Quantum walks, being the quantum analog of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the “glued trees” algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed and discuss potential applications to quantum search for marked vertices along these graphs.

We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. We compare the scheme with full state tomography.

We show that the thermal entanglement in a spin system using only magnetic-susceptibility measurements is restricted to the insulator materials. We develop a generalization of the thermal entanglement witness that allows us to get information about the system entanglement with variable local spin lengths that can be used experimentally in conductor or insulator materials. As an application, we study thermal entanglement for the half-filled Hubbard model for linear, square, and cubic clusters. We note that it is the itinerancy of electrons that favors the entanglement. Our results suggest a weak dependence between entanglement and external spin freedom degrees.

We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method for providing two faithful copies of a two-photon mixed state required for parity measurements: two photon pairs generated by two neighboring pump-laser pulses through optical parametric down-conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multiphoton mixed states.

We present an analysis of the recent measurements of the light-shift ratio in ${\text{Ba}}^{+}$ at two different wavelengths that enables us to reduce the uncertainty of the largest $E1$ dipole matrix elements of ${\text{Ba}}^{+}$. These matrix elements are, for instance, of interest for the proposed parity-nonconservation (PNC) experiment in ${\text{Ba}}^{+}$. We show that a new measurement of the light-shift ratio in ${\text{Ba}}^{+}$ at a wavelength of 350 nm could further reduce the uncertainty of the (for PNC studies most important) $⟨5D_{3/2}|\left|D\right||6P_{1/2}⟩$ matrix element. Finally, as groundwork for the planned PNC experiment at KVI, we present relativistic coupled-cluster calculations of the $E1$ matrix elements for ${\text{Ra}}^{+}$, and investigate the potential of similar light-shift ratio measurements in this ion.

In this paper, the $K$-shell ionization cross sections of Si element in the threshold energy region of 3–25 keV have been measured by using the thick-target method. With the Monte Carlo simulations, the effects of multiple scattering of incident electrons and from the bremsstrahlung photons and other secondary particles in the thick-target method have been discussed. The detection efficiency calibration in the lower-energy region has been performed by using the bremsstrahlung spectra of thick carbon target by electron impact in combination with the use of standard x-ray sources, and the detector thickness parameters have also been determined by a nonlinear least-squares fit. The ill-posed inverse problem involved in the thick-target method has been dealt with by the Tikhonov regularization method. The experimental $K$-shell ionization cross sections for Si element obtained in this paper have also been compared with some theoretical models, and it has been observed that the experimental data in this paper are in good agreement with the theoretical values based on the distorted-wave Born approximation model developed most recently.

It is the purpose of the present paper to study the dynamics underlying a three-pulse photon-echo process performed on a vibronic system coupled to non-Markovian baths, when a neighboring level enters into the global dynamical evolution because of broadband excitation required in these experiments. Particular emphasis is on the energy gap between the vibronic levels, but also on the fluctuation amplitudes and correlation times of their corresponding thermal baths. The photon-echo signal appears to be very sensitive to the additional interfering contributions introduced by the neighboring vibronic level. It is shown that these contributions associated to the pathways involving different vibronic states are modulated by their corresponding energy gap. As a consequence, these contributions to the integrated photon-echo signal strongly decrease for large energy gaps. Also, an oscillating behavior is observed on the time dependence of the photon-echo signal resulting from the summation of the contributions provided by the individual vibronic levels. Moreover, the influence of the non-Markovian character of the baths, accountable for inhomogeneous broadening, affects the amplitude and the time dependence of the photon-echo signal, as well as its dependence with the delay time of the laser pulses. Of course, for longer times a Markovian dynamical evolution is recovered.

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition and show that superfluidity is even more sensitive to imbalance than for three-dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allows to identify a phase-separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.

We examine the behavior of single photons at multiport devices and inquire if coherent effects are possible. In particular we study how single photons need to be manipulated in order to study coherent phenomena. We show that single photons need to be produced in $W$ states which lead to vanishing mean amplitude but nonzero correlations between the inputs at different ports. Such correlations restore coherent effects with single photons. As a specific example we demonstrate Bloch oscillations with single photons and thus provide strict analog of Bloch oscillation of electrons.

We consider thin lamellar and cylinder gratings, composed of silicon carbide and air, and investigate the conditions under which they can totally absorb an incident plane wave, for both $p$ and $s$ polarizations. We also consider thin-film equivalent in the quasistatic limit to the gratings, deriving the effective dielectric tensor for cylinder gratings. We show that the accuracy of the quasistatic models is a strong function of polarization, wavelength, and grating thickness due to the resonant nature of the optical constants of silicon carbide but that these models can be quantitatively accurate and give a good qualitative guide to the parameter values under which thin gratings can deliver high optical absorptance.

We consider in this paper a two-pulse photon echo sequence in the prospect of quantum light storage. We analyze the conditions where quantum storage could be realistically performed. We simply and analytically calculate the efficiency in that limit, and clarify the role of the exactly $\pi$-rephasing pulse in the sequence. Our physical interpretation of the process is well supported by its experimental implementation in a ${\text{Tm}}^{3+}$:yttrium aluminum garnet crystal thanks to an accurate control of the rephasing pulse area. We finally address independently the fundamental limitations of the quantum fidelity. Our work allows us to point out on one side the real drawbacks of this scheme for quantum storage and on the other side its specificities which can be a source of inspiration to conceive more promising procedures with rare-earth ion doped crystals.

A Bose gas with repulsive interactions in a generic power-law potential is studied in the Hartree-Fock approximation. The scaling parameter characterizing the role of two-body repulsive interactions is expressed in terms of the scaled scattering length and the trap parameter. The chemical potential obtained here provides a correction to the existing analytical result, especially in the critical region of Bose-Einstein condensation.

Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realms. As a result, a dynamical constant for the electromagnetic field is identified and linked to the symmetry operator which supports it.

By making use of the quantization rule of Raab and Friedrich [Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules.

We have measured cold inelastic collisions between neutral ground-state titanium atoms: collisions that cause transitions between the different magnetic sublevels of the $\left[3d^{2}4s^2\right]{{}^{3}F}_2$ ground state of ${}^{50}\text{T}\text{i}$, as well as collisions that cause transitions between the fine-structure levels of the $\left[3d^{2}4s^2\right]{{}^{3}F}_J$ electronic ground state. Both processes occur with large rate coefficients, as would be expected from titanium’s anisotropic electronic potential.

In one-dimensional quantum lattice models with open boundaries, we find and study localization at the lattice edge. We show that edge-localized eigenstates can be found in both bosonic and fermionic systems, specifically, in the Bose-Hubbard model with on-site interactions and in the spinless fermion model with nearest-neighbor interactions. We characterize the localization through spectral studies via numerical diagonalization and perturbation theory through considerations of the eigenfunctions and through the study of explicit time evolution. We concentrate on few-particle systems, showing how more complicated edge states appear as the number of particles is increased.

We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related, models: the sequential measurement model, the Arthurs-Kelly model, and the eight-port homodyne detection model. In each case, the method of moments gives the position and momentum distributions for a large class of initial states, the relevant condition being the exponential boundedness of the distributions.

The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic, and super-Ohmic environments, without performing the Markovian approximation. Our results allow one to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

An exact analytical approach is used to explore the dynamics of the decaying probability density and the probability current in multibarrier systems. We show that resonance state interference produces the appearance of breathing or bouncing modes in the dynamical behavior of the probability density along the internal region of the system. This dynamical process involves the reconstruction of the initial state and it is responsible for the pulsed features of the decay recently discussed for the survival probability in these systems.

We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a “classical state,” such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.