We establish an information-theoretic approach for quantitatively characterizing the non-Markovianity of open quantum processes. Here, the quantum Fisher information (QFI) flow provides a measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly analytic solution shows that for each fixed time the QFI flow is decomposed into additive subflows according to different dissipative channels.

In this work we generate two-photon hybrid entangled states (HESs), where the polarization of one photon is entangled with the transverse spatial degree of freedom of the second photon. The photon pair is created by parametric down-conversion in a polarization-entangled state. A birefringent double-slit couples the polarization and spatial degrees of freedom of these photons, and finally, suitable spatial and polarization projections generate the HES. We investigate some interesting aspects of the two-photon hybrid interference and present this study in the context of the complementarity relation that exists between the visibility of the one-photon and that of the two-photon interference patterns.

The pressure broadening and shift rates for the cesium ( ) transition with the noble gases and , , HD, , CH, H, CF, and were obtained for pressures less than 300 Torr at a temperature of C by means of laser absorption spectroscopy. The collisional broadening rate for He, Ne, Ar, Kr, Xe, , , HD, , CH, H, CF, and are 20.59, 9.81, 16.47, 15.54, 18.41, 19.18, 27.13, 28.24, 22.84, 25.84, 26.14, 17.81, and 22.35 MHz/Torr, respectively. The uncertainty in the broadening rates is typically less than . The corresponding pressure-induced shift rates are , , , , , , , , , , , , and MHz/Torr with an uncertainty of less than 0.04 MHz/Torr. With the exception of diatomic collision partners, the broadening rates for Cs are – less than the rates for Cs . For light collision partners with a blue shift, the is shifted more than the line. The broadening cross sections for Cs and Rb are similar. However, the cross sections for K are about larger and for Na, about less.

For a positron with wave number $k$, the rate of annihilation when scattered by an atom or molecule is proportional to $Z_{\mathrm{eff}}(k)$, the effective number of electrons in the target that are available to the positron for annihilation. There is currently great interest in the very large positron annihilation rates, and hence values of $Z_{\mathrm{eff}}(k)$, that have been observed in low-energy positron scattering by some molecules. These are observed experimentally to occur at energies just below the energies of excited vibrational states of the molecule concerned. This has been explained by Gribakin [Phys. Rev. A 61, 022720 (2000)] and Gribakin and Lee [Phys. Rev. Lett. 97, 193201 (2006)] as being due to Feshbach resonances involving excited quasibound vibrational states. These treatments make skilful use of approximate methods. It is of interest to determine how the expression obtained for the resonant contribution to $Z_{\mathrm{eff}}(k)$ from a quasibound state using a very accurate method is related to the expressions obtained in the previously mentioned articles. In view of this, in this article I carry out a detailed ab initio theoretical treatment of positron scattering by ${\mathrm{H}}_2$ using the Kohn variational method. ${\mathrm{H}}_2$ is the simplest molecule, which makes it easier to take into account all the interactions involved. However, a positron does not form a bound state with ${\mathrm{H}}_2$. To investigate resonant behavior in $Z_{\mathrm{eff}}(k)$, I increase the mass $m_p$ of the positron so that it forms a weakly bound state with ${\mathrm{H}}_2$. This gives rise to excited quasibound vibrational states. The expression I obtain for the resonant contribution to $Z_{\mathrm{eff}}(k)$ has some similarity with the expressions obtained by Gribakin and Lee. This gives some support to their explanation of the very large values of $Z_{\mathrm{eff}}(k)$. However, they make no explicit mention of corrections to the Born-Oppenheimer (BO) approximation. These play a key role in my treatment as they couple the quasibound states to the continuum. I am able to show how the BO corrections are taken into account implicitly in calculating the expressions obtained by Gribakin and Lee. The most important difference between my treatment and their treatments is that in my treatment $Z_{\mathrm{eff}}(k)$ may be infinite at the resonant energy, whereas in the other treatments it is likely to be large, but can never be infinite. Further investigation is necessary to determine the origin of this infinity in my treatment. My treatment could be applied to positron scattering by molecules such as methyl halides in which very high $Z_{\mathrm{eff}}(k)$ values are observed, though using the Kohn variational method would be considerably more complicated than in the case of ${\mathrm{H}}_2$.

A generalized approach is derived for the analysis of angle-resolved coherent optical wave mixing. Remarkably with this, a signal is calculated to remain efficiently generated for the arbitrary evolution of a quantum superposition state and for energy transfer spanning an ultrawide bandwidth in solution. This approach is compact and applies across matter processes and wave-mixing schemes. A high sensitivity and sampling rate are shown to be intrinsic to angle-resolved wave mixing and an angle-resolved six-wave mixing scheme is proposed for the mapping of molecular structure.

The technique of stimulated Raman adiabatic passage (STIRAP) is an efficient and robust technique for population transfer in three-state chain-wise connected quantum systems, 1-2-3. Here we analyze the transition time in STIRAP, that is the time it takes for the population to be transferred from state 1 to state 3. We derive a very simple formula for this transition time, which shows that it is inversely proportional to the nonadiabatic coupling $\mathrm{\vartheta ̇}(t_c)$, estimated at the time $t_c$ when the pump and Stokes couplings have the same value. Explicit formulas for several pulse shapes of the pump and Stokes fields are derived. Contrary to the naive expectation that the transition time might be proportional to the delay between the pump and Stokes pulses, or to the width of their overlap region, we find that the transition time is inversely proportional to the delay, i.e., larger delays produce faster transitions. We also calculate the transition time in two important variations of the STIRAP technique—bright-STIRAP and STIRAP in multistate systems—where similar features are found.

We demonstrate a simple technique to measure the resonant frequency of the 398.9-nm ${}^1{S}_0\leftrightarrow {}^1{P}_1$ transition for the different Yb isotopes. The technique, which works by observing and aligning fluorescence spots, has enabled us to measure transition frequencies and isotope shifts with an accuracy of 60 MHz. We provide wavelength measurements for the transition that differ from previously published work. Our technique also allows for the determination of Doppler-shifted transition frequencies for photoionization experiments when the atomic beam and the laser beam are not perpendicular and furthermore allows us to determine the average velocity of the atoms along the direction of the atomic beam.

We use our recently proposed model to extract information about the nuclear dynamics from the Coulomb explosion data of Staudte et al. [Phys. Rev. Lett. 98, 073003 (2007)]. Those data, taken at multiple intensities near the ionization appearance intensity for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ in linearly and circularly polarized light, show remarkable structure and regularity not easily explained by conventional models. Because our model does fit the spectra well, we can infer the qualitative time-dependent evolution of the system. In addition, it suggests a possible experimental signature of rescattering leading to above-threshold Coulomb explosion.

The dynamic process of fragmentation of ${\mathrm{CO}}^{q+}$ excited states is investigated using a pump-probe approach. EUV radiation (32–48 eV) generated by high-order harmonics was used to ionize and excite CO molecules and a time-delayed infrared (IR) pulse (800 nm) was used to influence the evolution of the dissociating multichannel wave packet. Two groups of states, separable experimentally by their kinetic-energy release (KER), are populated by the EUV and lead to ${\mathrm{C}}^{+}$-${\mathrm{O}}^{+}$ fragmentation: direct double ionization of the neutral molecule and fragmentation of the cation leading to ${\mathrm{C}}^{+}$-${\mathrm{O}}^{*}$, followed by autoionization of ${\mathrm{O}}^{*}$. The IR pulse was found to modify the KER of the latter group in a delay-dependent way which is explained with a model calculation.

Optical forces induced by a near field are calculated for a 1-mm-sized metal particle mimicked by a jellium model and for ${\mathrm{C}}_{60}$ in the framework of real-time and real-space time-dependent density-functional theory combined with a nonuniform light-matter interaction formalism, fully taking account of multipole interaction. A highly localized near field nonuniformly polarizes these molecules. The locally induced polarization charges in the molecules are partly canceled by the screening charges. The polarization and screening charges generally contribute to the attractive and repulsive forces, respectively, and a sensible balance between these charges results in several peaks in the optical force as a function of the frequency of the near field. The resonance excitation does not necessarily maximally induce the net force, and the force exerted on the molecules strongly depends on the details of their electronic structures. The optical force is larger in the metal particle than in ${\mathrm{C}}_{60}$. We also found that the optical force depends linearly on the intensity of the near field.

The quantum dynamics of particles optically trapped in a symmetrically pumped high-$Q$ ring cavity exhibits much richer physics than for a standing-wave resonator. In addition to modifying the lattice depth, light scattering by the particles shifts and reshapes the trapping potential. We calculate the corresponding changes in tunneling amplitudes and damping by an effective bipotential (two-level) model for the particle motion. As a crude truncation of the Bose-Hubbard model, expansion to the lowest band decouples particle and field dynamics. Only including excitations to higher bands can capture this essential additional physics and correctly describe decoherence, damping, and long-range correlations of the particle dynamics. The validity limits of the analytic models are confirmed by quantum Monte Carlo wave-function simulations, which exhibit correlated particle-field quantum jumps as unambiguous quantum signature of the system dynamics.

We study the process of copolarized spontaneous four-wave mixing in single-mode optical fibers, with an emphasis on an analysis of the conversion efficiency. We consider both the monochromatic-pump and pulsed-pump regimes, as well as both the degenerate-pump and nondegenerate-pump configurations. We present analytical expressions for the conversion efficiency, which are given in terms of double integrals. In the case of pulsed pumps we take these expressions to closed analytical form with the help of certain approximations. We present results of numerical simulations, and compare them to values obtained from our analytical expressions, for the conversion efficiency as a function of several key experimental parameters.

Based on mutually unbiased measurements, an optimal tomographic scheme for the multiqutrit states is presented explicitly. Because the reconstruction process of states based on mutually unbiased states is free of information waste, we refer to our scheme as the optimal scheme. By optimal we mean that the number of the required conditional operations reaches the minimum in this tomographic scheme for the states of qutrit systems. Special attention will be paid to how those different mutually unbiased measurements are realized; that is, how to decompose each transformation that connects each mutually unbiased basis with the standard computational basis. It is found that all those transformations can be decomposed into several basic implementable single- and two-qutrit unitary operations. For the three-qutrit system, there exist five different mutually unbiased-bases structures with different entanglement properties, so we introduce the concept of physical complexity to minimize the number of nonlocal operations needed over the five different structures. This scheme is helpful for experimental scientists to realize the most economical reconstruction of quantum states in qutrit systems.

We report on the dissipative dynamics of an entangled, bipartite interacting system. We show how to induce and control the so-called early-stage disentanglement (and “delayed” entanglement generation) dynamics by means of a driving laser field. We demonstrate that some of the features currently associated with pure non-Markovian effects in such entanglement behavior can actually take place in Markovian environments if background-noise quantum electrodynamics fluctuations are considered. We illustrate this for the case of a dimer interacting molecular system for which emission rates, interaction strength, and radiative corrections have been previously measured. We also show that even in the absence of collective decay mechanisms and qubit-qubit interactions, the entanglement still exhibits collapse-revival behavior. Our results indicate that zero-point energy fluctuations should be taken into account when formulating precise entanglement dynamics statements.

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum “walker” evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This “discontinuous” quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.

We formulate and investigate the simplest version of time-optimal quantum computation theory (TO-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version of TO-QCT is also considered as optimality by sub-Riemannian geodesic length. The work has two aims: One is to develop a TO-QCT itself based on a physically natural concept of time, and the other is to pursue the possibility of using TO-QCT as a tool to estimate the complexity in conventional gate-optimal quantum computation theory (GO-QCT). In particular, we investigate to what extent is true the following statement: Time complexity is polynomial in the number of qubits if and only if gate complexity is also. In the analysis, we relate TO-QCT and optimal control theory (OCT) through fidelity-optimal computation theory (FO-QCT); FO-QCT is equivalent to TO-QCT in the limit of unit optimal fidelity, while it is formally similar to OCT. We then develop an efficient numerical scheme for FO-QCT by modifying Krotov’s method in OCT, which has a monotonic convergence property. We implemented the scheme and obtained solutions of FO-QCT and of TO-QCT for the quantum Fourier transform and a unitary operator that does not have an apparent symmetry. The former has a polynomial gate complexity and the latter is expected to have an exponential one which is based on the fact that a series of generic unitary operators has an exponential gate complexity. The time complexity for the former is found to be linear in the number of qubits, which is understood naturally by the existence of an upper bound. The time complexity for the latter is exponential in the number of qubits. Thus, both the targets seem to be examples satisfyng the preceding statement. The typical characteristics of the optimal Hamiltonians are symmetry under time reversal and constancy of one-qubit operation, which are mathematically shown to hold in fairly general situations.

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use ${}^{13}\mathrm{C}$ nuclear spins as qubits and an environment of ${}^1\mathrm{H}$ nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 $\mu$s. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

A method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomiclike Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are generated by solving numerically the one-center Dirac and Dirac-Sturm equations by means of a finite-difference approach with the Coulomb potential taken as the sum of the exact reference-nucleus potential and of the other nucleus within the monopole approximation. An original procedure for calculating the two-center integrals with these orbitals is proposed. As a first test of the approach developed here, calculations of the charge-transfer and ionization cross sections for the H($1s$)-proton collisions at proton energies from 1 to 100 keV are performed. The obtained results are compared with related experimental and other theoretical data. To investigate the role of the relativistic effects, the charge-transfer cross sections in collisions of Ne${}^{9+}$($1s$)-Ne${}^{10+}$ (at energies from $0.1$ to $10$ MeV/u) and ${\mathrm{U}}^{91+}$($1s$)-U${}^{92+}$ (at energies from 6 to 10 MeV/u) are calculated for both relativistic and nonrelativistic cases.

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.

We propose an experiment to probe ferromagnetic phenomena in an ultracold Fermi gas, while alleviating the sensitivity to three-body loss and competing many-body instabilities. The system is initialized in a small pitch spin spiral, which becomes unstable in the presence of repulsive interactions. To linear order the exponentially growing collective modes exhibit critical slowing down close to the Stoner transition point. Also, to this order, the dynamics are identical on the paramagnetic and ferromagnetic sides of the transition. However, we show that scattering off the exponentially growing modes qualitatively alters the collective mode structure. The critical slowing down is eliminated and in its place a new unstable branch develops at large wave vectors. Furthermore, long-wavelength instabilities are quenched on the paramagnetic side of the transition. We study the experimental observation of the instabilities, specifically addressing the trapping geometry and how phase-contrast imaging will reveal the emerging domain structure. These probes of the dynamical phenomena could allow experiments to detect the transition point and distinguish between the paramagnetic and ferromagnetic regimes.