The generation of specific unitary transformations is central to a variety of quantum control problems. Given a target unitary transformation, the optimal control landscape is defined as the Hilbert-Schmidt distance between the target and controlled unitary transformation as a function of the control variables. The critical topology of the landscape is analyzed for controllable quantum systems evolving under unitary dynamics over a finite dimensional Hilbert space. It is found that the critical regions of the landscape corresponding to global optima are isolated points, and the local optima are Grassmannian submanifolds. The volumes of the critical submanifolds corresponding to suboptimal critical values asymptotically vanish in the limit of large Hilbert space dimension. Furthermore, these critical submanifolds have saddle-point topology, which cannot act as traps when searching for optimal controls. These favorable properties of the local optima suggest that the landscape topology is generally amenable to optimization. The analysis is independent of the particular structure of the system Hamiltonian, except for the assumption of full controllability, and the results are universal to the control of unitary transformations of any quantum system.

Calculations of positron and electron ejection cross sections are made for collisions of Ps $\left(1s\right)$ with the noble gases He, Ne, Ar, Kr, and Xe, allowing for target excitation (i.e., discrete excitation and ionization). Cross sections doubly differential and singly differential with respect to ejected energy and angle are reported, as well as total ionization cross sections. Our results show clearly that excitation of the target becomes very important at impact energies greater than about 2 times the ionization threshold of the atom. Comparison is made with absolute experimental measurements on He and Xe targets and, with one exception, good agreement is found at both total and single differential levels. Unfortunately, most of the measurements are at impact energies where target excitation is small or negligible. There is a need for experiments at higher impact energies to assess the predictions for target excitation.

We propose a method to measure the duration of ultrashort electron pulses. The electron pulse to be measured impinges on a solid target, causing the emission of Auger electrons through impact ionization. The energy spectrum of the Auger electrons is altered in the presence of an intense femtosecond laser field. Due to the extremely short lifetime of the Auger effect, this effect can be used to generate cross correlation between a laser and an electron pulse. The method is applicable to electron pulses ranging from hundreds of attoseconds to hundreds of femtoseconds in duration, and for a few hundreds of electron volts to relativistic energies.

We investigate beam propagation in a heavy-metal-oxide glass of the group ${\text{Nb}}_2{\text{O}}_5–\text{PbO}–{\text{GeO}}_2$ using picosecond pulses in the near infrared. We observe a wavelength-dependent self-focusing, with beam collapse and modulation instability in the Kerr regime at $1.064\mu \text{m}$ and stable spatial solitons at 820 nm where multiphoton absorption is present. We report near-infrared beam self-confinement and solitons, filamentation, interactions, and conical emission in the ps regime and discuss them with the aid of a numerical model.

The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work—on thermal-state and biphoton-state imagers—and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross correlations between the two detected fields, plus a background. Because any pair of cross correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical autocorrelation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.

We present an efficient quantum computation protocol on a special class of systems in which the positions of all quantum bits are fixed. This protocol is a generalized scheme based on L.-M. Duan and R. Raussendorf [Phys. Rev. Lett. 95, 080503 (2005)].

We study the dynamics of a single control atom and an atomic sample interacting with a nonresonant cavity mode. The control atom is driven by an auxiliary classical field. Under certain conditions, the coherent energy exchange between the control atom and the atomic sample induced by the cavity mode is described by the Jaynes-Cummings model. The idea provides a possibility for quantum-state engineering and reconstruction for collective atomic modes.

Alignment dependence of structural deformation in the production process of multiply charged ${\mathrm{CO}}_2$ molecules in an intense femtosecond laser field has been revealed by using aligned sample molecules. Our properly ordered observations clarify that the structural change takes place in the charge state of ${\mathrm{CO}}_2^{2+}$. The bending angle decreases monotonically from the maximum value of $24°$ with the laser polarization parallel to the molecular axis to the minimum value of $16°$ with the polarization perpendicular to the molecular axis. The alignment dependence is discussed in terms of the field-induced nonadiabatic transition between the lowest two adiabatic states formed by the coupling between the electronically excited and the ground states of ${\mathrm{CO}}_2^{2+}$ ions.

The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.

In both molecular physics and condensed matter theory, deeper understanding of the correlation energy density ${ϵ}_c\left(\mathbf{r}\right)$ remains a high priority. By adopting Löwdin’s definition of correlation energy as the difference between the exact and the Hartree-Fock values, here we propose two alternative routes to define this. One of these involves both exact and Hartree-Fock (HF) wave functions, while the second requires a coupling constant integration. As an exact analytical example of the first route, we treat the two-electron model atom of Moshinsky, for which both confinement potential and interactions are harmonic. Though the correlation energy density ${ϵ}_c\left(\mathbf{r}\right)$ is known analytically, we also investigate numerically its relation to the exact ground-state density in this example.

We investigate nuclear-resonant electron scattering as occurring in the two-step process of nuclear excitation by electron capture (NEEC) followed by internal conversion. The nuclear excitation and decay are treated by a phenomenological collective model in which nuclear states and transition probabilities are described by experimental parameters. We present capture rates and resonant strengths for a number of heavy-ion collision systems considering various scenarios for the resonant electron-scattering process. The results show that for certain cases resonant electron scattering can have significantly larger resonance strengths than NEEC followed by the radiative decay of the nucleus. We discuss the impact of our findings on the possible experimental observation of NEEC.

We have performed a combined theoretical and experimental study of the energy loss of Li ions in Zn, on a wide range of energies, together with comparative studies for H and He ions on the same target. By using Zn films and the Rutherford backscattering technique, we were able to determine the stopping power for Li ions in the (0.3 to 5) MeV energy interval. The experimental results cover an energy range which includes the maximum of the stopping power. The values obtained agree well with previous measurements performed in a limited energy interval and with the semiempirical code SRIM 2006. On the other hand, we have performed ab initio theoretical calculations based on the extended Friedel sum rule–transport cross section formulation for the valence electrons and the shellwise local plasma approximation for the inner shells. This theoretical description reproduces reasonably well the experimental results on the whole studied energy range. The same occurs with previous measurements performed with H and He on the same target. The importance of the screened potential on the stopping power due to the valence electrons is stressed in the present description.

We have studied the relaxation of triply charged ${\text{C}}_{60}$ obtained in collisions ${\text{F}}^{2+}+{\text{C}}_{60}\to {\text{F}}^{-}+\text{C}_{60}{}^{3+\ast }$ at low impact energy $\left(E=6.8\text{keV}\right)$. Depending on the excitation energy, these initial parent ions decay following a variety of channels, such as thermal electronic ionization, evaporation of ${\text{C}}_2$ units, asymmetrical fission, and multifragmentation. Using a recently developed experimental method, named collision-induced dissociation under energy control, we were able to measure the energy deposited in $\text{C}_{60}{}^{3+\ast }$ for each collision event and to obtain an excitation energy profile of the parent ions associated with each decay channel. In our chosen observation time scale of the order of $1\mu \text{s}$, evaporations and asymmetrical fissions of $\text{C}_{60}{}^{3+,4+}$ occur when the internal energy is in the range from 40 to 100 eV. The multifragmentation becomes dominant for multicharged $\text{C}_{60}{}^{4+,5+}$ parent ions from 100 to 210 eV. In the case of $\text{C}_{60}{}^{4+}$, the multifragmentation channel is opened at low energy (40 eV). Therefore, in the energy range 40–100 eV, the asymmetrical fission, evaporation, and multifragmentation channels are in competition.

We show that the position of a dark matter-wave soliton can be determined with a precision that scales with the atomic density as $n^{-3/4}$. This surpasses the standard shot-noise detection limit for independent particles, without use of squeezing and entanglement, and it suggests that interactions among particles may present new advantages in high-precision metrology. We also take into account quantum density fluctuations due to phonon and Goldstone modes and we show that they, somewhat unexpectedly, actually improve the resolution. This happens because the fluctuations depend on the soliton position and make a larger amount of information available.

We study anharmonic (optical or magnetic) periodic potentials and demonstrate that they may exhibit unusual features in the band-gap spectra and the nature of the matter-wave Bloch waves and solitons. We reveal that the band gaps may be strongly modified and even close, and show that changing the potential shape may change the symmetry of the gap-edge Bloch waves and affect the symmetry of higher-order gap solitons. We introduce a mixed-gap matter-wave interface soliton which belongs simultaneously to two different spectral gaps and describe interface localized states in chirped periodic potentials. Finally, we generalize our results to two-dimensional periodic potentials and examine the band-gap structure, matter-wave gap solitons, and lattice vortex states.

In the limit of very fast rotation atomic Bose-Einstein condensates may entirely reside in the lowest two-dimensional Landau level (LLL). For small enough filling factor of the LLL, one may have formation of fractional quantum Hall states. We investigate the case of bosons with dipolar interactions as may be realized with chromium-52 atoms. We show that at a filling factor equal to unity the ground state is a Moore-Read (or Pfaffian) paired state as is the case of bosons with purely $s$-wave scattering interactions. This Pfaffian state is destabilized when the interaction in the $s$-wave channel is small enough and the ground state is a stripe phase with unidimensional density modulation. For filling factor 1/3, we show that there is formation of a Fermi sea of “composite fermions.” These composites are made of one boson bound with three vortices. This phase has a wide range of stability and the effective mass of the fermions essentially depends only on the scattering amplitude in momentum channels larger or equal to 2. The formation of such a Fermi sea opens up a new possible route to detection of the quantum Hall correlations.

We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in $\Lambda$-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the nonadiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening.

We report the complete measurement of the spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion pumped by a cw laser in both the collinear and the noncollinear regimes. The measurement includes the single-photon spectra as well as the two-photon joint spectra. Our results reveal interesting yet subtle differences between the collinear and the noncollinear regimes of frequency-degenerate type-I spontaneous parametric down-conversion. The single-photon and two-photon spectral measurements are in good agreement with the numerical simulation taking into account the tuning curve and the experimental geometry.

We study many-body correlations in the ground state of a general quantum system of bosons or fermions by including an additional Jastrow function in our recently proposed variational coupled-cluster method. Our approach combines the advantages of state-dependent correlations in the coupled-cluster theory and of the strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wave function and provide a detailed analysis for practical evaluation of the Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for the higher-order contributions are provided. Our energy functional does not suffer the divergence as most coupled-cluster calculations often do when applying to Hamiltonians with hardcore potentials. We also discuss possible applications of our technique, including applications to strongly correlated fermion systems.