We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state generated in spontaneous parametric down-conversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down-converting crystals and waist of the pump beam. The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.

An in-depth theoretical study is carried out to examine the quasideterministic entanglement of two atoms inside a leaky cavity. Two $\Lambda$-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than $50\%.$ However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.

While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic structure of protons that could be extracted from the experimental values of the ground state hyperfine splitting in hydrogen and muonic hydrogen. Using recent theoretical results on the proton polarizability effects and the experimental hydrogen hyperfine splitting we obtain for the Zemach radius of the proton the value 1.037(16) fm. We compare it to the various theoretical estimates the uncertainty of which is shown to be larger than 0.016 fm. This point of view gives quite convincing arguments in support of projects to measure the hyperfine splitting of muonic hydrogen.

We investigate the behavior of ${}^{85}\mathrm{Rb}$ atoms in the field of a sequence of frequency-chirped short laser pulses. The analysis is based on a numerical solution of equations for the probability amplitudes of the hyperfine levels of the ${5S}_{1/2}{-5P}_{3/2}$ transition in the ${}^{85}\mathrm{Rb}$ atom and the dressed-states analysis. We analyze different regimes of interaction, including relatively short laser pulses (when the width of the pulse envelope spectrum is of the order of or exceeds the frequency interval between the hyperfine levels resulting in effective mixing of them) and relatively long ones (when the ground hyperfine levels are resolved but the excited ones are not resolved). In the latter case dependence of the population transfer efficiency on the initial coherence of the ground states is analyzed. The case of long laser pulses when all working hyperfine levels are resolved is also discussed using numerical simulations and a dressed-states analysis. We show that in all regimes considered, the interaction of a frequency-chirped laser pulse with the multilevel ${}^{85}\mathrm{Rb}$ system is similar to the interaction with an effective two-level atom at sufficiently large peak intensities of the pulses. It allows us to perform efficient excitation of the multilevel atom by transferring populations of two hyperfine ground states to the excited ones and back to the ground states using a pair of frequency-chirped laser pulses. We propose to utilize this scheme of population transfer for the coherent manipulation of a beam of ${}^{85}\mathrm{Rb}$ atoms using sequences of counterpropagating frequency-chirped short laser pulses.

The collinear $\mathrm{eZe}$ configuration of helium, with the electrons on opposite sides of the nucleus, is studied in the presence of an external electromagnetic (laser or microwave) field. We show that the classically unstable “asymmetric stretch” orbit, on which doubly excited intrashell states of helium with maximum interelectronic angle are anchored, can be stabilized by means of a resonant driving where the frequency of the electromagnetic field equals the frequency of Kepler-like oscillations along the orbit. A static magnetic field, oriented parallel to the oscillating electric field of the driving, can be used to enforce the stability of the configuration with respect to deviations from collinearity. Quantum Floquet calculations within a collinear model of the driven two-electron atom reveal the existence of nondispersive wave packets localized on the stabilized asymmetric stretch orbit, for double excitations corresponding to principal quantum numbers of the order of $N\gtrsim 10.$

Mode-mixing of coherent excitations of a trapped Bose-Einstein condensate is modeled using the Bogoliubov approximation. Calculations are presented for second-harmonic generation between the two lowest-lying even-parity $m=0\mathrm{}$ modes in an oblate spheroidal trap. Hybridization of the modes of the breather $\mathrm{}(l=0\mathrm{})\mathrm{}$ and surface $\mathrm{}(l=4\mathrm{})\mathrm{}$ states leads to the formation of a Bogoliubov dark state near phase-matching resonance so that a single mode is coherently populated. Efficient harmonic generation requires a strong coupling rate, sharply-defined and well-separated frequency spectrum, and good phase matching. We find that in all three respects the quantal results are significantly different from hydrodynamic predictions. Typically the second-harmonic conversion rate is half that given by an equivalent hydrodynamic estimate.

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice having arbitrary spatial dimensions. Of primary interest is the long-wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the phonon sound speed by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.

We study the quantum properties of the polarization of the light produced in type-II spontaneous parametric down-conversion in the framework of a multimode model valid in any gain regime. We show that the microscopic polarization entanglement of photon pairs survives in the high gain regime (multiphoton regime), in the form of nonclassical correlation of all the Stokes operators describing polarization degrees of freedom.

We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.

Laser radiation propagating through a hollow-core fiber exerts a central force on atoms toward the beam axis. Motion of Cs atoms guided through a glass capillary by the optical gradient force is experimentally investigated by the parametric excitation method, in which periodic modulation of the potential depth resonantly enhances atomic oscillations around the fiber axis. Broadband structure of the observed excitation spectrum reflects an amplitude dependence of the characteristic frequency of oscillation in the nonlinear potential. Numerical analysis predicts that transverse atomic motion becomes chaotic when the optical potential depth is periodically modulated.

We study the relative phase fluctuations of two one-dimensional condensates coupled along their whole extension with a local single-atom interaction. The thermal equilibrium is defined by the competition between independent longitudinal thermally excited phase fluctuations and the coupling between the condensates which locally favors identical phase. We compute the relative phase fluctuations and their correlation length as a function of the temperature and the strength of the coupling.

A fully quantum-mechanical modification to the R-matrix method is introduced to include the recapture of slow photoelectrons following Auger decay of an inner-shell vacancy state and is applied to the photodetachment of ${\mathrm{Li}}^{-}$ above the ${1s}^{-1}$ threshold. The results show excellent agreement with experiment and resolve a large discrepancy in the cross section near the $1s$ threshold between theory and experiment.

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)] is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker, and Bell theorems that shed some light on the relationship between these three theorems.

The properties of group delay for Dirac particles traveling through a potential well are investigated. A necessary condition is put forward for the group delay to be negative. It is shown that this negative group delay is closely related to its anomalous dependence on the width of the potential well. In order to demonstrate the validity of stationary-phase approach, numerical simulations are made for a Gaussian-shaped temporal wave packet. A restriction to the potential-well’s width is obtained that is necessary for the wave packet to remain distortionless in the traveling. Numerical comparison shows that the relativistic group delay is larger than its corresponding nonrelativistic one.

The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an “all versus nothing” contradiction between Ernstein, Podelsky, and Rosen’s local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ’s proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.

Transient time-domain resonances found recently in time-dependent solutions to Schrödinger’s equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time-frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to nontunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum $t_{\max }$ of the time-domain resonance corresponds to under-the-barrier tunneling. We argue that $t_{\max }$ represents the relevant tunneling time scale through the classically forbidden region.

We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling J negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.

With 2.5-MeV proton beams incident on a carbon foil of $1.8\mu {\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ in thickness, the statistical distributions of the number of simultaneously emitted secondary electrons (SEs) have been measured as a function of the emergent angle of ions penetrating the foil in the range from 0.0 mrad to 2.0 mrad for every 0.5-mrad step. The measurement of SEs was carried out at the forward and backward directions of the incident beam separately. For all of the measured angles, the probability of simultaneous n electron emission per projectile, $W_n,$ exhibits roughly an exponential decrease with increasing n. Up to $\sim 1\mathrm{mrad},$ however, the decreasing rate becomes smaller with an increase in the emergent angle. On the other hand, $W_n$ reaches saturation at larger angles. This behavior is common to the forward and backward SE emission. In terms of this angular dependence, the average SE yields per projectile at the forward direction, ${\gamma }_{\mathrm{F}},$ and at the backward direction, ${\gamma }_{\mathrm{B}},$ increase as high as about 50% at 1.0 mrad compared with corresponding ones at 0.0 mrad and saturate at larger angles. As a result of a Monte Carlo simulation taking account of the impact parameter dependent energy loss in a single collision of a proton with a carbon atom, it is found that the calculated energy losses exhibit a quite similar emergent angle dependence to that of the measured SE yields.

It is now well known that electron-capture processes in high impact parameter collisions between slow highly charged ions and clusters (as ${\mathrm{C}}_{60}$ for instance) or surfaces populate high Rydberg levels of the projectile forming a so-called “hollow atom.” We present in this paper a statistical energy distribution (SED) model for the analysis of the decay of such hollow atoms. The overbarrier model is employed to estimate the initial binding energy of captured electrons and total geometrical cross sections. We show that although the model firstly derived by Russek was incomplete, a simple modification to it that accounts for hollow atom specifications leads to a better agreement with experimental cross sections over a wide range of projectile ions of different atomic numbers (Ar, Kr, Xe) and different charge states $(q=16\mathrm{}–30).$ We present also a quantum-mechanics-based formulation of a SED model that allows us to reproduce rather nicely experimental cross sections too. The presented model applied better for high projectile charge states allowing the capture of a great number of electrons that populate a quasicontinuum of Rydberg states for which we do not have to take into account individual Auger transitions.

We study nonlinear optical effects in the laser excitation of Rydberg states. ${5S}_{1/2}$ and ${5P}_{3/2}$ levels of ${}^{85}\mathrm{Rb}$ are coupled by a strong laser field and probed by a weak laser tuned to the ${5P}_{3/2}-44D$ Rydberg resonance. We observe high contrast Autler-Townes spectra which are dependent on the pump polarization, intensity, and detuning. The observed behavior agrees with calculations, which include the effect of optical pumping.