We consider a two-state system driven by an on-resonance, continuous wave pump laser and a much weaker pulsed probe laser that is slightly detuned from the pump laser frequency (usually this detuning is about ${\omega }_p-{\omega }_P=\Delta \approx 1\mathrm{kHz}$). The upper state population is assumed to be slowly decaying, but the off-diagonal element of the density matrix decays rapidly due to homogeneous broadening. This model has been solved by others in rare-earth-element-doped fibers and crystals in a usual steady state approximation for slow optical wave propagation. We show that in general the usual steady state approximation does not apply unless either $\Delta \tau ⪢1$ or $(2S+1){\gamma }_2\tau ⪢1$ where ${\gamma }_2$ is the decay rate of the excited state population, $\tau$ is the pulse length of the probe field, and $2S$ is the saturation parameter. Both conditions, however, are not satisfied in many population-oscillation- and corresponding group-velocity-reduction-related studies. Our theory and corresponding numerical simulations have indicated that for probe pulses that are much shorter than the lifetime of the upper state, there is no analytical theory for the amplitude, pulse shape, and group velocity of the probe field. In addition, there is no reason to assume that the group velocity remains small when ${\gamma }_2\tau ⪡1$ and there is no reason to believe that many pulse length decays can be obtained for such short pulses.

We propose a scheme for implementing a two-qubit quantum phase gate for intracavity fields. In the scheme, two qubits are encoded in zero- and one-photon Fock states of two intracavity modes, and a four-level $\mathsf{N}$-type atomic ensemble trapped in a cavity mediates the conditional phase gate within a given interaction time. We also discuss the influence of the atomic spontaneous emission and the decay of the cavity modes on the photon loss and gate fidelity, showing the scheme is within the current experiment technology.

Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pairwise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere, and the system of hyperradial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyperradial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyperradius $\rho$ is studied, and the universal logarithmic dependence $\sim {\ln }^3\rho$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $(2+1)$-scattering length are calculated.

The cross section for ionization $\overline{p}+{\mathrm{He}}^{+}\to \overline{p}+{\mathrm{He}}^{2+}+e$ at collision energies ranging from threshold to $1\mathrm{MeV}$ is calculated using a quantum-classical hybrid (i.e., semiclassical) method. Due to the bending effect of $\overline{p}+{\mathrm{He}}^{+}$ trajectories, the ionization cross section shows a local minimum at the center-of-mass energy of $\sim 150\mathrm{eV}$. Also reported is the excitation cross section, which is expected to remain finite at threshold for the same reason as the Gailitis jump appears in excitation of ions by electron impacts.

Using $\mathrm{He}@{\mathrm{C}}_{60}$ as an example, we demonstrate that the static potential of the fullerene core essentially alters the cross section of the two-electron ionization differential in one-electron energy $d{\sigma }^{++}\left(\omega \right)∕d\epsilon$. We found that at high photon energy prominent oscillations appear in it due to reflection of the second slow electron wave on the ${\mathrm{C}}_{60}$ shell, which “dies out” at relatively high $\epsilon$ values, of about 2–3 two-electron ionization potentials. The results were presented for ratios $R_{{\mathrm{C}}_{60}}(\omega ,\epsilon )\equiv d{\sigma }^{++}(\omega ,\epsilon )∕d{\sigma }^{a++}(\omega ,\epsilon )$, where $d{\sigma }^{a++}(\omega ,\epsilon )∕d\epsilon$ is the two-electron differential photoionization cross section. We have calculated the ratio $R_{i,\mathrm{ful}}={\sigma }_i^{++}\left(\omega \right)∕{\sigma }_i^{a++}\left(\omega \right)$, that accounts for reflection of both photoelectrons by the ${\mathrm{C}}_{60}$ shell. We have also calculated the value of two-electron photoionization cross section ${\sigma }^{++}\left(\omega \right)$ and found that this value is close to that of an isolated He atom. Results similar to $\mathrm{He}@{\mathrm{C}}_{60}$ are presented for $\mathrm{He}@{\mathrm{C}}_{70}$ and $\mathrm{He}@{\mathrm{C}}_{76}$.

The optimized structure, electronic and magnetic properties of La clusters consisting of up to 14 atoms have been investigated using ab initio theoretical methods based on density-functional theory. Structural and spin isomers have been determined. We show that increase in cluster symmetry can promote ferromagnetic instability in La clusters. A giant enhancement of magnetism in ${\mathrm{La}}_4$, ${\mathrm{La}}_6$, and ${\mathrm{La}}_{13}$ clusters is predicted. We also found that the ground states of ${\mathrm{La}}_2$, ${\mathrm{La}}_3$, ${\mathrm{La}}_5$, ${\mathrm{La}}_7$, ${\mathrm{La}}_9–{\mathrm{La}}_{11}$, and ${\mathrm{La}}_{14}$ clusters possess nonzero magnetic moments, that ranged from $\sim 0.1{\mu }_B$ to $1.0{\mu }_B$ per atom. Strong dependence of the magnetic moment on temperature for $T>300\mathrm{K}$ is predicted. The results obtained are compared with the available experimental data and the results of other theoretical works.

A time-dependent quantum wave packet method is used to calculate the branching ratio of photodissociation products of the HI molecule in two-color intense few-cycle laser pulses with varying relative phase. It is demonstrated that the relative phase between two intense few-cycle pulses ($\omega$ and $2\omega$) can be used for controlling the branching ratio of the photodissociation products $\mathrm{I}\left({}^{2}P_{3∕2}\right)$ and $\mathrm{I}\left({}^{2}P_{1∕2}\right)$ of the HI molecule. The nonadiabatic effect of the crossing potential energy curves on the photodissociation product yields of the HI molecule is also discussed.

We determine the effects on the BCS-BEC crossover of the energy dependence of the effective two-body interaction, which at low energies is determined by the effective range. To describe interactions with an effective range of either sign, we consider a single-channel model with a two-body interaction having an attractive square well and a repulsive square barrier. We investigate the two-body scattering properties of the model, and then solve the Eagles-Leggett equations for the zero temperature crossover, determining the momentum dependent gap and the chemical potential self-consistently. From this we investigate the dependence of the crossover on the effective range of the interaction.

The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: $⟨{\widehat{a}}_j^{†}{\widehat{a}}_{j+r}⟩$ and $⟨{\widehat{n}}_j{\widehat{n}}_{j+r}⟩$. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.

We study numerically the polarization dynamics of vertical-cavity surface-emitting lasers (VCSEL’s) operating in the fundamental transverse mode. We use an extension of the spin-flip model that not only accounts for the vector nature of the laser field, but also considers spatial transverse effects. The model assumes two orthogonal, linearly polarized fields, which are coupled to two carrier populations, associated with different spin sublevels of the conduction and valence bands in the quantum-well active region. Spatial effects are taken into account by considering transverse profiles for the two polarizations, for the two carrier populations, and for the carrier diffusion. The optical profile is the ${\mathrm{LP}}_{01}$ mode, suitable for describing index-guided VCSEL’s with cylindrical symmetry emitting on the fundamental transverse mode for both polarizations. We find that in small-active-region VCSEL’s, fast carrier diffusion induces self-sustained oscillations of the total laser output, which are not present in larger-area devices or with slow carrier diffusion. These self-pulsations appear close to threshold, and, as the injection current increases, they grow in amplitude; however, there is saturation and the self-pulsations disappear at higher injection levels. The dependence of the oscillation amplitude on various laser parameters is investigated, and the results are found to be in good qualitative agreement with those reported by Van der Sande et al. [Opt. Lett. 29, 53 (2004)], based on a rate-equation model that takes into account transverse inhomogeneities through an intensity-dependent confinement factor.

Recent experiments demonstrating atomic quantum memory for light [B. Julsgaard et al., Nature 432, 482 (2004)] involve two macroscopic samples of atoms, each with opposite spin polarization. It is shown here that a single atomic cell is enough for the memory function if the atoms are optically pumped with suitable linearly polarized light, and quadratic Zeeman shift and/or ac Stark shift are used to manipulate rotations of the quadratures. This should enhance the performance of our quantum memory devices since less resources are needed and losses of light in crossing different media boundaries are avoided.

We study the security of quantum string commitment (QSC) protocols with group covariant encoding scheme. First we consider a class of QSC protocol, which is general enough to incorporate all the QSC protocols given in the preceding literatures. Then among those protocols, we consider group covariant protocols and show that the exact upperbound on the binding condition can be calculated. Next using this result, we prove that for every irreducible representation of a finite group, there always exists a corresponding nontrivial QSC protocol which reaches a level of security impossible to achieve classically.

We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The discriminator is a fixed measurement that has two kinds of input registers: the program registers and the data register. The quantum state in the data register is what users want to identify, which is confirmed to be among the $n$ states in program registers. The task of the discriminator is to tell the users which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if $m=n$, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary $n$ quantum states.

We study the influence of the external dc electric field on the process of single-photon double ionization of helium at photon energies of 85 and $90\mathrm{eV}$. Calculation is based on a numerical solution of the time-dependent Schrödinger equation and subsequent projection of the solution on a final state furnished by the convergent close coupling expansion. We find that for the range of the field strengths studied $(F_{\mathrm{dc}}⩽3\times {10}^{-2}\mathrm{a.u.})$ the presence of the external dc field leads to a monotonous decrease of the total probability of single-photon double electron ionization. This decrease is achieved primarily due to decreasing probability to detect electrons with unequal energy sharing.

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-$\frac{1}{2}$ system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows unusual diffusion anisotropy in both dipole and quadrupole modes. Moreover, the lack of spin isotropy in the interactions leads to the nonconservation of transverse spin, which in turn has significant effects on the hydrodynamic modes.

Using the example of the $\mathrm{S}{\mathrm{O}}_2$ molecule, we will discuss photodissociation at threshold as a possibility for producing cold molecules or atoms. The fragments SO and O have low excess energy and are free radicals with high interest for applications like cold chemistry. The threshold behavior is tunable by external fields and shows great similarity to Feshbach resonance studies in cold atom collisions. To take full advantage of the cold fragmentation, it is necessary to dissociate within a cold sample of molecules. In our initial experiments we have demonstrated substantial Stark deceleration of $\mathrm{S}{\mathrm{O}}_2$.

We observe Lyman-$\alpha$ radiation produced by the direct excitation of ${{\mathrm{H}}_2}^{+}$ by 23-fs 800-nm laser pulses. The laser pulse first ionizes ${\mathrm{H}}_2$ molecules and dissociates the ions through bond softening, leaving the molecules in the repulsive $2p{\sigma }_u$ state. The expanding ${{\mathrm{H}}_2}^{+}$ ions enter a region of strong multiphoton coupling leading to a resonant seven-photon excitation of the $2s{\sigma }_g$ state. Finally, the $2s{\sigma }_g$ state dissociates into the $\mathrm{H}\left(2s\right)$ and $\mathrm{H}\left(2p\right)$ atomic limits. The latter state then decays through Lyman-$\alpha$ emission.

We present a setup of two coupled micromaser cavities for studying decoherence. The system is prepared in a state where, initially, one photon is contained in one of the two cavities. The coupling of the two resonators allows the photon to tunnel into the other cavity with a certain probability. The system thus oscillates between the two states $\mid 1{⟩}_L\mid 0{⟩}_R$ and $\mid 0{⟩}_L\mid 1{⟩}_R$. It is shown how to map these states onto the states $\mid g⟩$ and $\mid e⟩$ of probe atoms used to investigate the status of the cavity system. It is an important result that the symmetry of our special setup allows decoherence to be monitored by measuring just the diagonal elements of the atomic density matrix. This property relies on the fact that only $\mid 0⟩$ and $\mid 1⟩$ states are relevant. To our knowledge, this is the first proposal that tries to exploit this particular property.

We investigate an active Raman gain scheme for significant group velocity reduction. We show that this scheme, which is fundamentally different from the electromagnetically induced transparency scheme, is capable of achieving ultraslow and distortion-free propagation of a pulsed probe field. We demonstrate the group velocity behavior that is drastically different from the conventional electromagnetically induced transparency scheme, and we show that the new scheme can be used to accurately determine the decoherence rate of a long-lived state. In addition, the Raman gain scheme has the advantage of being broadly tunable, an important feature that may have potential applications.