We define the condition of the quasiclassical state of free particles, which is useful in the approximate treatment of quantum systems. Then we introduce classical pure ensembles. Their states are represented using distribution functions on phase space. We compare distribution functions of classical pure ensembles and Wigner distribution functions of quasiclassical states for free particles and draw two conclusions: (i) A wave function does not describe an individual particle but a classical pure ensemble. (ii) Given a quasiclassical wave function, we can tell which classical pure ensemble is described by it.

A two-sphere (“Bloch” or ‘‘Poincare’’) is familiar for describing the dynamics of a spin-$1∕2$ particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs evolution operators for higher-dimensional $\mathrm{SU}\left(N\right)$ in terms of lower-dimensional ones. We focus, in particular, on the SU(4) of two qubits which describes all possible logic gates in quantum computation and entangled states in quantum-information sciences. For a general Hamiltonian of SU(4) with 15 parameters, and for Hamiltonians of its various subgroups so that fewer parameters suffice, we derive Bloch-like rotation of unit vectors analogous to the one familiar for a single spin in a magnetic field. The unitary evolution of a quantal spin pair is thereby expressed as rotations of real, many-dimensional vectors. Correspondingly, the manifolds involved are Bloch two-spheres along with higher dimensional manifolds such as a four-sphere for the SO(5) subgroup and an eight-dimensional Grassmannian manifold for the general SU(4). The latter may also be viewed as two, mutually orthogonal, real six-dimensional unit vectors moving on a five-sphere with an additional phase constraint. This geometrical picture for two spins provides the extension and generalization of the Bloch sphere that has proved invaluable for the understanding of the dynamics of a single spin.

By solving the three-dimensional time-dependent Schrödinger equation, we study how to control the high-order harmonic generation (HHG) in a hydrogenlike neon, which is exposed to an extreme-ultraviolet (xuv) attosecond laser pulse followed by an infrared (ir) femtosecond pulse. The xuv pulse prepares the atom as a superposition of the ground state, the excited states, and the continuum. These three types of states provide different contributions to the high-order harmonics generated by the following ir pulse. In particular, the contributions from the excited states and the continuum extend the cutoff frequency of the harmonic spectrum. Moreover, the effect of the carrier-envelope phase of the ir pulse on the HHG has been studied. The structure of the laser-dressed atom can be imaged using this two-color scheme.

Ionization of ${\mathrm{H}}_2\mathrm{O}$ is caused by four-cycle pulses of intense $800\text{−}\mathrm{nm}$ light in the temporal regime where processes like enhanced ionization and spatial alignment are “switched off” and recollision dominates the laser-molecule interaction. Nonadiabatic effects drive the overall dynamics in the few-cycle regime and give rise to multiple ionization of the molecule to electronically excited ionic states. The direct experimental manifestation of such nonadiabatic effects is in significantly higher amounts of kinetic energy being released upon dissociation into atomic fragments. The energy spectrum of ${\mathrm{H}}^{+}$ fragments enables us to deduce that recollision of the optical-field-ejected electron with the molecular ion drives the overall dynamics.

The quantum Monte Carlo method for spin-$\frac{1}{2}$ fermions at finite temperature is formulated for dilute systems with an $s$-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature $T_c$ for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $-0.5⩽{\left(k_{F}a\right)}^{-1}⩽0.2$, where $a$ is the $s$-wave scattering length and $k_F$ is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature $T_0>T_c$, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For $T_c<T<T_0$ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.

The density distributions of the two components of a trapped, ultracold Fermi gas with population imbalance reveal the effect of imbalance on superfluid pairing. We develop a path-integral derivation of the density, that takes into account both fluctuations beyond mean-field and effects of nonzero temperature. The calculated density profiles compare favorably to the measured density profiles, and illustrate the necessity to incorporate both quantum fluctuations and finite temperature effects. The temperature dependence of the density profiles, especially near the superfluid-normal interface, allows for determining the temperature of the superfluid core in current experiments.

We report on a complete free-space field implementation of a modified Ekert protocol for quantum key distribution using entangled photon pairs. For each photon pair we perform a random choice between key generation and a Bell inequality. The amount of violation is used to determine the possible knowledge of an eavesdropper to ensure security of the distributed final key.

We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval.

Using a generalization of Cayley’s hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six “single-particle” states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single-particle states we propose to use the Plücker relations as a sufficient and necessary condition of separability.

A physical implementation of the adiabatic Grover search is theoretically investigated in a system of $N$ identical three-level atoms trapped in a single-mode cavity. Some of the atoms are marked through the presence of an energy gap between their two ground states. The search is controlled by two partially delayed lasers which allow a deterministic adiabatic transfer from an initially entangled state to the marked states. Pulse schemes are proposed to satisfy the Grover speedup either exactly or approximately, and the success rate of the search is calculated.

The electric quadrupole moments of the metastable $n{d}_{3∕2}$ and $n{d}_{5∕2}$ states of ${\mathrm{Ca}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all nonlinear single and double terms are also calculated for the case of ${\mathrm{Ca}}^{+}$ for comparison of our approach with results of the coupled-cluster method with singles, doubles, and perturbative triples. Third-order many-body perturbation theory is used to evaluate the contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. An extensive study of the uncertainty of our calculations is carried out to establish the accuracy of our recommended values as 0.5–1 % depending on the particular ion. A comprehensive comparison of our results with other theoretical values and experimental results is carried out. Our result for the quadrupole moment of the $3d_{5∕2}$ state of the ${\mathrm{Ca}}^{+}$ ion, $1.849\left(17\right)e{a}_0^2$, is in agreement with the most precise recent measurement $1.83\left(1\right)e{a}_0^2$ by Roos et al. [Nature (London) 443, 316 (2006)].

We study the production of low-atom-number Fock states by sudden reduction of the potential trap in a one-dimensional strongly interacting (Tonks-Girardeau) gas. The fidelity of the Fock-state preparation is characterized by the average and variance of the number of trapped atoms. Two different methods are considered: making the trap shallower (atom culling [Dudarev et al., Phys. Rev. Lett. 98, 063001 (2007)], also termed “trap weakening” here) and making the trap narrower (trap squeezing). When used independently, the efficiency of both procedures is limited as a result of the truncation of the final state in momentum or position space with respect to the ideal atom-number state. However, their combination provides a robust and efficient strategy to create ideal Fock states.

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reproduce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.

We have performed precision electrostatic calibrations in the sphere-plane geometry and observed anomalous behavior. Namely, the scaling exponent of the electrostatic signal with distance was found to be smaller than expected on the basis of the pure Coulombian contribution and the residual potential found to be distance dependent. We argue that these findings affect the accuracy of the electrostatic calibrations and invite reanalysis of previous determinations of the Casimir force.

We have used the analogy between gravitational systems and nonhomogeneous fluid flows to calculate the density-density correlation function of an atomic Bose-Einstein condensate in the presence of an acoustic black hole. The emission of correlated pairs of phonons by Hawking-like process results into a peculiar long-range density correlation. Quantitative estimations of the effect are provided for realistic experimental configurations.

We provide a characterization and analysis of the effects of dissipation on oscillator assisted (qubus) quantum gates. The effects can be understood and minimized by looking at the dynamics of the signal coherence and its entanglement with the continuous variable probe. Adding loss in between successive interactions we obtain the effective quantum operations, providing an approach to loss analysis in such hybrid settings. We find that in the presence of moderate dissipation the gate can operate with a high fidelity. We also show how a simple iteration scheme leads to independent single qubit dephasing, while retaining the conditional phase operation regardless of the amount of loss incurred by the probe.

Two-qubit entanglement can be induced by a quantum data bus interacting with them. In this paper, with the quantum spin chain in the transverse field as an illustration of the quantum data bus, we show that such induced entanglement can be enhanced by the quantum phase transition (QPT) of the quantum data bus. We consider two external spins simultaneously coupled to a transverse field Ising chain. By adiabatically eliminating the degrees of the chain, the effective coupling between these two spins is obtained. The matrix elements of the effective Hamiltonian are expressed in terms of the dynamical structure factor (DSF) of the chain. The DSF is the Fourier transformation of the Green function of an Ising chain and can be calculated numerically by a method introduced by Derzhko and Krokhmalskii [Phys. Rev. B 56, 11659 (1997)]. Since all characteristics of QPT are embodied in the DSF, the dynamical evolution of the two external spins displays singularity in the vicinity of the critical point.

We review the generation of random pure states using a protocol of repeated two-qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism, the quantum analogue to the brachistochrone problem in classical mechanics [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006)]. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.

Simultaneously, the vibrational nuclear dynamics and full dimensional electronic dynamics of a deuterium molecular ion exposed to a linear polarized intense laser field are studied. The time-dependent Schrödinger equation of an aligned $\mathrm{D}_2{}^{+}$ ion with electric laser field is solved for a simulation of complicated dissociative ionization processes and compared with recent related experimental results. We introduce and calculate the $R$-dependent ionization rate and the enhanced ionization phenomenon beyond the Born-Oppenheimer approximation. The substructure of the nuclear kinetic energy release spectra is revealed as the Coulomb explosion energy spectra and dissociation energy spectra in the dissociation-ionization channel. The significance and trace of these distinct subspectra in the total spectra are comparatively displayed and discussed.