Recently, Markham and Vedral [Phys. Rev. A 67, 042113 (2003)] investigated the effect of beam splitting on the spin, or SU(2), coherent states for a single mode field. The spin coherent state is a binomial coherent state related to the Holstein-Primakoff realization of the su(2) Lie algebra given in terms of a set of single mode bose annihilation and creation operators. Upon beam splitting, the ordinary (or Glauber) coherent states merely split into products of ordinary coherent states with reduced amplitudes without becoming entangled, as one would expect for a classical-like field. The above authors expected the spin coherent states to go over to the ordinary coherent states in the limit of high spin, $j\to \infty$, and thus to become product states after beam splitting. But this expectation was not confirmed through numerical calculation of the entropy which, instead of going to zero, leveled off with increasing spin. In this paper we find similar behavior for SU(1,1) coherent states of the Perelomov type for large Bargman index $k$, but also find that the Barut-Girardello SU(1,1) coherent states appear to rapidly become product states after beam splitting for increasing $k$. We explain these results by showing that, in reality, neither the spin coherent states nor the Perelomov SU(1,1) coherent states go over to ordinary coherent states in the limits of large $j$ or $k$, and that the Barut-Girardello coherent states merely go over to the vacuum in the large $k$ limit. Finally, we examine the correct limiting procedure for obtaining separable states (i.e., products of coherent states) upon beam splitting by performing contractions of the su(2) and su(1,1) Lie algebras and of their associated coherent states.

We calculate the relative entropy between two quantum Gaussian states with given correlation matrices by demonstrating a practical method of transforming one of the correlation matrices into an exponential quadratic operator matrix. We show that the closest Gaussian separable state achieving the Gaussian relative entropy of entanglement is at the border between separable and inseparable Gaussian state sets. For a two-mode Gaussian state, the calculation of the Gaussian relative entropy of entanglement is greatly simplified by deducing a matrix with ten undetermined parameters to one with only three. The two-mode Gaussian states are classified into four types. Numerical calculations strongly suggest that the Gaussian relative entropy of entanglement for each type is realized by a Gaussian separable state within the same type. For a symmetric Gaussian state it is strictly proven that the Gaussian relative entropy of entanglement is achieved by a symmetric Gaussian separable state.

State estimation is usually analyzed in the situation when copies are in a product state, either mixed or pure. We investigate here the concept of state estimation on correlated copies. We analyze state estimation on correlated $N$-qubit states, which are permutationally invariant. Using a correlated state we try to estimate as good as possible the direction of the Bloch vector of a single-particle reduced density matrix. We derive the optimal fidelity for all permutation invariant states. We find the optimal state, which yields the highest estimation fidelity among the states with the same reduced density matrix. Interestingly, this state is not a product state. We also point out that states produced by optimal universal cloning machines are the worst, from the point of view of estimating the reduced density matrix.

We study how photon absorption losses degrade the bipartite entanglement of entangled states of light. We consider two questions: (i) What state contains the smallest average number of photons given a fixed amount of entanglement? (ii) What state is the most robust against photon absorption? We explain why the two-mode squeezed state is the answer to the first question but not quite to the second question.

We present a semirelativistic model for the description of the ionization process of atomic hydrogen by electron impact in the first Born approximation by using the Darwin wave function to describe the bound state of atomic hydrogen and the Sommerfeld-Maue wave function to describe the ejected electron. This model, accurate to first order in $Z∕c$ in the relativistic correction, shows that, even at low kinetic energies of the incident electron, spin effects are small but not negligible. These effects become noticeable with increasing incident electron energies. All analytical calculations are exact and our semirelativistic results are compared with the results obtained in the nonrelativistic Coulomb Born approximation both for the coplanar asymmetric and the binary coplanar geometries.

We present a theoretical study of dissociative multiphoton ionization of the $\mathrm{H}_2{}^{+}$ molecular ion in perturbative and nonperturbative regimes including both electronic and nuclear degrees of freedom. Differential (in proton and electron energy) ionization cross sections have been evaluated for various photon energies, laser intensities, and pulse lengths. We have found that the proton energy distribution is modulated by vertical Franck-Condon transitions but also by vibrational resonances associated with intermediate electronic states. We have also found that, as expected, nonperturbative results tend to the time-independent perturbative ones when both the pulse length increases and the laser intensity decreases. No divergence near intermediate-state resonances is found in the perturbative results when the nuclear motion is properly taken into account in the calculations.

The origin and mechanism of backward stimulated Rayleigh scattering in two-photon absorbing media are studied theoretically and experimentally. This type of stimulated scattering has the unusual features of no frequency shift and low pump threshold requirement compared to all other known stimulated scattering effects. This frequency-unshifted stimulated Rayleigh scattering effect can be well explained by a two-photon-excitation-enhanced Bragg grating reflection model. The reflection of the forward pump beam from this stationary Bragg grating may substantially enhance the backward Rayleigh scattering beam, providing a positive feedback mechanism without causing any frequency shift. A two-counterpropagating-beam-formed grating experiment in a two-photon absorbing dye solution is conducted. The measured dynamic behavior of Bragg grating formation and reflectivity properties are basically consistent with the predictions from the proposed model.

We have studied the large-scale beam breakup and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission, and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines (constellation), then filaments form on the constellations, and finally the filaments release a fraction of their energy through conical emission. We observed a phase transition to a faster filamentation rate at the onset of conical emission. We attribute this to the interaction of conical emissions with the constellation which creates additional filaments. Numerical simulations show good agreement with the experimental results.

A “dipole” laser is proposed consisting of a nanoparticle and a two-level system with population inversion. If the threshold conditions are fulfilled, the dipole interaction between the two-level system and the nanoparticle leads to coherent oscillations in the polarization of the particles, even in the absence of an external electromagnetic field. The emitted radiation has a dipolar distribution. It does not need an optical cavity, and has a very small volume, $\sim 0.1\mu {\mathrm{m}}^3$, which can be important for applications in microelectronics. Estimates of the threshold conditions are carried out for a dipole laser composed of a quantum dot and a silver nanoparticle.

We present a scheme to realize a quantum key distribution using vacuum–one-photon entangled states created both from Alice and Bob. The protocol consists of an exchange of spatial modes between Alice and Bob and in a recombination which allows one of them to reconstruct the bit encoded by the counterpart in the phase of the entangled state. The security of the scheme is analyzed against some simple kind of attack. The model is shown to reach higher efficiency with respect to prior schemes using phase encoding methods.

Ionization rates of the hydrogen molecular ion $\mathrm{H}_2{}^{+}$ under linearly polarized pulse of intense laser fields are simulated by direct solution of the fixed-nuclei time-dependent Schrödinger equation for the Ti:sapphire laser lines $\lambda =790$ and 800 nm at high intensities starting from just above the Coulomb explosion threshold (i.e., $6.0\times {10}^{13}$, $1.0\times {10}^{14}$, $3.2\times {10}^{14}$, and $1.4\times {10}^{15}\mathrm{W}{\mathrm{cm}}^{-2}$). Results obtained in this research exhibit a high degree of complexity for the $R$-dependent enhanced ionization rates for the $\mathrm{H}_2{}^{+}$ system in these intense laser fields. The $R$-dependent ionization peaks move towards small internuclear distances and their structure becomes simpler and smoother with the increase in the intensity of the laser pulse, i.e., with the decrease in the Keldysh parameter. Results obtained in this research are comparable to and even more reliable than the results of other theoretical calculations reported recently and successfully simulate the experimental ionization data.

Microscopic theories of Feshbach resonance phenomena in fermionic alkali-metal gases have, in the main, relied upon the intuition afforded by a “Fermi-Bose” theory which presents the Feshbach molecule as a featureless pointlike Bose particle. While this model may provide a suitable platform to explore the condensation phenomena in the ${}^6\mathrm{Li}$ system, it has been argued recently that its application to the ${}^{40}\mathrm{K}$ system, where the hyperfine structure is inverted, is inappropriate. Here, the formation of a Feshbach resonance involves the formation of a Feshbach molecule which shares a spin state with the open channel. In such an arrangement, the mechanism of condensate formation cannot escape the effects of Pauli exclusion. Building on a model three-state fermion Hamiltonian recently introduced by Parish et al. to describe the ${}^{40}\mathrm{K}$ system, we elucidate the mean-field structure of the model, investigate the internal structure of the condensate wave function in the crossover region, and develop a field theory of the transition.

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.

For the analysis of high-order harmonics generated in a long gas jet by intense chirped femtosecond laser pulses, calculations of the laser propagation and harmonic generation were performed in terms of a nonadiabatic three-dimensional model. The self-guided propagation, observed at the conditions of bright harmonic generation, was confirmed by the model calculations. When using negatively chirped pulses, the calculated distribution of the harmonic field is spatially and spectrally confined, being generated on axis with a narrow spectral profile. The positively chirped pulses generate broad spectral distribution on axis, and narrow off axis, but in the latter case with a large emission angle. The estimation of harmonic beam divergence agreed well with experimentally measured data, showing the lowest divergence at the conditions of the brightest harmonic generation. Spectral, temporal, and spatial modifications of the propagated laser pulse are found to influence decisively the single-atom response and ultimately the harmonic field, providing a coherent picture of harmonic generation.

We present a time-dependent analysis of high-order harmonics generated by a self-guided femtosecond laser pulse propagating through a long gas jet. A three-dimensional model is used to calculate the harmonic fields generated by laser pulses, which only differ by the sign of their initial chirp. The time-frequency distributions of the single-atom dipole and harmonic field reveal the dynamics of harmonic generation in the cutoff. A time-dependent phase-matching calculation was performed, taking into account the self-phase modulation of the laser field. Good phase matching holds for only few optical cycles, being dependent on the electron trajectory. When the cutoff trajectory is phase matched, emitted harmonics are locked in phase and the emission intensity is maximized.

The charge migration models which account for the creation of a second-order nonlinear susceptibility in poled silica glasses give significant results if the sample thickness is at least 1 order of magnitude larger than the induced nonlinear layer thickness. We present herein a model valid for thin samples applicable to twin-hole optical fibers or waveguides.

Using the method of dynamical algebras, the solution of a homotriparticle linear spin cluster (each particle with $S=1∕2$) in a rotating magnetic field is obtained. We derive degeneracy energy levels and each level’s Berry phase of this system. The Berry phase as a function of $\omega$ and $\theta$ has been determined by using the relation between the Berry phase and the angular velocity $\omega$ of the rotating magnetic field as well as the angle $\theta$ between the magnetic field and $Z$ axis. We obtain the changing diagram of the Berry phase of the basis state.

We propose an experimentally feasible scheme to realize the nonlocal gate between two different quantum network nodes. With an entangled qubit (ebit) acts as a quantum channel, our scheme is resistive to actual environment noise and can get high fidelity in current cavity quantum electrodynamics system.

The spontaneous emission rate of an atom in dielectric slabs is shown to exhibit multiperiodic oscillations when the system scale is varied. These oscillations are calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The extracted frequencies in the emission rates by Fourier transform agree well with actions of short photon closed orbits. The oscillations in the spontaneous emission rates are interpreted as interferences of emitted photon propagating on closed orbits leaving and returning to the emitting atom. This study provides a new understanding of the spontaneous emission process for atoms in the presence of environments.

We analyze the finite-size properties of the two-level BCS model. Using the continuous unitary transformation technique, we show that nontrivial scaling exponents arise at the quantum critical point for various observables such as the magnetization or the spin-spin correlation functions. We also discuss the entanglement properties of the ground state through the concurrence which appears to be singular at the transition.