We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

The relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate the multipole ($E1,M1,E2,M2$, and $E3$) matrix elements to determine the $3s3p{}^3{P}_2$ lifetime and multipole polarizabilities in Mg-like ions. The electric multipole matrix elements are determined in length and velocity forms. The calculations start from a $1s^{2}2s^{2}2p^6$ Dirac-Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients, and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order multipole matrix elements to ensure gauge independence of transition amplitudes. The details of our calculations of the multipole polarizabilities are illustrated for Mg-like $\mathrm{Si}{}^{2+}$, $\mathrm{Fe}{}^{14+}$, $\mathrm{Kr}{}^{24+}$, $\mathrm{Mo}{}^{30+}$, $\mathrm{Xe}{}^{42+}$, and $\mathrm{W}{}^{62+}$ ions. Our RMBPT results are compared with available theoretical results and experimental measurements. Trends of the line strengths, transition rates, and contributions in the ground-state multipole polarizabilities as functions of $Z$ are illustrated graphically in Mg-like ions with $Z=14–100$.

On the basis of the quasipotential method in quantum electrodynamics we calculate corrections of orders ${\alpha }^5$ and ${\alpha }^6$ to the hyperfine structure of $S\text{-wave}$ energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure, and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{\mathrm{HFS}}\left(1S\right)=50.2814$ meV $(1S$ state) and $\Delta E^{\mathrm{HFS}}\left(2S\right)=6.2804$ meV $(2S$ state) represent reliable estimates for a comparison with forthcoming experimental data of the CREMA Collaboration. The hyperfine structure interval ${\Delta }_{12}=8\Delta E^{\mathrm{HFS}}\left(2S\right)-\Delta E^{\mathrm{HFS}}\left(1S\right)=-0.0379$ meV can be used for a precision check of the quantum electrodynamics prediction for muonic deuterium.

We present two analytical methods, Taylor expansion and Gegenbauer expansion, to efficiently and accurately calculate the two-electron screened Coulomb potential matrix elements with Slater-type configuration-interaction basis functions. The former permits great advantages in fast computation of the potential matrices at small screening parameters and the latter allows accurate calculation of the matrices at all screening parameters. The bound and resonant states of a He atom embedded in the screening environment are calculated by employing the variational and complex-scaling methods, respectively, and the results are compared with other theoretical predictions. The expectation values of some physical quantities for He ground state are compared with the recent calculation of Ancarani and Rodriguez [Phys. Rev. A 89, 012507 (2014)] and extended to stronger screening environment. The energies and widths for the doubly excited resonant states are in good agreement with previous calculations, while the interelectronic angle $arccos\langle cos\left({\theta }_{12}\right)\rangle$ show significant discrepancies with the Feshbach projection calculation of Ordóñez-Lasso et al. [Phys. Rev. A 88, 012702 (2013)]. The expectation values of $\langle {\mathbf{p}}_{\mathbf{1}}·{\mathbf{p}}_{\mathbf{2}}\rangle$ are also calculated for the resonant states investigated here. We conclude that the present methods in the framework of complex scaling enable us to get reliable energy, width, and other physical quantities of the resonant states in a variety of screening conditions.

We present relativistic convergent close-coupling and Breit-Pauli $R$-matrix calculations for the polarization of the light emitted after electron-impact excitation of the $\left(5s\right){}^2{S}_{1/2}\to \left(5p\right){}^2{P}_{3/2}$ transition in ${\mathrm{Cd}}^{+}$. While we find consistency between the theoretical predictions, a discrepancy persists with the measurements of Goto et al. [Phys. Rev. A 27, 1844 (1983)]. Cascade contributions and hyperfine depolarization effects were calculated and found to have negligible effect on the polarization fraction. We also present angle-integrated cross sections for the $\left(5p\right){}^2{P}_{3/2}$ state to compare with the measurements of Gomonai [Optc. Spect. 94, 488 (2003)]. Agreement between theory and experiment is far from perfect, especially at low energies, where they disagree both in the absolute values and the energy dependence of the cross sections.

While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path-integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wavelength is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal-to-noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a noninteracting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase-transition-like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.

Motivated by recent experimental observations [Parker, Hua, and Chin, Nat. Phys. 9, 769 (2013)], we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such a system there is no thermodynamic ground state, but there may be a long-lived steady state, described as an eigenstate of a “Floquet Hamiltonian.” We calculate how scattering processes lead to a decay of the Floquet state. We map out the phase diagram of the system and find regions where the BEC is stable and regions where the BEC is unstable against atomic collisions. We show that Parker et al. performed their experiment in the stable region, which accounts for the long lifetime of the condensate $(\sim 1\mathrm{s})$. We also estimate the scattering rate of the bosons in the region where the BEC is unstable.

We theoretically investigate collective modes of a one-dimensional (1D) interacting Bose gas in a harmonic tras at finite temperatures, by using a variational approach and the local density approximation. We find that the temperature dependence of collective mode frequencies is notably different in the weakly and strongly interacting regimes. Therefore, the experimental measurement of collective modes could provide a sensitive probe for different quantum phases of a 1D trapped Bose gas, realized by tuning the interatomic interaction strength and temperature. Our prediction on the temperature dependence of the breathing mode frequency is in good qualitative agreement with an earlier experimental measurement for a weakly interacting 1D Bose gas of rubidium-87 atoms in harmonic traps [Moritz et al., Phys. Rev. Lett. 91, 250402 (2003)].

The ac Stark shift (or light shift) of the $6{}^2{S}_{1/2}(F=3\leftrightarrow 4)$ transition in ${}^{133}$Cs, as observed through coherent population trapping under pulsed excitation, is measured using a ${}^{133}$Cs gas cell and the $D$${}_1$-line vertical-cavity surface-emitting laser. This light shift can be calculated using density-matrix analysis. We derive an expression for this shift as a function of light intensity, showing that it varies linearly with respect to light intensity only with intensities higher than 1.0 mW/cm${}^2$. For pulsed excitation of high laser intensity, the variation in light shift is 20 times lower than that when using a continuous wave. The differences between the results of theory and experiment are discussed, taking into account the difference in conditions assumed; the results from theoretical analysis, taking the attenuation of the first-order sideband into account, approximately agree with the experimental results. The light shift is reduced by shortening the observation times.

We revisit the scheme of single-photon weak-coupling optomechanics using postselection, proposed by Pepper, Ghobadi, Jeffrey, Simon, and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the postselected state of the photon is orthogonal to the initial state, which cannot be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time.

We apply the classical data-processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a quantum data-processing inequality to show that coherent manipulation of quantum data also cannot improve the precision in estimation. In addition, we comment on the assumptions necessary to arrive at these inequalities and how they might be avoided, providing insights into enhancement procedures which are not provably wrong.

The effect of an electric quadrupole moment $Q$ is studied for positron-atom bound systems. It is demonstrated that for $Q>50$ a.u. the electric quadrupole potential is sufficiently strong to bind a positron (or an electron) even in the absence of the dipole polarization potential. Such large values of $Q$ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the $2s2p^3{P}_2^o$ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a $\mathrm{Be}{}^{+}$ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.

We show that violation of genuine multipartite Bell inequalities can be obtained with sampled, probabilistic phase-space methods. These genuine Bell violations cannot be replicated if any part of the system is described by a local hidden variable theory. The Bell violations are simulated probabilistically using quantum phase-space representations. We treat mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60 qubits, using both a multipartite $\text{SU(2)-}Q$ representation and the positive-$P$ representation. Surprisingly, we find that sampling with phase-space distributions can be exponentially faster than experiment. This is due to the classical parallelism inherent in the simulation of quantum measurements using phase-space methods. Our probabilistic sampling method predicts a contradiction with local realism of “Schrödinger-cat” states that can be realized as a GHZ spin state, either in ion traps or with photonic qubits. We also present a quantum simulation of the observed superdecoherence of the ion-trap “cat” state, using a phenomenological noise model.

We develop a complete resource theory of charge-parity-time (CPT) inversion symmetry for both massive and massless relativistic particles of arbitrary spin. We show that a unitary representation of CPT can be consistently constructed for all spins and develop the resource theory associated with CPT superselection, thereby identifying and quantifying the resources required to lift the superselection rule.

A version of the method of accurate calculations for few-valence-electron atoms which combines linearized single-double–coupled-cluster method with the configuration-interaction technique is presented. The use of the method is illustrated by calculations of the energy levels for Ba, ${\mathrm{Ba}}^{+}$, Lu, ${\mathrm{Lu}}^{+}$, and ${\mathrm{Lu}}^{2+}$. Good agreement with experiment is demonstrated and comparison with previous version of the method [M. S. Safronova et al., Phys. Rev. A 80, 012516 (2009)] is made.

Natural orbital theory is a computationally useful approach to the few- and many-body quantum problems. While natural orbitals have been known and applied for many years in electronic structure applications, their potential for time-dependent problems started being investigated only recently. Correlated two-particle systems are of particular importance because the structure of the two-body reduced density matrix expanded in natural orbitals is known exactly in this case. However, in the time-dependent case the natural orbitals carry time-dependent phases that allow for certain time-dependent gauge transformations of the first kind. Different phase conventions will, in general, lead to different equations of motion for the natural orbitals. A particular phase choice allows us to derive the exact equations of motion for the natural orbitals of any (laser-) driven two-electron system explicitly, i.e., without any dependence on quantities that, in practice, require further approximations. For illustration, we solve the equations of motion for a model helium system. Besides calculating the spin-singlet and spin-triplet ground states, we show that the linear response spectra and the results for resonant Rabi flopping are in excellent agreement with the benchmark results obtained from the exact solution of the time-dependent Schrödinger equation.

A series of computations based on multichannel quantum defect theory have been performed in order to produce the cross sections of rotational transitions (excitations $N_i^{+}-2\to$ $N_i^{+}$, deexcitations $N_i^{+}$ $\to$ $N_i^{+}-2$, with $N_i^{+}=2$ to 10) and of their competitive process, the dissociative recombination, induced by collisions of ${\mathrm{HD}}^{+}$ ions with electrons in the energy range ${10}^{-5}$ to 0.3 eV. Maxwell anisotropic rate coefficients, obtained from these cross sections in the conditions of the Heidelberg Test Storage Ring (TSR) experiments $(k_B{T}_t=2.8$ meV and $k_B{T}_l=45$ $\mu$eV), have been reported for those processes in the same electronic energy range. Maxwell isotropic rate coefficients have been presented as well for electronic temperatures up to a few hundred Kelvins. Very good overall agreement is found between our results for rotational transitions and the former theoretical computations as well as with experiment. Furthermore, due to the full rotational computations performed, the accuracy of the resulting dissociative recombination cross sections is improved considerably.