Experimental measurements of the ionization cross section for ${\mathrm{O}}^{q+},$ where $q=1\mathrm{}–4,$ performed with a crossed-beam apparatus are presented and compared with theoretical calculations. For ${\mathrm{O}}^{+},$ the experimental measurements are in very good agreement with configuration-average time-dependent close-coupling calculations. For the remaining oxygen ions, the experimental measurements are in good agreement with time-independent distorted-wave calculations. As expected, the accuracy of the perturbative distorted-wave calculations improves with increasing ion charge.

We model an experiment in which an iron slab target is irradiated by superimposing the six beams of the LULI facility onto a $22\mathrm{mm}\times 100\mu \mathrm{m}$ focal line. The driving laser is composed of two Gaussian pulses of 130-ps duration (full width at half maximum), preceded by a prepulse. A strong enhancement of the $3p-3s$ 0-1 x-ray line at 25.5 nm in neonlike iron was observed. Saturation is attained for plasma lengths near 1 cm. A ray-trace code working as a postprocessor to a hydroatomic code is used to model the x-ray laser beam refraction due to the variation of the electron density versus the distance to the target surface. Knowing the hydrodynamic conditions, i.e., electron density, and electron and ion temperatures, along the ray paths, the radiative transfer equation, and the population equations are solved self-consistently by using a Maxwell-Bloch approach. A more tractable approach, requiring also the intensity of saturation as a function of time and space, is also presented. In this case, calculation time is much less than in the Maxwell-Bloch approach.

Interference between the halves of a double-well trap containing a Bose-Einstein condensate is studied. It is found that when the atoms in the two wells are initially in the coherent state, the intensity exhibits collapses and revivals, but it does not for the initial Fock states. Whether the initial states are in the coherent states or in a Fock state, the fidelity time has nothing to do with collision. We point out that interference and its fidelity can be adjusted experimentally by properly preparing the number and initial states of the system.

The fragmentation statistics of $({\mathrm{H}}_2\mathrm{O}{)}_N$ and $({\mathrm{NH}}_3{)}_N$ clusters $(N=100\mathrm{}–1000)$ is investigated by molecular-dynamics simulations. The fragment size distributions are found to be well described by power laws over a wide range of excitation energies. The maximum fragment size depends linearly on the cluster size. A compact analytical model, implying the maximum fragment size and the power-law exponent of the fragment size distribution, is shown to fit the average fragment size profiles quite well. It is demonstrated that the proposed relationship can be used to predict reliable fragment size distributions, starting from fits of the maximum and the average fragment sizes.

It is shown that Maxwell’s equations in a vacuum do not allow for a local maximum in the value of the electric field $E^2,$ but do allow for a local minimum. Such a field minimum creates a trap of neutral particles that exhibit a Stark effect. Specific criteria are given for the design of such a trap and results of numerical calculations of sample trap potentials are presented.

Solid-state quantum bits are promising candidates for the realization of a scalable quantum computer. However, they are usually strongly limited by decoherence due to the many extra degrees of freedom of a solid-state system. We investigate a system of two solid-state qubits that are coupled via ${\sigma }_z^{\mathrm{}\left(i\right)\mathrm{}}\otimes {\sigma }_z^{\mathrm{}\left(j\right)\mathrm{}}$ type of coupling. This kind of setup is typical for pseudospin solid-state quantum bits such as charge or flux systems. We evaluate decoherence properties and gate quality factors in the presence of a common and two uncorrelated baths coupling to ${\sigma }_z,$ respectively. We show that at low temperatures, uncorrelated baths do degrade the gate quality more severely. In particular, we show that in the case of a common bath, optimum gate performance of a controlled-PHASE gate can be reached at very low temperatures, because our type of coupling commutes with the coupling to the decoherence, which makes this type of coupling interesting as compared to previously studied proposals with ${\sigma }_y^{\mathrm{}\left(i\right)\mathrm{}}\otimes {\sigma }_y^{\mathrm{}\left(j\right)\mathrm{}}$ coupling. Although less pronounced, this advantage also applies to the controlled-NOT gate.

We study the radial Schrödinger equation for a particle of mass m in the field of a singular attractive $\alpha {/r}^2$ potential with $2m\alpha >1/4.\mathrm{}$ This potential is relevant to the fabrication of nanoscale atom optical devices, is said to be the potential describing the dipole-bound anions of polar molecules, and is the effective potential underlying the universal behavior of three-body systems in nuclear physics and atomic physics, including aspects of Bose-Einstein condensates, first described by Efimov. New results in three-body physical systems motivate the present investigation. Using the regularization method of Beane et al., we show that the corresponding “renormalization-group flow” equation can be solved analytically. We find that it exhibits a limit cycle behavior and has infinitely many branches. We show that a physical meaning for self-adjoint extensions of the Hamiltonian arises naturally in this framework.

Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.

We propose a model for the measurement of an arbitrary multimode entangled state of the cavity field using two-photon correlated emission laser. We consider two cases: (a) The modes have different frequencies and are detected separately and (b) the modes consist of two orthogonal polarization states and are detected using a single balanced homodyne detector. The basic idea is to amplify the initial multimode state such that there is no-noise in the quadrature of interest and all the noise is fed into the conjugate quadrature component. The amplified noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial multimode entangled state is then reconstructed by using inverse Radon transformation. This scheme is insensitive to the noise associated with the nonunit efficiency of the detector in the homodyne detection measurement scheme.

We examine three possible implementations of nondeterministic linear optical controlled NOT gates with a view to an in-principle demonstration in the near future. To this end we consider demonstrating the gates using currently available sources, such as spontaneous parametric down conversion and coherent states, and current detectors only able to distinguish between zero and many photons. The demonstration is possible in the coincidence basis and the errors introduced by the nonoptimal input states and detectors are analyzed.

A selective excitation technique based on light interference is proposed to control quantum systems by frequency-chirped laser fields. Interference of two identical, delayed and phase-shifted pulses is used to modulate the laser spectrum and project it onto the time domain. By adjusting the delay and phase shift, selected transitions can be brought into the “holes” of the spectrum and thus remain nonexcited. The possibility to selectively manipulate or even “shut down” resonant transitions, making the medium transparent to the field, is shown for the Rb atom.

We explore the design of atom-optic components, such as mirrors, to manipulate ultracold atoms. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the interaction potential between atoms and the component. We illustrate the concept by calculating the reflection probability for ultracold sodium atoms incident on a bichromatic evanescent-wave atomic mirror created by lasers red and blue detuned from resonance with intensities and detunings chosen to enhance quantum reflection of a purely attractive potential. With realistic parameters for sodium atoms incident on glass at 10 cm/s, up to 30% reflection can be obtained.

We predict multifrequency spatial soliton propagation in a strongly driven Raman medium. The essential idea is the adiabatic preparation of a near-maximum molecular coherence.

It is shown that a quantum shutter, preselected and postselected in particular quantum states, can close simultaneously arbitrary number of slits preventing the passage of a single photon in an arbitrary state. A set of K preselected and postselected shutters can close the slits preventing the passage of K or less photons. This result indicates that the surprising properties of preselected and postselected quantum systems are even more robust than previously expected.

An original method to exactly solve the non-Markovian master equation describing the interaction of a single harmonic oscillator with a quantum environment in the weak-coupling limit is reported. By using a superoperatorial approach, we succeed in deriving the operatorial solution for the density matrix of the system. Our method is independent of the physical properties of the environment. We show the usefulness of our solution deriving explicit expressions for the dissipative time evolution of some observables of physical interest for the system, such as, for example, its mean energy.

The exact energy spectrum and wave function of a charged particle moving in the Coulomb field and Aharonov-Bohm’s magnetic flux are solved by the nonintegrable phase factor. The universal formula for the matrix elements of the radial operator $r^{\alpha }$ of arbitrary power $\alpha$ is given by an analytical solution. The difference between the classical limit of matrix elements of inverse radius in quantum mechanics and the Fourier components of the corresponding quantity for the pure Coulomb system in classical mechanics is examined in reference to the correspondence principle of Heisenberg. Explicit calculation shows that the influence of nonlocal Aharonov-Bohm effect exists even in the classical limit. The semiclassical quantization rule for systems containing the topological effect is presented in the light of Heisenberg’s corresponding principle.

The long-time evolution of a system in interaction with an external environment is usually described by a family of linear maps ${\gamma }_t,$ generated by master equations of Block-Redfield type. These maps are, in general, nonpositive; a widely adopted cure for this physical inconsistency is to restrict the domain of definition of the dynamical maps to those states for which ${\gamma }_t$ remains positive. We show that this prescription has to be modified when two systems are immersed in the same environment and evolve with the factorized dynamics ${\gamma }_t\otimes {\gamma }_t$ starting from an entangled initial state.

Several recent experiments have demonstrated the promise of atomic ensembles for quantum teleportation and quantum memory. In these cases, the collective internal state of the atoms is well described by continuous variables corresponding to the operators $X_1{,P}_1$ and the interaction with the optical field ${(X}_2{,P}_2)$ by a quadratic Hamiltonian $X_1{X}_2.$ We show how this interaction can be used optimally to create entanglement and squeezing. We derive conditions for the efficient simulation of quadratic Hamiltonians and the engineering of all Gaussian operations and states.

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle, and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalized with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.

The quantum random walk is a possible approach to construct quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper, we present the experimental implementation of the quantum random-walk algorithm on a nuclear-magnetic-resonance quantum computer. We observe that the quantum walk is in sharp contrast to its classical counterpart. In particular, the properties of the quantum walk strongly depends on the quantum entanglement.