The quasistatic limit of the velocity-gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields is derived. It is shown that in the low-frequency limit the ionization rate is proportional to the laser frequency, if a Coulombic long-range interaction is present. An expression for the corresponding proportionality coefficient is given. Since neither the saddle-point approximation nor the one of a small kinetic momentum is used in the derivation, the obtained expression represents the exact asymptotic limit. This result is used to propose a Coulomb correction factor. Finally, the applicability of the found asymptotic expression for nonvanishing laser frequencies is investigated.

Atom interferometers using Bose-Einstein condensate that is confined in a waveguide and manipulated by optical pulses have been limited by their short coherence times. We present a theoretical model that offers a physically simple explanation for the loss of contrast and propose the method for increasing the fringe contrast by recombining the atoms at a different time. A simple, quantitatively accurate, analytical expression for the optimized recombination time is presented and used to place limits on the physical parameters for which the contrast may be recovered.

Magnetic trapping potentials for atoms on atom chips are determined by the current flow in the chip wires. By modifying the shape of the conductor we can realize specialized current flow patterns and therefore microdesign the trapping potentials. We have demonstrated this by nano-machining an atom chip using the focused ion beam technique. We built a trap, a barrier, and using a Bose-Einstein Condensate as a probe we showed that by polishing the conductor edge the potential roughness on the selected wire can be reduced. Furthermore, we give different other designs and discuss the creation of a one-dimensional magnetic lattice on an atom chip.

We propose a measurement protocol to generate path-entangled $\mid N,0⟩+\mid 0,N⟩$ states conditionally from two pulsed type II optical parametric oscillators. We calculate the fidelity of the produced states and the success probability of the protocol. The trigger detectors are assumed to have finite dead time, and for short pulse trigger fields they are modeled as on-off detectors with finite efficiency. Continuous-wave operation of the parametric oscillators is also considered.

We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.

We propose a scheme for realizing a two-qubit quantum phase gate between atoms inside a high-$Q$ optical cavity. In the scheme, the dispersive interaction between atoms and the cavity field induces photon-number Stark shift, which can yield a resonant interaction inside one selected atom-field subspace and leave the others in a highly dispersive regime. Due to the selective atom-cavity interaction, (1) the scheme only requires commonly addressing the atoms inside the optical cavity during the gate operation, and (2) it can be directly used to implement an $N$-qubit conditional phase gate. These properties can significantly reduce the number of operations for implementing quantum computation and quantum algorithms.

It is demonstrated that three-dimensional propagation effects essentially influence attosecond-pulse generation by few-cycle, carrier-envelope-phase stabilized laser pulses used in a polarization-gating configuration. The rapidly changing polarization status gives rise to electron trajectories even longer than those observed with linearly polarized light, but the off-axis contributions and the propagation effects can efficiently act as a filter to produce a single attosecond pulse. It is also found that the attosecond beams can have a significant spatial divergence.

In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation of the spin-boson model. The effects of the decoupling pulses are then incorporated. A wide class of decoupling pulses can be described equally within this approach. We have performed a comprehensive investigation on the renormalized dynamics within various noise models, including the Ornstein-Uhlenbeck noise and the spin-boson model. The renormalized dynamics under bang-bang control and continuous dynamical decoupling are simulated. The condition for efficient decoupling is assessed for each scenario. Our results indicate that the renormalization of the non-Markovian dynamics critically depends on the spectral density of the environment and the envelope of the decoupling pulses. Consequently, it is difficult to have a simple universal condition that ensures the efficiency. The framework developed in this work provides a unified approach to investigate the efficiency of realistic decoupling pulses. It also opens an avenue to further optimize the decoupling via pulse shaping.

We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod systems and show how to generate purely geometric phase changes of the quantum states involved. The geometric phases are controlled by three laser fields where pulse shapes, relative field strength, and phases can be controlled. We present a robust set of universal gates for quantum computing based on these geometric phases: a one-qubit phase gate, a Hadamard gate, and a two-qubit phase gate.

Several physics-based algorithms for factorizing large numbers were recently presented. A notable recent algorthm by Schleich et al. uses Gauss sums for distinguishing between factors and nonfactors. We demonstrate two NMR techniques that evaluate Gauss sums and thus implement their algorithm. The first one is based on differential excitation of a single spin magnetization by a cascade of rf pulses. The second method is based on spatial averaging and selective refocusing of magnetization for Gauss sums corresponding to factors. All factors of 16 637 and 52 882 363 are successfully obtained.

We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral band gaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bistability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, $\Delta$, between the OLs in the two cores is also studied. It is concluded that $\Delta =\pi ∕2$ only mildly deforms the picture, while $\Delta =\pi$ changes it drastically, replacing the symmetry-breaking bifurcations by pseudobifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the interspecies nonlinear interaction becomes stronger than the intraspecies nonlinearity.

We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining—internal—fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespective of the values of the system parameters, we study which are the better squeezed modes at the different bifurcations that the cavity soliton can suffer, as well as the squeezing level attainable when the homodyne detection is made with a plane-wave local oscillator field. In this last case, the squeezing level is quite large in most of the existence domain of the cavity soliton. We then take into account the effect of the detector size and find that, in general, squeezing degrades as the detector is made smaller, except for detector sizes around the cavity soliton size, in which case there is an interesting deviation from the general trend.

We propose and quantitatively develop two schemes to quickly and accurately generate a stable initial configuration of neutral atoms in optical microtraps by extraction from the Mott-insulator state in optical lattices. We show that thousands of atoms may be extracted and stored in the ground states of optical microtrap arrays with one atom per trap in one operational process demonstrating massive scalability. The failure probability during extraction in the first scheme can be made sufficiently small $(\sim {10}^{-4})$ to initialize a large-scale quantum register with high fidelity. A complementary faster scheme with more extracted atoms but lower fidelity is also developed.

We study the quantum dynamics of an ultracold atomic gas trapped in an optical lattice within an optical high-$Q$ resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband so that stimulated gain of the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattice band. Including output coupling of ground-state atoms and replenishing of hot atoms into the cavity volume leads to a coherent, quantum correlated atom-photon pair source very analogous to twin light beam generation in a nondegenerate optical parametric oscillator.

Given a single copy of a mixed state of the form $\rho =\lambda {\rho }_1+(1-\lambda ){\rho }_2$, what is the optimal measurement to estimate the parameter $\lambda$ if ${\rho }_1$ and ${\rho }_2$ are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated value and the true value of $\lambda$. We explicitly determine the optimal measurements for a general two-dimensional system and for important higher dimensional cases.

X-ray emission yields, which are defined as the total number of emitted x-ray photons per incident ion, and dissipated fractions of potential energies through x-ray emission have been measured for slow highly charged ions of I, Pr, Ho, and Bi colliding with a W surface. A larger amount of potential energy was consumed for the x-ray emission with increasing the atomic number and the charge state. The present measurements show that x-ray emission is one of the main decay channels of hollow atoms produced in collisions of very highly charged ions of heavy elements.

We trace out the transition from weak- to strong-field coherent control, focusing on multiphoton population transfer in atomic sodium. We show how dynamic Stark shifts and ground-state depletion mark the departure from perturbative to strong-field excitation, and how a time-domain picture yields insight into the dynamics when a static resonance, frequency-domain approach breaks down. Experimental measurements are interpreted with the help of calculations that numerically integrate the Schrödinger equation.

We construct the phase diagram of a homogeneous two-component Fermi gas with population imbalance under a Feshbach resonance. In particular, we study the physics and stability of the Larkin-Ovchinnikov phase. We show that this phase is stable over a much larger parameter range than has been previously reported by other authors.

Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation $G^{\left(2\right)}$, (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a $\Lambda$ and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the $G^{\left(2\right)}$ for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength $\lambda ∕4$. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states ${\mid \pm ⟩}_{{\mathbf{k}}_0}=e^{i{\mathbf{k}}_0\bullet {\mathbf{r}}_1}\mid a_1,b_2⟩\pm e^{i{\mathbf{k}}_0\bullet {\mathbf{r}}_2}\mid b_1,a_2⟩$ by a laser pulse with wave vector ${\mathbf{k}}_0$. Photon emission is directionally suppressed along ${\mathbf{k}}_0$ for the phased-antisymmetric state. The directionality ceases for interatomic distances less than $\lambda ∕2$.

We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present day, nonideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical postprocessing. This allows one to improve the effective signal statistics and achievable distance.