I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

Anharmonicity of the quantized motional states of ions in a Paul trap can be utilized to address the state-to-state transitions selectively and control the motional modes of trapped ions coherently and adiabatically [Zhao and Babikov, Phys. Rev. A 77, 012338 (2008)]. In this paper we study two sources of the vibrational anharmonicity in the ion traps: the intrinsic Coulomb anharmonicity due to ion-ion interactions and the external anharmonicity of the trapping potential. An accurate numerical approach is used to compute energies and wave functions of vibrational eigenstates. The magnitude of the Coulomb anharmonicity is determined and shown to be insufficient for successful control. In contrast, anharmonicity of the trapping potential allows one to control the motion of ions very efficiently using the time-varying electric fields. Optimal control theory is used to derive the control pulses. One ion in a slightly anharmonic trap can be easily controlled. In the two- and three-ion systems the symmetric stretching mode is dark and cannot be controlled at all. The other two normal modes of the three-ion system can be controlled and used, for example, to encode a two-qubit system into the motional states of ions. A trap architecture that allows the necessary amount of vibrational anharmonicity to be achieved is proposed.

We discuss theoretically ion-atom collisions at low energy and predict the possibility of the formation of a cold molecular ion by photoassociation. We present results from radiative homo- and heteronuclear atom-ion cold collisions that reveal threshold behavior of atom-ion systems.

We present combined experimental and theoretical results on strong-field ionization of oriented carbonyl sulfide molecules by circularly polarized laser pulses. The obtained molecular frame photoelectron angular distributions show pronounced asymmetries perpendicular to the direction of the molecular electric dipole moment. These findings are explained by a tunneling model invoking the laser-induced Stark shifts associated with the dipoles and polarizabilities of the molecule and its unrelaxed cation. The focus of the present article is to understand the strong-field ionization of one-dimensionally-oriented polar molecules, in particular asymmetries in the emission direction of the photoelectrons. In the following article [Phys. Rev. A 83, 023406 (2011)] the focus is to understand strong-field ionization from three-dimensionally-oriented asymmetric top molecules, in particular the suppression of electron emission in nodal planes of molecular orbitals.

We present a combined experimental and theoretical study on strong-field ionization of a three-dimensionally-oriented asymmetric top molecule, benzonitrile (${\mathrm{C}}_7{\mathrm{H}}_5\mathrm{N}$), by circularly polarized, nonresonant femtosecond laser pulses. Prior to the interaction with the strong field, the molecules are quantum-state selected using a deflector and three-dimensionally (3D) aligned and oriented adiabatically using an elliptically polarized laser pulse in combination with a static electric field. A characteristic splitting in the molecular frame photoelectron momentum distribution reveals the position of the nodal planes of the molecular orbitals from which ionization occurs. The experimental results are supported by a theoretical tunneling model that includes and quantifies the splitting in the momentum distribution. The focus of the present article is to understand strong-field ionization from 3D-oriented asymmetric top molecules, in particular the suppression of electron emission in nodal planes of molecular orbitals. In the preceding article [Dimitrovski et al., Phys. Rev. A 83, 023405 (2011)] the focus is to understand the strong-field ionization of one-dimensionally-oriented polar molecules, in particular asymmetries in the emission direction of the photoelectrons.

We present an efficient method for subrecoil cooling of neutral atoms by applying Raman cooling in two dimensions to a four-level tripod system. The atoms can be cooled simultaneously in two directions using only three laser beams. We describe the cooling process with a simple model showing that the momentum distribution can be rapidly narrowed to velocity spread down to $0.1v_{\mathrm{rec}}$, corresponding to effective temperature equal to $0.01T_{\mathrm{rec}}$. This method opens new possibilities for cooling of neutral atoms.

Quantum Monte Carlo simulations of a two-component Bose mixture of trapped dipolar atoms of identical masses and dipole moments, provide numerical evidence of demixing at low finite temperatures. Demixing occurs as a consequence of quantum statistics, which results in an effective attraction between like bosons. Spatial separation of two components takes place at low temperature with the onset of long exchanges of identical particles, underlying Bose-Einstein condensation of both components. Conversely, at higher temperature the system is miscible due to the entropy of mixing. Exchanges are also found to enhance demixing in the case of mixtures of nonidentical and distinguishable species.

It has now been possible to prepare a chain of ions in an entangled state and thus the question arises: How will the optical properties of a chain of entangled ions differ from say a chain of independent particles? We investigate nonlinear optical processes in such chains. Since light scattering is quite a versatile technique to probe matter, we explicitly demonstrate the possibility of entanglement-produced super Raman scattering. Our results suggest the possibility of similar enhancement factors in other nonlinear processes like four-wave mixing.

We theoretically investigate the mode-splitting phenomenon in a high-$Q$ whispering-gallery-mode (WGM) microresonator coupled to multiple subwavelength Rayleigh scatterers. It is shown that the phase factors of the WGMs play the central role in such a system. Unlike the single-scatterer case, these phase factors in a multiscatterer system significantly influence both the modal coupling strength and the scattering-induced loss of a pair of counterpropagating WGMs. We scrutinize the condition for observing the splitting of transmission spectra. The mechanism can be used for highly sensitive biosensing, and the size of nanoparticles that can be detected is extended down to tens of nanometers.

We have used x-ray waveguides as highly confining optical elements for nanoscale imaging of unstained biological cells using the simple geometry of in-line holography. The well-known twin-image problem is effectively circumvented by a simple and fast iterative reconstruction. The algorithm which combines elements of the classical Gerchberg-Saxton scheme and the hybrid-input-output algorithm is optimized for phase-contrast samples, well-justified for imaging of cells at multi-keV photon energies. The experimental scheme allows for a quantitative phase reconstruction from a single holographic image without detailed knowledge of the complex illumination function incident on the sample, as demonstrated for freeze-dried cells of the eukaryotic amoeba Dictyostelium discoideum. The accessible resolution range is explored by simulations, indicating that resolutions on the order of $20$ nm are within reach applying illumination times on the order of minutes at present synchrotron sources.

The scattering of temporally shaped intense laser pulses off electrons is discussed by means of manifestly covariant quantum electrodynamics. We employ a framework based on Volkov states with a time-dependent laser envelope in light-cone coordinates within the Furry picture. An expression for the cross section is constructed unambiguously in respect of the pulse length. A broad distribution of scattered photons with a rich pattern of subpeaks like that obtained in Thomson scattering is found. These broad peaks may overlap at sufficiently high laser intensity, rendering inappropriate the notion of individual harmonics. The limit of monochromatic plane waves as well as the classical limit of Thomson scattering are discussed. As a main result, a scaling law is presented connecting the Thomson limit with the general result for arbitrary kinematics. In the overlapping regions of the spectral density, the classical and quantum calculations give different results, even in the Thomson limit. Thus, a phase-space region is identified where the differential photon distribution is strongly modified by quantum effects.

We study the emission of $L\alpha$, $L\beta$, and $L\gamma$ characteristic x rays by the impact of electrons on Hf, Ta, W, Re, Os, Au, Pb, and Bi atoms. To this end, ionization cross sections of the $L_1$, $L_2$, and $L_3$ subshells of these atoms are calculated within the distorted-wave Born approximation. The considered energy interval spans from the ionization threshold up to 50 keV. Atomic relaxation parameters (i.e., Coster-Kronig and radiative transition probabilities, fluorescence yields, and emission rates) taken from the literature are then used to evaluate x-ray production cross sections. The theoretical predictions are compared with published experimental information. Good agreement is found for Ta, W, Os, Au, Pb, and Bi. In the case of Hf and Re, the measured cross sections are lower than the theoretical estimates by around 30%. The observed discrepancies might be attributed to the methods employed to correct the raw experimental data for the excess of detected characteristic x rays caused by the finite thickness of the sample’s active layer and the presence of the thick substrate.

We report the results of semiclassical calculations of the asymmetric molecular-frame photoelectron angular distributions for C 1$s$ ionization of CO${}_2$ measured with respect to the CO${}^{+}$ and ${\mathrm{O}}^{+}$ ions produced by subsequent Auger decay, and show how the decay event can be used to probe ultrafast molecular dynamics of the transient cation. The fixed-nuclei photoionization amplitudes were constructed using variationally obtained electron–molecular-ion scattering wave functions. The amplitudes are then used in a semiclassical manner to investigate their dependence on the nuclear dynamics of the cation. The method introduced here can be used to study other core-level ionization events.

Improving and controlling the efficiency of a gain medium is one of the most challenging problems of laser research. By measuring the gain length in an opal-based photonic crystal doped with laser dye, we demonstrate that optical amplification is more than twenty-fold enhanced along the $\Gamma$-$K$ symmetry directions of the face-centered-cubic photonic crystal. These results are theoretically explained by directional variations of the density of states, providing a quantitative connection between density of the states and light amplification.

Controlling the depolarization of light is a long-standing open problem. In recent years, many demonstrations have used the polarization of single photons to encode quantum information. The depolarization of these photons is equivalent to the decoherence of the quantum information they encode. We present schemes for building various depolarizing channels with controlled properties using birefringent crystals. Three such schemes are demonstrated, and their effects on single photons are shown by quantum process tomography to be in good agreement with a theoretical model.

We report results of many-electron calculations that predict the presence of a regular series of autoionizing doubly excited states (DESs) of ${}^1{P}^o$symmetry embedded inside one- as well as two-electron continua of neon, in the range of excitation 105.9–121.9 eV above the ground state. The limit of 121.9 eV represents the two-electron ionization threshold (TEIT) labeled by Ne${}^{2+}$ $1s^{2}2p^6$ ${}^{1}S$. The wave functions of these unstable states and their properties are computed according to the theoretical framework, which is explained and justified in the text. Their formal structure is $({\psi }_{\mathrm{core}}){}^{1}S\otimes \Phi (\overrightarrow{r_1},\overrightarrow{r_2}){}^1{P}^o$, where both ${\psi }_{\mathrm{core}}$ and $\Phi ({\mathrm{r⃗}}_1,{\mathrm{r⃗}}_2)$ are correlated wave functions, the latter being represented reasonably accurately by a self-consistently obtained superposition of $\mathrm{nsnp}$ and $\mathit{np}(n+1)d$ configurations $n$$=$3–7. By fitting the calculated lowest energies at each value of $n$, (five states), an effective hydrogenic formula is obtained, which gives the whole energy spectrum up to the TEIT. The autoionization widths are small and decrease with excitation energy. Oscillator strengths for the excitation of these narrow resonance states by absorption of one photon are also small. Because of their electronic structure, these states are compared to ${}^1{P}^o$ DESs in He, which were found in the 1980s to constitute a regular ladder with wave-function characteristics that tend to those of the so-called Wannier state at threshold. In the present case, the presence of the core and the concomitant interactions do not permit the emergence of such geometrical features.

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green’s function. The results of both calculations were shown to agree for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green’s function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.

We present a unified treatment of the prevalence of different nonsequential double ionization pathways in strongly driven helium as a function of the sum of the final electron energies and of the laser frequency and intensity. At high total energy the pathway that dominates is the one where one electron is ionized with a delay following recollision. At low total energy, a double ionization pathway dominates where recollision the two electrons and the nucleus form a bound compound for at least a quarter of a laser cycle. We also identify asymptotic observables that trace the prevalence of these pathways.

Naively, one may think that increasing temperature causes quantum coherence to decrease. Using finite-temperature perturbation theory and exact calculations for the strongly correlated bosonic Mott insulating state, we show a practical counterexample that can be explored in optical lattice experiments: the short-range coherence of the Mott insulating phase can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near-zero temperature coherence properties have been measured with high precision, we expect these results to be verifiable in current experiments.

Private queries allow a user, Alice, to learn an element of a database held by a provider, Bob, without revealing which element she is interested in, while limiting her information about the other elements. We propose to implement private queries based on a quantum-key-distribution protocol, with changes only in the classical postprocessing of the key. This approach makes our scheme both easy to implement and loss tolerant. While unconditionally secure private queries are known to be impossible, we argue that an interesting degree of security can be achieved by relying on fundamental physical principles instead of unverifiable security assumptions in order to protect both the user and the database. We think that the scope exists for such practical private queries to become another remarkable application of quantum information in the footsteps of quantum key distribution.