This work presents a theoretical investigation on the spin-exchange effects in the low-energy elastic electron–${\mathrm{C}}_2\mathrm{O}$ radical collisions. Spin-polarization differential and integral cross sections calculated in the $1–10\text{−}\mathrm{eV}$ energy range are reported. Our calculation has shown that the exchange between the scattering and unpaired target electron is strongly influenced by the occurrence of shape resonances. More specifically, our calculated rotationally summed spin-polarization fractions show significant deviation from unity in the resonance region. An analysis of the contributions from individual rotational transitions is also made.

We investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott-insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system’s temperature at energies of the order of the atoms’ interaction energy.

We theoretically investigate the feasibility of using intensity distributions of light of a single laser beam diffracted by a circular aperture as optical dipole traps for cold neutral atoms. Localized and cylindrically symmetric traps on the central axis of the circular aperture exist for both blue- and red-detuned laser light. Experimental mapping of the spots of interest using ${\mathrm{CO}}_2$ laser light demonstrates the existence of these light distributions for laboratory conditions and their agreement with theoretical predictions.

We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.

A common approximate way to study the time evolution of a superfluid Fermi gas is to consider the mean-field time-dependent BCS equations. We show that, by inclusion of an appropriate fluctuating term in these mean-field equations, the exact quantum evolution of the Fermi gas is recovered, after an average over all possible realizations of the noise term: this leads to an exact quantum Monte Carlo technique for the real-time evolution of an interacting fermionic system. In practice, we derive the general conditions on the noise term, ensuring that the exact dynamics is reproduced, and we explore several explicit realizations of this noise term, trying to minimize the statistical spreading of the quantum Monte Carlo simulations. The convergence issue is discussed in detail, with upper bounds obtained on the statistical spreading, and the relation between the stochastic and the mean-field equations is analyzed. Finally, we apply the method to a simple two-site model, to exemplify that the simulations can display effects out of reach of the mean-field approximation.

With phase space analysis approach, we investigate the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BECs) in a symmetric double well potential. We identify two kinds of self-trapping by their different relative phase behavior. By applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, in other words, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high- and low-frequency modulations. For an intermediate-frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affect the tunneling dynamics and demonstrate many phenomena. Finally, we study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.

We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time evolution of optical and matter-wave fields is performed in the framework of the semiclassical Maxwell-Schrödinger equations. Our theory is not only able to explain many of the known experimental observations, e.g., the behavior of the atomic side-mode distributions, but also provides further detailed insights into the coupled dynamics of optical and matter-wave fields. To work out the significance of propagation effects, we compare our results to other theoretical models in which these effects are neglected.

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.

In this paper, we describe a surface-plasmon-based electron acceleration model, the results of which were supported by our recent experimental observations [S. E. Irvine et al., Phys. Rev. Lett. 93, 184801 (2004)]. The model incorporates femtosecond electromagnetic field dynamics and nonlinear electron photoemission characteristics of metallic surfaces. To account for the electromagnetic field structure in space and time, we numerically solve Maxwell’s equations in two dimensions. Photoelectron emission is treated quasiclassically in accordance with empirical multiphoton statistics, whereas electron dynamics and energy gain are governed by the Lorentz force. Various aspects of the acceleration mechanism are discussed including surface plasmon coupling and evanescent decay, kinetic energy spectra, angular distributions, angle-resolved energy spectra, and the dependence of maximum energy on the surface electric field.

Orientation effects for electron transfer in keV ${\mathrm{He}}^{2+}\text{−}{\mathrm{H}}_2^{+}$ collisions are calculated based on a semiclassical close coupling model which accurately describes the electronic dynamics. When direct processes dominate it is shown that a configuration where the molecule is perpendicular to the ion momentum is always most favorable. At lower collision energies, rotational couplings and important contributions from low impact parameters can lead to dominant capture cross sections from molecular target aligned parallel with the collision beam.

We discuss on general grounds some local indicators of entanglement that have been proposed recently for the study and classification of quantum phase transitions. In particular, we focus on the capability of entanglement in detecting quantum critical points and related exponents. We show that the singularities observed in all local measures of entanglement are a consequence of the scaling hypothesis. In particular, as every nontrivial local observable is expected to be singular at criticality, we single out the most relevant one (in the renormalization group sense) as the best suited for finite-size scaling analysis. The proposed method is checked on a couple of one-dimensional spin systems. The present analysis shows that the singular behavior of local measures of entanglement is fully encompassed in the usual statistical mechanics framework.

We show that the de-excitation process of a dipole emitter can be altered controllably when it is embedded in a dielectric wedge of an arbitrary angle $0<{\varphi }_0⩽2\pi$. We focus here on the case of a dielectric wedge bounded by a perfect conductor and show that the de-excitation process for different wedges, distinguished by ${\varphi }_0$, displays a wide range of features. Besides the dependence on the emitter location at the narrow end, the de-excitation process exhibits a strong dipole orientational dependence, suggesting that the system might serve as a qubit in a controllable scalable hardware architecture for the purpose of quantum information processing.

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, $I$, is at least several times larger than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.

In , Gottesman, Kitaev, and Preskill described a method to encode a qubit in the continuous Hilbert space of an oscillator’s position and momentum variables. This encoding provides a natural error-correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We then use these bounds to constrain the quality of input qubit and ancilla states.

A single-mode cavity ring-down spectrometer, which incorporates a stabilized and tuneable comb of resonant frequencies and a continuous-wave external-cavity diode probe laser, was used to study rovibrational absorption line shapes within the and vibrational bands of water vapor. This spectrometer, which has a noise-equivalent absorption coefficient of and frequency resolution of , enables high-precision measurements of line-shape effects and pressure shifting of relatively weak absorption transitions. We investigated the room-temperature pressure dependence over the range from of two transitions perturbed by He, , and . Foreign-gas broadening and pressure-shift coefficients were determined for a relatively strong transition at , and for a weaker transition at the self- and -broadening and pressure-shift parameters were measured. In the low-pressure limit the room-temperature Doppler width was measured within 0.2% of its expected value. Doppler-free saturation effects were also observed with linewidths below . The data were compared to semiclassical line-shape models that considered the influence of Dicke narrowing as well as the speed dependence of pressure broadening and pressure shifting. Taking both of these effects into account gave the best agreement with our observations and allowed us to model the observed asymmetries of experimental profiles. Hard- and soft-collision as well as billiard-ball collision models were considered. These results allowed us to quantify systematic errors in line intensity and in pressure broadening associated with oversimplified models of line shape.

We show that the breathing mode of a rapidly rotating, harmonically trapped Bose-Einstein condensate may be described by a generalized lowest Landau level (LLL) wave function, in which the oscillator length is treated as a variable. Using this wave function in a variational Lagrangian formalism, we show that the frequency of the breathing mode for a two-dimensional cloud is $2{\omega }_{\perp }$, where ${\omega }_{\perp }$ is the trap frequency. We also study large-amplitude oscillations and confirm that the above result is not limited to linear oscillations. The resulting mode frequency can be understood in terms of orbits of a single particle in a harmonic trap. The mode frequency is also calculated for a cloud in three dimensions and the result for the axial breathing mode frequency agrees with recent experimental data in the rapid rotation regime.

For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It separates elements that depend only on the dynamics from those that depend on the state of the two systems. While the equivalent linear map is generally not completely positive, the homogeneous part of the affine maps is, and is shown to be composed of multiplication operations that come simply from the Hamiltonian for the larger system. The inhomogeneous part is shown to be zero if and only if the map does not increase the trace of the square of any density matrix. Properties are worked out in detail for two-qubit examples.

The problem of a geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of the existing methods to define geometric phase, one by Uhlmann’s approach and the other by a kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based upon purification of a density matrix by its uniform decomposition and a generalization of the parallel transport condition obtained from this decomposition. It is shown that the generalized parallel transport condition can be satisfied when Uhlmann’s condition holds. However, it does not mean that all solutions of the generalized parallel transport condition are compatible with those of Uhlmann’s. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.

The clocked Schrödinger equation was proposed by Sokolovski using the Feynman path integral with constraint (Phys. Rev. A 52, R2, 1995). Sokolovski pointed out that the clocked Schrödinger equation cannot be derived directly from the Schrödinger equation. In this paper, we show that the clocked Schrödinger equation can be derived by starting from the normal Schrödinger equation for a composite system, composed of the observed system and the measuring device, as defined by von Neumann. Details of the derivation and the physical meaning of the clocked Schrödinger equation are given.