The equations that govern the temporal evolution of two photons in the Schrödinger picture are derived, taking into account the effects of loss, group-velocity dispersion, temporal phase modulation, linear coupling among different optical modes, and four-wave mixing. Inspired by the formalism, we propose the concept of quantum temporal imaging, which uses dispersive elements and temporal phase modulators to manipulate the temporal correlation of two entangled photons. We also present the exact solution of a two-photon vector soliton, in order to demonstrate the ease of use and intuitiveness of the proposed formulation.

We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable within the current experimental capabilities.

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.

It is shown that when a magnetic field is used to support neutral atoms against the gravitational force $mg$, the total curvature of the field magnitude $B$ must be larger than $m^2{g}^2∕\left(2{\mu }^{2}B\right)$, where $\mu$ is the magnetic moment of the atoms. This limits the minimum confinement strength obtainable for a trapped atomic gas. It is also conjectured that the curvature must be larger than twice this value for a magnetic potential that varies in only one or two dimensions, such as an atomic waveguide.

The multimode operation of an optical parametric oscillator (OPO) operating below threshold is calculated. We predict that squeezing can be generated in a comb that is limited only by the phase matching bandwidth of the OPO. Effects of technical noise on the squeezing spectrum are investigated. It is shown that maximal squeezing can be obtained at high frequency even in the presence of seed laser noise and cavity length fluctuations. Furthermore the spectrum obtained by detuning the laser frequency off OPO cavity resonance is calculated.

Photonic-band-gap cavities are prime solid-state systems to investigate light-matter interactions in the strong coupling regime. However, as the cavity is defined by the geometry of the periodic dielectric pattern, cavity control in a monolithic structure can be problematic. Thus, either the state coherence is limited by the read-out channel, or in a high-$Q$ cavity, it is nearly decoupled from the external world, making measurement of the state extremely challenging. We present here a method for ameliorating these difficulties by using a coupled cavity arrangement, where one cavity acts as a switch for the other cavity, tuned by control of the atomic transition.

It has been shown in an earlier publication [J. Pendlebury et al. Phys. Rev. A 70, 032102 (2004)] that magnetic-field gradients applied to particles in traps can induce Larmor frequency shifts that may falsely be interpreted as electric-dipole moment signals. This study has now been extended to include nonuniform magnetic-field gradients due to the presence of a local magnetic dipole. It is found that, in the high orbit-frequency regime, .the magnitude of the shifts can be enhanced beyond the simple expectation of proportionality to the volume-averaged magnetic-field gradient $⟨\partial B_z∕\partial z⟩$.

We compare the performance of Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols, the latter of which was proposed by V. Scarani et al. [Phys. Rev. Lett. 92, 057901 (2004)]. Specifically, in this paper, we investigate the SARG04 protocol with two-way classical communications and the SARG04 protocol with decoy states. In the first part of the paper, we show that the SARG04 scheme with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than the SARG04 one with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for the SARG04 protocol with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in the SARG04 scheme to obtain unconditional security even when realistic devices are used. We compare the performance of the SARG04 protocol with decoy states and the BB84 one with decoy states. We find that the optimal mean-photon number for the SARG04 scheme is higher than that of the BB84 one when the bit error rate is small. Also, we observe that the SARG04 protocol does not achieve a longer secure distance and a higher key generation rate than the BB84 one, assuming a typical experimental parameter set.

The effects of the adiabatic approximation in time-dependent density-functional theory (TDDFT) on dynamic polarizabilities and van der Waals $C_6$ coefficients have been analyzed quantitatively. These effects are shown to be small in the off-resonance region of the perturbation frequencies by comparing the results from the exact-exchange TDDFT employing the optimized effective potentials and the corresponding frequency-dependent kernel [time-dependent optimized effective potentials (TDOEP)] and those from the frequency-independent kernel [adiabatic TDOEP (ATDOEP)]. The magnitude of the computed dynamic polarizabilities near the static limit is found to be in the order: time-dependent Hartree-Fock $\left(\mathrm{TDHF}\right)>\mathrm{ATDOEP}>\mathrm{TDOEP}$, whereas that of $C_6$ is: $\mathrm{TDHF}>\mathrm{TDOEP}>\mathrm{ATDOEP}$.

We report on the simultaneous trapping of two fermionic species, ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$, and a bosonic species, ${}^{87}\mathrm{Rb}$, demonstrating the first three-species magneto-optical trap (“triple MOT”). The apparatus including the atom sources and the three laser systems is described, and the single-species MOTs and the triple MOT are characterized. In triple MOT operation, typical atom numbers of $3.2\times {10}^7$ for ${}^6\mathrm{Li}$, $1.5\times {10}^7$ for ${}^{40}\mathrm{K}$, and $5.4\times {10}^9$ for ${}^{87}\mathrm{Rb}$ were achieved. Trap loss due to interspecies collisions was observed. We describe our way to optimize the triple MOT and turn it into a suitable source for the goal to achieve quantum degeneracy by evaporative and sympathetic cooling.

In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the recently proposed post-Markovian master equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function and bring to light the limits of usability of master equations with memory for the system under consideration.

A device to generate polarization-entangled light in the continuous-variable regime is introduced. It consists of an optical parametric oscillator with two type-II phase-matched nonlinear crystals orthogonally oriented, associated with birefringent elements for adjustable linear coupling. We give in this paper a theoretical study of its classical and quantum properties. It is shown that two optical beams with adjustable frequencies and well-defined polarization can be emitted. The Stokes parameters of the two beams are entangled. The principal advantage of this setup is the possibility to directly generate polarization-entangled light without the need of mixing four modes on beamsplitters as required in current experimental setups. This device opens up different directions for the study of light-matter interfaces and a generation of multimode nonclassical light and higher dimensional phase space.

We show that the KLM scheme [Knill, Laflamme, and Milburn, Nature 409, 46 (2001)] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order ${10}^{-6}$ conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.

We study the dynamics of momentum entanglement generated in the lowest-order QED interaction between two massive $\mathrm{spin}\text{−}\frac{1}{2}$ charged particles, which grows in time as the two fermions exchange virtual photons. We observe that the degree of generated entanglement between interacting particles with initial well-defined momentum can be infinite. We explain this divergence in the context of entanglement theory for continuous variables, and show how to circumvent this apparent paradox. Finally, we discuss two different possibilities of transforming momentum into spin entanglement, through dynamical operations or through Lorentz boosts.

We investigate quantum entanglement properties between two interacting atoms in a one-dimensional harmonic trap. We provide detailed results for the dependencies of atom-atom entanglement on the statistical nature of atoms being bosonic or fermionic, the interaction strength as parameterized by a contact pseudo-potential, and temperature.

We investigate the resonant process of nuclear excitation by electron capture (NEEC), in which a continuum electron is captured into a bound state of an ion with the simultaneous excitation of the nucleus. In order to derive the cross section a Feshbach projection operator formalism is introduced. Nuclear states and transitions are described by a nuclear collective model and making use of experimental data. Transition rates and total cross sections for NEEC followed by the radiative decay of the excited nucleus are calculated for various heavy-ion collision systems.

Angle-resolved two-dimensional photoelectron spectroscopy has been used to study $\mathrm{HBr}$ in the vicinity of the Br $3d$ ionization thresholds. The energy positions of the two $3d_{5∕2,3∕2}\to {\sigma }^{*}$ resonances have been measured directly and found to be at $70.89\left(6\right)\mathrm{eV}$ and $71.92\left(6\right)\mathrm{eV}$, respectively, giving a spin-orbit splitting of $1.03\left(3\right)\mathrm{eV}$ for the two Br $3d$ components. Br Auger lines $(26\mathrm{eV}<\mathrm{KE}<54\mathrm{eV})$, produced by dissociation of $\mathrm{HBr}$ after $3d\to {\sigma }^{*}$ transitions, are tentatively assigned according to their kinetic-energy positions and their profiles as a function of photon energy are found to be asymmetric. The angular distribution asymmetry parameters $\beta$ of these lines, which have not been measured before, have also been derived. The alignment parameters for the two intermediate atomic states (${}^{2}D_{5∕2}$ and ${}^{2}D_{3∕2}$) have been found and used to derive intrinsic anisotropy parameters ${\alpha }_2$ from the $\beta$ parameters. These were found to be similar to those of the equivalent $M_{4,5}NN$ normal Auger lines in the isoelectronic counterpart Kr calculated by Tulkki et al. [Phys. Rev. A 48, 1277 (1993)].

We show that light-induced atom desorption (LIAD) can be used as a flexible atomic source for large ${}^{87}\mathrm{Rb}$ and ${}^{40}\mathrm{K}$ magneto-optical traps. The use of LIAD at short wavelengths allows for fast switching of the desired vapor pressure and permits experiments with long trapping and coherence times. The wavelength dependence of the LIAD effect for both species was explored in a range from $630\text{to}253\mathrm{nm}$ in an uncoated quartz cell and a stainless steel chamber. Only a few $\mathrm{mW}∕{\mathrm{cm}}^2$ of near-UV light produce partial pressures that are high enough to saturate a magneto-optical trap at $3.5\times {10}^9$ ${}^{87}\mathrm{Rb}$ atoms or $7\times {10}^7$ ${}^{40}\mathrm{K}$ atoms. Loading rates as high as $1.2\times {10}^9$ ${}^{87}\mathrm{Rb}$ atoms/s and $8\times {10}^7$ ${}^{40}\mathrm{K}$ atoms/s were achieved without the use of a secondary atom source. After the desorption light is turned off, the pressure quickly decays back to equilibrium with a time constant as short as $200\mu \mathrm{s}$, allowing for long trapping lifetimes after the MOT loading phase.

Fragmentation of a two-boson system in an external potential with contact interaction (i.e., $\delta$-function interaction) is studied using a full variational treatment. The results are compared to those obtained by the standard mean-field method (Gross-Pitaevskii equation) and the more recently developed best mean-field method. The numerically exact calculations show a transition to fragmentation as a function of the boson-boson interaction strength. The Gross-Pitaevskii solution cannot describe fragmentation. The respective energy exhibits a bifurcation which can be viewed as a hint that fragmentation may take place in reality. The best mean-field approach, on the other hand, can predict the fragmentation of the system and give the correct physical description of the fragmented state. The Gross-Pitaevskii energy diverges as the boson-boson interaction goes to infinity, while the exact and the best mean-field energies saturate.