g^{+}(v=0,J=3)$ level. The calculations have been used to characterize the role of hyperfine, spin-rotational, and pf interactions in rotational autoionization and have revealed a very strong dependence of the autoionization lifetimes of high Rydberg states on the value of the total angular momentum quantum number $F$.

Measured fine-structure patterns of high-$L$ Rydberg states have often been used to extract measurements of both the dipole and the quadrupole polarizability of their positive ion cores. Dipole polarizabilities deduced in this way are apparently quite accurate, judging by comparison with calculated values, but the accuracy of quadrupole polarizabilities is questionable. The polarizabilities of Na-like silicon are a good example. Recent fine-structure measurements seem to imply a quadrupole polarizability, in clear disagreement with calculations. This apparent discrepancy is due to misinterpretation of the experimental data, neglecting the effects of higher-order terms in the polarization potential that significantly alter the slope of the traditional polarization plots. When these terms are calculated, and their magnitude estimated, the discrepancy is eliminated. The implications of the higher-order terms for analysis of high-$L$ fine-structure patterns are discussed.

Absolute cross sections for photoionization and electron-impact ionization of ${\mathrm{Ar}}^{5+}$ have been measured using two different interacting-beams setups. The spectra consist of measurements of the yield of products due to single ionization as a function of electron or photon energy. In addition, absolute photoionization and electron-impact ionization cross sections were measured to normalize the measured ${\mathrm{Ar}}^{6+}$ product-ion yield spectra. In the energy range from $90\text{to}111\mathrm{eV}$, both electron-impact ionization and photoionization of ${\mathrm{Ar}}^{5+}$ are dominated by indirect $3s$ subshell excitation-autoionization. In the energy range from $270\text{to}285\mathrm{eV}$, resonances due to $2p\text{−}3d$ excitation-autoionization are prominent in the photoionization spectrum. In the range from $225\text{to}335\mathrm{eV}$, an enhancement due to $2p\text{−}nl$ $(n>2)$ excitations are evident in the electron-impact ionization cross section. The electron and photon impact data show some features due to excitation of the same intermediate autoionizing states.

Three-body recombination rates for cold ${}^4\mathrm{He}$ are calculated with a method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the $S$-matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for ${}^4\mathrm{He}$ are governed by “Efimov physics,” they depend on universal functions of a scaling variable. The computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions.

Quantum scattering calculations are carried out down to very low energy for collisions of electrons with ${\mathrm{CF}}_4$ molecules in the gas phase. The interaction forces are obtained from ab initio data for the static interaction and through model potentials for the exchange and correlation-polarization effects. A numerical analysis is performed to evaluate the partial wave convergence behavior over the whole energy range, to assess the reliability of modified effective range theory close to zero energy, and to extract the value and the sign of the scattering length. A comparison with experiments and earlier calculations in the low-energy domain is also presented.