Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor’s algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to $N=943$ show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength ${ϵ}_c$ which drops only polynomially with ${\log }_{2}N$. The numerical dependence of ${ϵ}_c$ on ${\log }_{2}N$ is explained by analytical estimates that allows one to obtain the scaling for functionality of Shor’s algorithm on realistic quantum computers with a large number of qubits.

In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.

We analyze, both experimentally and via semiclassical Monte Carlo simulations, a cold atom ratchet with multifrequency driving. We investigate the relationship between symmetries and transport both in the case of a periodic driving and in the quasiperiodic limit. We also study quantitatively the line shape and linewidth of the ratchet current, and their dependence on the interaction parameters.

We study the Hartree ground state of a dipolar condensate of atoms or molecules in a three-dimensional anisotropic geometry and at $T=0$. We determine the stability of the condensate as a function of the aspect ratios of the trap frequencies and of the dipolar strength. We find numerically a rich phase space structure characterized by various structures of the ground-state density profile.

We consider an atomic quantum dot confined between two weakly coupled Bose-Einstein condensates, where the dot serves as an additional tunneling channel. It is shown that the thus-embedded atomic quantum dot is a pseudospin subject to an external torque, and therefore equivalent to a quantum top. We demonstrate by numerical analysis of the time-dependent coupled evolution equations that this microscopic quantum top is very sensitive to any deviation from linear oscillatory behavior of the condensates. For sufficiently strong dot-condensate coupling, the atomic quantum dot can induce or modify the tunneling between the macroscopic condensates in the two wells.

The electromagnetic wave momentum is derived for a Lorentz medium and applied to study the momentum transfer to stationary, isotropic left-handed materials. The model includes material dispersion and losses, which are necessary for a causal medium with negative index of refraction. The results provide a rigorous proof of the force on free currents in a lossy medium and a validation of the theoretical separation of force based on the real and imaginary parts of the permittivity and permeability. The resulting electromagnetic wave momentum conservation theorem proves that the momentum flux of a monochromatic wave in an isotropic left-handed material is opposite to the power flow direction. However, the momentum density in a lossy medium with a negative index of refraction may be parallel or antiparallel to the power flow. The results are applied to predict the reversal of radiation pressure on free currents in a material with a negative index of refraction. Furthermore, conservation of momentum at a material boundary states that the tangential component of the wave momentum is conserved. Thus there is no electromagnetic shear force at the boundary between isotropic media, regardless of the sign of the refractive index.

We report strong even-odd effects in multiple ionization yields of van der Waals dimers in slow ${\mathrm{Xe}}^{30+}+\left[{\mathrm{C}}_{60}{]}_2\right(\left[{\mathrm{C}}_{60}{\mathrm{C}}_{70}\right])\to \cdots +{[{\mathrm{C}}_{60}{]}_2}^{r+}({\left[{\mathrm{C}}_{60}{\mathrm{C}}_{70}\right]}^{r+})$ electron-transfer collisions as functions of $r\le 7$. This behavior may be due to even-odd variations in the sequences of dimer ionization energies as calculated with an electrostatic model including an electrical fullerene-fullerene contact at the $19a_0$ center-center separation in ${[{\mathrm{C}}_{60}{]}_2}^{+}$. Prompt dissociations predominantly yield intact fullerenes ${[{\mathrm{C}}_{60}{]}_2}^{r+}\to {{\mathrm{C}}_{60}}^{r_1+}+{{\mathrm{C}}_{60}}^{r_2+}$ in the same ($r_1=r_2$, even $r$) or nearby ($r_1=r_2\pm 1$, odd $r>1$) charge states.

Relativistic differential equations for bound states of $n$ Dirac particles $(n=1,2,3)$ are put into forms that depend only on the square of the total center-of-mass system energy. Instead of coupling $4^n$ Dirac components, they decompose into two equivalent equations for $4^n∕2$ components $\psi$ and $\chi$ of total chiralities $+1$ and $-1$, respectively. Their time-dependent versions are of the Klein-Gordon type; they reproduce the relativistic kinematics for the emission of photons or pions. Although the equations are presently extended to mesons and baryons within perturbative QCD only, the necessity of free Klein-Gordon equations for closed systems implies $E^2$ spectra not only for mesons, but also for baryons. For binaries, there exists an intricate transformation which turns the equation for $\psi$ into an effective one-body Dirac equation. The corresponding transformation for $\chi$ is derived here.

Rydberg level energies for ${}^7\mathrm{Li}$ were measured using triple-resonance laser excitation, followed by drifted field ionization. In addition to the principal $n{}^{2}P$ series, weak Stark mixing from residual electric fields allowed observation of $n{}^{2}S$ and hydrogenic Stark manifold series at higher $n$. Limit analyses for the series yield the spectroscopic ionization energy $E_I\left({}^7\mathrm{Li}\right)=43487.15940\left(18\right){\mathrm{cm}}^{-1}$. The ${}^{6,7}\mathrm{Li}$ isotope shift (IS) was measured in selected $n{}^{2}P$ Rydberg levels and extrapolation to the series limit yields $\mathrm{IS}{\left(E_I\right)}^{7,6}=18067.54\left(21\right)\mathrm{MHz}$. Results are compared with recent theoretical calculations: $E_I$ values from experiment and theory agree to within $0.0011{\mathrm{cm}}^{-1}$, with the remaining discrepancy comparable to uncertainty in QED corrections of order ${\alpha }^{4}Ry$. The difference between experiment and calculated mass-based $\mathrm{IS}\left(E_I\right)$ yields a change in nuclear charge radii between the two isotopes $\delta {⟨r^2⟩}^{7,6}=-0.60\left(10\right){\mathrm{fm}}^2$.

Simple and effective techniques for loading barium ions into linear Paul traps are demonstrated. Two-step photoionization of neutral barium is achieved using a weak intercombination line ($6s^2{}^{1}S_0\leftrightarrow 6s6p{}^{3}P_1$, $\lambda =791\mathrm{nm}$) followed by excitation above the ionization threshold using a nitrogen gas laser $(\lambda =337\mathrm{nm})$. Isotopic selectivity is achieved by using a near Doppler-free geometry for excitation of the triplet $6s6p{}^{3}P_1$ state. Additionally, we report a particularly simple and efficient trap loading technique that employs an inexpensive uv epoxy curing lamp to generate photoelectrons.

Axially phase-matched parametric six-wave mixing (PSWM) has been observed in Rb vapor by two-photon excitation of the atom $(5s\to \to 7s,5d)$ with $\sim 150\mathrm{fs}$ pulses, centered at $\lambda \sim 769\mathrm{nm}$ and generated by a $\mathrm{Ti}:{\mathrm{Al}}_2{\mathrm{O}}_3$ laser system. For a peak laser pulse intensity of $30\mathrm{GW}{\mathrm{cm}}^{-2}$, PSWM is observed for Rb number densities $\left(\right[\mathrm{Rb}\left]\right)>2.5\times {10}^{15}{\mathrm{cm}}^{-3}$ whereas, for $\left[\mathrm{Rb}\right]=2.2\times {10}^{16}{\mathrm{cm}}^{-3}$, the PSWM process is detectable for pump intensities above $\sim 3\mathrm{GW}{\mathrm{cm}}^{-2}$. Upconversion of the $1.367\mathrm{\mu }\mathrm{m}$ and $1.323\mathrm{\mu }\mathrm{m}$ signal waves into the visible $(\lambda \sim 494\mathrm{nm})$ has been accomplished by sum frequency generation in ${\mathrm{LiIO}}_3$, and quantum beating in Rb at $18.3\mathrm{THz}$ $(\sim 608{\mathrm{cm}}^{-1})$ has been observed by monitoring the upconverted signal wave intensity produced in pump-probe experiments. These results broaden the scope of the wave packet detection scheme reported by Tran et al. [Opt. Lett. 23, 70 (1998)] in that a variety of coherent nonlinear optical processes $({\chi }^{\left(3\right)},{\chi }^{\left(5\right)},\dots )$ appear to be suitable for observing the amplitude and phase of atomic (or molecular) wave packets.

We investigate the mixing-demixing transition and the collapse in a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex. We solve numerically a quantum-hydrodynamic model based on a new density functional which accurately takes into account the dimensional crossover. It is demonstrated that with the increase of interspecies repulsion, a mixed state of DBFM could turn into a demixed state. The system collapses for interspecies attraction above a critical value which depends on the vortex quantum number. For interspecies attraction just below this critical limit there is almost complete mixing of boson and fermion components. Such mixed and demixed states of a DBFM could be experimentally realized by varying an external magnetic field near a boson-fermion Feshbach resonance, which will result in a continuous variation of interspecies interaction.

We describe a resonator-based optical gyroscope whose sensitivity for measuring absolute rotation is enhanced via use of the anomalous dispersion characteristic of superluminal light propagation. The enhancement is given by the inverse of the group index, saturating to a bound determined by the group velocity dispersion. We also show how the offsetting effect of the concomitant broadening of the resonator linewidth may be circumvented by using an active cavity. For realistic conditions, the enhancement factor is as high as ${10}^6$. We also show how normal dispersion used for slow light can enhance relative rotation sensing in a specially designed Sagnac interferometer, with the enhancement given by the slowing factor.

We formulate a quantum theory of dynamic multiple light scattering in fluctuating disordered media and calculate the fluctuation and the autocorrelation function of the photon number operator for light transmitted through a disordered slab. The effect of disorder on the information capacity of a quantum communication channel operating in a disordered environment is estimated, and the use of squeezed light in diffusing-wave spectroscopy is discussed.

We discuss localization and center-of-mass wave-function measurement of a quantum particle using multiple simultaneous dispersive interactions of the particle with different standing-wave fields. In particular, we consider objects with an internal structure consisting of a single ground state and several excited states. The transitions between ground and the corresponding excited states are coupled to the light fields in the dispersive limit, thus giving rise to a phase shift of the light field during the interaction. We show that multiple simultaneous measurements allow both an increase in the measurement or localization precision in a single direction and the performance of multidimensional measurements or localization. Further, we show that multiple measurements may relax the experimental requirements for each individual measurement.

A scheme for generating the maximally entangled mixed state of two atoms on-resonance asymmetrically coupled to a single mode optical cavity field is presented. The part frontier of both maximally entangled mixed states and maximal Bell violating mixed states can be approximately reached by the evolving reduced density matrix of two atoms if the ratio of coupling strengths of two atoms is appropriately controlled. It is also shown that exchange symmetry of global maximal concurrence is broken if and only if coupling strength ratio lies between $\frac{\sqrt{3}}{3}$ and $\sqrt{3}$ for the case of one-particle excitation and asymmetric coupling, while this partial symmetry breaking cannot be verified by detecting maximal Bell violation.

We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions; in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; the 2D analog of such a structure, a vortex-lump, is also observed.

We propose a scheme for purification and distillation of squeezed and entangled continuous-variable states of light transmitted through a channel exhibiting phase fluctuations. The outstanding advantage of the suggested protocol is its experimental feasibility since it only involves an interference of two copies of the decohered state on a balanced beam splitter, a homodyne measurement on one of the output beams, and a conditioning on the measurement outcome. The purification can counteract the detrimental effects of phase fluctuations in optical quantum-communication networks.

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of ${\mathrm{Na}}_5$ and $\mathrm{Na}_9{}^{+}$, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.