We examine the collective scattering of a superfluid droplet impinging on a mesoscopic Bose-Einstein condensate (BEC) as a target. The BEC consists of an atomic gas with two internal electronic states, each of which is trapped by a finite-depth external potential. An off-resonant optical laser field provides a localized coupling between the BEC components in the trapping region. This mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles, when a bound state of one submanifold is embedded in the scattering continuum of the other submanifold. Within the mean-field picture, we obtain resonant scattering phase shifts from a linear response theory in agreement with an exact numerical solution of the real-time scattering process and simple analytical approximations thereof. We find an energy-dependent transmission coefficient that is controllable via the optical field between 0 and 100%.

Geometric phase of an open quantum system that is interacting with a thermal environment (bath) is studied through some simple examples. The system is considered to be a simple spin-half particle which is weakly coupled to the bath. It is seen that even in this regime the geometric phase can vary with temperature. In addition, we also consider the system under an adiabatically time-varying magnetic field which is weakly coupled to the bath. An important feature of this model is that it reveals existence of a temperature scale in which adiabaticity condition is preserved and beyond which the geometric phase is varying quite rapidly with temperature. This temperature is exactly the one in which the geometric phase vanishes. This analysis has some implications in realistic implementations of geometric quantum computation.

The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] in several specific physical systems, including some that occur in condensed-matter physics. The entanglement of particles is relevant when the identical particles are itinerant and so not distinguished by their position as in spin models. We show that entanglement of particles can behave differently than other approaches that have been used previously, such as entanglement of modes (occupation-number entanglement) and the entanglement in the two-spin reduced density matrix. We argue that the entanglement of particles is what could actually be measured in most experimental scenarios and thus its physical significance is clear. This suggests that entanglement of particles may be useful in connecting theoretical and experimental studies of entanglement in condensed-matter systems.

We propose a potential quantum-computer hardware-architecture model on a silicon chip in which the basic cell gate is the atom-photon controlled-phase-flip gate. This gate can be implemented through a single-photon pulse’s scattering by a toroidal microcavity trapping a neutral atom, and it does not require very strict strong-coupling regime and can work beyond the Lamb-Dicke limit with high fidelity and success probability under practical noise environments. Especially, good and bad losses of the toroidal cavity are discussed in detail. Finally, a possibly simple experiment based on current experimental technology is proposed to demonstrate our scheme.

We show the decrease of spin-spin entanglement between two $s=\frac{1}{2}$ fermions or two photons due to local transfer of correlations from the spin to the momentum degree of freedom of one of the two particles. We explicitly show how this phenomenon operates in the case where one of the two fermions (photons) passes through a local homogeneous magnetic field (optically active medium), losing its spin correlations with the other particle.

We search for translationally invariant states of qubits on a ring that maximize the nearest-neighbor entanglement. This problem was initially studied by O’Connor and Wootters [Phys. Rev. A 63, 052302 (2001)]. We first map the problem to the search for the ground state of a spin-1/2 Heisenberg $XXZ$ model. Using the exact Bethe ansatz solution in the limit $N\to \infty$, we prove the correctness of the assumption of O’Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins “down” (or, alternatively, spins “up”). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest-neighbor entanglement necessarily contain pairs of neighboring spins “down.”

The quantum baker map possesses two symmetries: a canonical “spatial” symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker’s map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter that determines whether the entangling properties of the baker map are universal or not. For power-of-2 dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker map is consistent with random matrix theories. We also derive a general formula that relates the asymptotic entangling power of an arbitrary unitary with properties of its reduced eigenvectors.

A scheme is presented for realizing a tunable phase gate for two atoms. The scheme is based on atom-cavity interaction and linear optics elements. In comparison with previous schemes, the distinct advantage is that the fidelity of the gate is not affected by the atomic spontaneous emission, cavity decay, and imperfection of the photodetectors, which is important for implementing high-fidelity quantum gates under realistic conditions.

Accurate quantum calculations have been carried out at ultralow energies (from ${10}^{-2}\text{to}{10}^{-6}{\mathrm{cm}}^{-1}$) for the vibrational deexcitation of ${\mathrm{Li}}_2\left({}^1\Sigma _g^{+}\right)$ by collisions with He, starting from a broad range of initial highly excited vibrational levels. The results indicate the clear dominance of a few transitions with the smallest $\Delta \nu$ changes and show the overall deexcitation cross sections to markedly depend on the initial vibrational state of the molecule, in line with earlier results on ${\mathrm{H}}_2+\mathrm{He}$ [Balakrishan et al. Phys. Rev. Lett. 80, 3224 (1998)] vibrational quenching. A connection is made with very recent measurements on the vibrational quenching of ultracold ${\mathrm{Cs}}_2$ molecules in optical traps that were instead found to behave in a very different manner. Numerical experiments on the present system as well as on the ${\mathrm{H}}_3$ reaction strongly suggest a possible explanation for such differences.

The problem of the choice of gauge in the relativistic strong-field approximation (SFA) is analyzed. The main motivation is to obtain a relativistic ionization amplitude in the SFA which in the nonrelativistic limit coincides with the conventional well-accepted results of the SFA in the length gauge. A gauge-invariant formulation of the SFA is derived which is applicable both in the nonrelativistic as well as in the relativistic regime of laser-induced strong-field ionization phenomena. The gauge invariance is achieved by means of employment of an eigenstate of the physical energy operator for the initial atomic state. As an example, a comparison of predictions of the gauge-invariant theory with conventional SFA results in the radiation gauge is given for above-threshold ionization in the relativistic regime.

Repetitively nanosecond pulse-width transverse pattern formation in a plane-parallel microchip $\mathrm{Cr},\mathrm{Nd}$: yttrium-aluminum-garnet (YAG) self-$Q$-switched laser was investigated. The complex point-symmetric transverse patterns were observed by varying the pump beam diameter incident on the $\mathrm{Cr},\mathrm{Nd}:\mathrm{YAG}$ crystal. The gain guiding effect and the thermal effect induced by the pump power in microchip $\mathrm{Cr},\mathrm{Nd}:\mathrm{YAG}$ laser control the oscillating transverse modes. These transverse pattern formations were due to the variation of the saturated inversion population and the thermal induced index profile along radial and longitudinal direction in the $\mathrm{Cr},\mathrm{Nd}:\mathrm{YAG}$ crystal induced by the pump power incident on the $\mathrm{Cr},\mathrm{Nd}:\mathrm{YAG}$ crystal. These were intrinsic properties of such a microchip self-$Q$-switched laser. The longitudinal distribution of the saturated inversion population inside the gain medium plays an important role on the transverse pattern formation. Different sets of the transverse patterns corresponds to the different saturated inversion population distribution inside microchip $\mathrm{Cr},\mathrm{Nd}:\mathrm{YAG}$ crystal.

We show that the revivals structure of Gaussian wave packets for a charged particle with nonzero linear momentum placed in a circular billiard can be considerably improved by applying a perpendicular constant magnetic field of correct chosen intensity. To obtain the desired enhancement, the field must be turned on only at certain time values. We also briefly investigate how the shape of the evoluted packet at the revivals, with and without an external $B$, compares with the initial state.

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.

In view of recently achieved extreme laser powers for which the ponderomotive energy $U_p\gg 2m{c}^2$, it has become of interest to reconsider fundamental processes of quantum electrodynamics in such powerful laser fields. In the present work, we evaluate the rates of producing electron-positron pairs by the impact of laser pulses of extreme power on highly charged ions at rest. Contrary to previous investigations, we shall consider a linearly polarized laser pulse, since at extreme laser powers the contribution of the $A^2$ part of the electromagnetic interaction becomes significant. As long as the duration of the laser pulses considered is in the femtosecond domain, the description of the laser beam by a powerful, monochromatic electromagnetic plane wave will still be justified, which simplifies considerably the calculations required.

The alignment dynamics of a symmetric top molecule, tert-butyliodide, induced by two picosecond, nonresonant, linearly polarized pulses is studied experimentally and numerically using a combination of time-resolved photofragment imaging and nonperturbative solution of the time-dependent Schrödinger equation. It is shown that the strongest degree of one-dimensional (single axis) field-free alignment obtainable with a single pulse can be enhanced using the two-pulse sequence in a parallel polarization geometry. The conditions for alignment enhancement are: (1) The second pulse must be sent near the time where the degree of alignment, due to the first pulse, peaks. (2) The intensity of the first pulse must be smaller than the intensity of the second pulse, the optimal intensity ratio being determined by the duration of the pulses. Numerically, we also discuss the existence of an optimal pulse duration, the effect of focal averaging on the degree of alignment, and compare two-pulse alignment to adiabatic alignment.

We show that light confined in a circularly polarized fundamental mode of a nanofiber has a finite angular momentum, with both spin and orbital components. We derive exact analytical expressions for the angular momentum and its spin and orbital components. We show that the spin component is dominant when the fiber radius is small or large compared to the light wavelength. For intermediate fiber radii, a substantial orbital component appears, which is absent in the two limits mentioned above. The orbital component is maximized when the fiber radius is about one-fourth of the light wavelength.

Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic parameters of the Lieb-Liniger model, is valid for all values of the dimensionless coupling $\gamma$ and contains the previously known results for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also investigate finite-size effects by calculating the correlation function for small systems of three, four, five, and six particles.

The Friedel sum rule for massless Weyl fermions is given. Due to the parity violation of Weyl fermions it is shown that the global phases of spinors are important in determining the accurate sum rule, and the Levinson theorem is proved to be determined only by the number of discrete zero modes. For potential barriers that do not allow any zero modes it is revealed that a particular duality relation exists between the phase shifts at the Fermi surface and the critical point of zero momentum.

Electromagnetic waves with phase defects in the form of vortex lines combined with a constant magnetic field are shown to pin down cyclotron orbits (Landau orbits in the quantum mechanical setting) of charged particles at the location of the vortex. This effect manifests itself in classical theory as a trapping of trajectories and in quantum theory as a Gaussian shape of the localized wave functions. Analytic solutions of the Lorentz equation in the classical case and of the Schrödinger or Dirac equations in the quantum case are exhibited that give precise criteria for the localization of the orbits. There is a range of parameters where the localization is destroyed by the parametric resonance. Pinning of orbits allows for their controlled positioning: They can be transported by the motion of the vortex lines.