A systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a two-level system and the Dirac electron that comes to light when the two-level system is described within the formalism of second quantization in terms of fermionic creation and annihilation operators. The analogy enables one to introduce all the powerful tools of relativistic QED (albeit in a greatly simplified form). The Feynman diagrams and the propagators turn out to be very useful. In particular, the QED concept of the vacuum polarization finds its close counterpart in the photon scattering off a two level system leading via the linear response theory to the general formulas for the atomic polarizability and the dynamic single spin susceptibility. To illustrate the usefulness of these methods, we calculate the polarizability and susceptibility up to the fourth order of perturbation theory. These ab initio calculations resolve some ambiguities concerning the sign prescription and the optical damping that arise in the phenomenological treatment. We also show that the methods used to study two-level systems (qubits) can be extended to many-level systems (qudits). As an example, we describe the interaction with the quantized electromagnetic field of an atom with four relevant states: one $S$ state and three degenerate $P$ states.

We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among $N$ linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.

We propose several robust schemes to prepare entangled states among spatially separated $\Lambda$-type atoms via stimulated Raman adiabatic passage and fractional stimulated Raman adiabatic passage techniques. The atomic spontaneous radiation, the cavity decay, and the fiber loss are efficiently suppressed by engineering adiabatic passage and controlling appropriately atom-field couplings. The schemes can be extended to generate the $n$-cavity mode $W$ state.

In this paper, photonic entanglement and interference are described and analyzed with the language of quantum information processing. Correspondingly, a photon state involving several degrees of freedom is represented in an expression based on the permutation symmetry of bosons. In this expression, each degree of freedom of a single photon is regarded as a qubit and operations on photons as qubit gates. The two-photon Hong-Ou-Mandel interference is well interpreted with it. Moreover, the analysis reveals the entanglement between different degrees of freedom in a four-photon state from parametric down conversion, even if there is no entanglement between them in the two-photon state. The entanglement will decrease the state purity and photon interference visibility in the experiments on a four-photon polarization state.

Motivated by the prospect of an optical frequency standard based on ${}^{43}\mathrm{Ca}^{+}$, we calculate the blackbody-radiation (BBR) shift of the $4s_{1∕2}-3d_{5∕2}$ clock transition, which is a major component of the uncertainty budget. The calculations are based on the relativistic all-order single-double method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. Additional calculations are conducted for the dominant contributions in order to evaluate some omitted high-order corrections and estimate the uncertainties of the final results. The BBR shift obtained for this transition is $0.38\left(1\right)\mathrm{Hz}$. The tensor polarizability of the $3d_{5∕2}$ level is also calculated and its uncertainty is evaluated as well. Our results are compared with other calculations.

The quantity “component instantaneous ionization rate” introduced by M. Vafaee et al. [Phys. Rev. A 74, 043416 (2006)] for the analysis of ionization of $\mathrm{H}_2{}^{+}$ in intense laser pulses is discussed. It is shown that the meaning of this quantity as defined in that work is dubious, since there exists a lower time limit below which a quantum mechanical transition does not scale linearly in time and thus does not fulfill the requirements of a rate. Therefore, in a laser field it is impossible to define a rate with subcycle resolution. The analysis of a characteristic photoelectron spectrum reveals also that the “instantaneous rate” that is shown to be the electron flux through some boundary cannot be related to ionization without a deconvolution procedure. Finally, the “negative ionization” is identified as caused by the well-known quiver motion in strong laser fields.

In response to the preceding Comment, results of our research show that rate is not necessarily linearly time-dependent and it is possible to define and calculate instantaneous ionization rate. We show that a negative ionization rate and the quiver motion in strong laser field are not necessarily correlated and may occur independently. Furthermore, a negative ionization rate is not identical to recombination. Details of the instantaneous ionization rate and photoelectron kinetic energy release are calculated and analyzed for the evolution of the electron wave packet of $\mathrm{H}_2{}^{+}$ in a 25-cycle ultrashort intense linearly polarized laser pulse of $\mathrm{I}=1.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ intensity and $\lambda =1064\mathrm{nm}$ wavelength with a ${\sin }^2$-shaped envelope.

The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When these observables do not commute, we may obtain information about joint properties of a quantum system that would be forbidden in the usual strong measurement scenario. As an application, we provide a physically compelling characterization of the notion of counterfactual quantum computation.

The multiconfiguration Dirac-Fock (MCDF) method was used to calculate the excitation energies of the levels of ${}^{3}P$ and ${}^{1}P$ in the lowest excited configurations for the two homolog elements of No I and Yb I. Also the transition probability of the $7s7p{{}^{1}P}_1\to 7s^2{{}^{1}S}_0$ transition and the ground-state ionization energy of No I were calculated. The results for Yb I agree very well with the available experiments, with deviations of below 0.6% for the triplets and below 4% for the singlet. The result for the No I excitation energies clears the situation of conflicting results between Borschevsky et al., $30056{\text{cm}}^{-1}$ (3.726 eV) [Phys. Rev. A 75, 042514 (2007)], and Fritzsche, 3.36 eV [Eur. Phys. J. D 33, 15 (2005)] for the $7s7p{{}^{1}P}_1$ level, which is planned to be measured in the near future with a newly developed experimental technique by Backe et al. [Eur. Phys. J. D 45, 99 (2007)]. The ionization energy result obtained in this work, $53701{\text{cm}}^{-1}$, is in excellent agreement with the scaled result of $53600\left(600\right){\text{cm}}^{-1}$.

Cross sections have been determined for electron transfer, direct excitation, and ionization in collisions between $\alpha$ particles and $\text{H}\left(1s\right)$ atoms at $\alpha$ energies 3 keV–38.4 MeV, extending earlier work [Phys. Rev. A 25, 697 (1982)] restricted to total transfer at 20–200 keV. Transfer as well as excitation cross sections into individual states up to $3d$ have been determined with several coupled-Sturmian pseudostate bases, and tests of basis sensitivity have been carried out. These and ionization cross sections have been compared with existing experimental and other coupled-state results. Structure is observed in the lower-energy excitation cross sections, which is believed not to be an artifact of the bases used. Ionization and excitation cross sections have also been compared with corresponding Born results at higher energies.

We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multicomponent Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a function of superfluid velocities and interaction parameters, in several cases, for two-component and spinor condensates. In the two-species case we find that the presence of the other condensate component can stabilize the superfluid flow of an otherwise unstable condensate and that the free space dynamical miscibility condition of the two species can be reversed by tuning the superfluid flow velocities. In spin-1 condensates, we find the steady-state Bloch wave solutions and characterize their stability criteria. We find that generally more regions of dynamical instability arise for the polar than for the ferromagnetic solutions. In the presence of magnetic Zeeman shifts, we find a richer variety of condensate solutions and find that the linear Zeeman shift can stabilize the superfluid flow in several cases of interest.

Experimental and theoretical studies are presented related to the ground-state magneto-optical resonance observed in cesium vapor confined in an extremely thin cell (ETC), with thickness equal to the wavelength of the irradiating light. It is shown that utilization of the ETC allows one to examine the formation of a magneto-optical resonance on the individual hyperfine transitions, thus distinguishing processes resulting in dark (reduced absorption) or bright (enhanced absorption) resonance formation. We report experimental evidence of bright magneto-optical resonance sign reversal in Cs atoms confined in an ETC. A theoretical model is proposed based on the optical Bloch equations that involves the elastic interaction processes of atoms in the ETC with its walls, resulting in depolarization of the Cs excited state, which is polarized by the exciting radiation. This depolarization leads to the sign reversal of the bright resonance. Using the proposed model, the magneto-optical resonance amplitude and width as a function of laser power are calculated and compared with the experimental ones. The numerical results are in good agreement with those of experiment.

Radio-frequency $E1$ transitions between nearly degenerate, opposite-parity levels of atomic dysprosium (Dy) were monitored over an 8-month period to search for a variation in the fine-structure constant $\alpha$. During this time period, data were taken at different points in the gravitational potential of the Sun. The data are fitted to the variation in the gravitational potential yielding a value of $(-8.7\pm 6.6)\times {10}^{-6}$ for $k_{\alpha }$, the variation of $\alpha$ in a changing gravitational potential. This value gives the first laboratory limit independent of assumptions regarding other fundamental constants. In addition, our value of $k_{\alpha }$ combined with other experimental constraints is used to extract the first limits on $k_e$ and $k_q$. These coefficients characterize the variation of $m_e∕m_p$ and $m_q∕m_p$ in a changing gravitational potential, where $m_e$, $m_p$, and $m_q$ are electron, proton, and quark masses. The results are $k_e=(4.9\pm 3.9)\times {10}^{-5}$ and $k_q=(6.6\pm 5.2)\times {10}^{-5}$. All these results indicate the absence of significant variation at the present level of sensitivity.

The decoherence dynamics of two charge qubits in a double quantum dot is investigated theoretically. We consider the quantum dynamics of two interacting electrons in a vertically coupled quantum dot driven by an external electric field. We derive the equations of motion for the density matrix, in which the presence of an electron confined in the double dot represents one qubit. A Markovian approach to the dynamical evolution of the reduced density matrix is adopted. We evaluate the concurrence of two qubits in order to study the effect of acoustic phonons on the entanglement. We also show that the disentanglement effect depends on the double dot parameters and increases with the temperature.

We specify the formally exact multiconfigurational time-dependent Hartree method originally developed for systems of distinguishable degrees of freedom to mixtures consisting of two types of identical particles. All three cases, Fermi-Fermi, Bose-Bose, and Bose-Fermi mixtures, are treated on an equal footing making explicit use of the reduced one- and two-body density matrices of the mixture. The theory naturally contains as specific cases the versions of the multiconfigurational time-dependent Hartree method for single-species fermions and bosons. Explicit and compact equations of motion are derived and their properties and usage are briefly discussed.

In an evanescent wave magnetometer the Zeeman polarization is probed at micrometer to submicrometer distances from the cell surface. The electron paramagnetic resonance lines of an evanescent wave magnetometer in the presence of a magnetic field gradient exhibit edge enhancement seen previously in nuclear magnetic resonance lines. We present a theoretical model that describes quantitatively the shape of the magnetic resonance lines of an evanescent wave magnetometer under a wide range of experimental conditions. It accounts for diffusion broadening in the presence of a magnetic field gradient as well as interactions of spin polarized Rb atoms with the coated Pyrex glass surfaces. Depending on the field gradient, cell thickness, and buffer gas pressure, the resonance line may have the form of a single asymmetric peak or two peaks localized near the front and back surfaces in frequency space. The double-peaked response depends on average characteristics of the surface interactions. Its shape is sensitive to the dwell time, relaxation probability, and average phase shift of adsorbed spin polarized Rb atoms.

The successive dynamical evolution of a Bose-Einstein condensate confined in a cylindrical well is numerically studied in the framework of the time-dependent Gross-Pitaevskii equation. Interference in the nonlinear matter wave leads to concentric density rings. The phase distribution exhibits a discontinuous sequence of plateaulike belts. Abrupt jumps in the phase between adjacent belts imply large radial superfluid velocity at the borderline. This, however, does not mean large particle current because the corresponding superfluid density is nearly zero. The density zeros along with the large gradient are identified as ring dark solitons, which have a brief lifetime before evolving into other soliton states.

We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only.

It is known that entangling capacities of bipartite unitary operations may be used to place upper bounds on communication capacities. Here we present alternative definitions of entangling capacities for unitary operations and use them to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Thus entangling capacities may be used to place both upper and lower bounds on the communication capacities for arbitrary bipartite unitaries, allowing them to be more easily estimated. We elucidate the connection between these results and the standard formula for the entanglement assisted capacity of channels. In addition, we present more general methods for producing ensembles for communication from initial states for entanglement creation, and thereby derive sufficient conditions such that the usual forms of entangling capacity provide lower bounds on communication capacities.

We investigate the two-electron capture with emission of a single photon to the ground state in the Coulomb field of a heavy nucleus in its collision with a light atom. Describing electron-electron interactions in the bound state perturbatively, we obtained an analytical formula for the high-energy limit of the cross section. In combination with previous results obtained in the same approach we calculated the cross section in a broad interval of energies of the collision. We show that the amplitude of the process at high energy depends on the behavior of the bound state wave function near the triple coalescence point. We analyze the properties of the approximate wave functions which are necessary for the description of the high-energy limit.