It is shown how a classical system can possess such quantum properties as indeterminism, interference of probabilities, unitary transformations, wave functions, and noncommuting operators, and be used in quantumlike computations.

We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular, we describe several Bell inequalities which appear to be optimal with respect to inefficient detectors for small dimensionality $d=2,3,4\mathrm{}$ and two or more measurement settings at each side. We also generalize the family of Bell inequalities described by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)] to take into account the inefficiency of detectors. In addition, we consider the possibility for pairs of entangled particles to be produced with probability less than 1. We show that when the pair production probability is small, one should in general use different Bell inequalities than when the pair production probability is high.

This paper investigates the connection between quantization of periodic orbits and invariant tori satisfying Einstein-Brillouin-Keller (EBK) quantization conditions. We define Bohr-Sommerfeld (BS) conditions on periodic orbits, EBK conditions on the invariant torus, and a hybrid condition on periodic orbits, first introduced by Takatsuka, and here called BS-EBK quantization. It is found that as BS-EBK periodic orbits converge to the quantizing torus, their energies and actions converge to the torus exponentially. These periodic orbits contribute to the semiclassical wave function coherently as they converge to the quantizing torus. Together, the BS-EBK condition with the demand of collective phase coherence appear to be a powerful criterion for determining approximate semiclassical energies and wave functions from periodic orbits, with possible applications to situations where EBK tori do not exist, including chaotic dynamics.

The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.

A technique is developed for lifetime measurements of partially autoionizing levels using the time of flight method of the beam-foil and two-foil techniques at various beam energies. The decay curve of the 5.17-keV peak in heliumlike vanadium shows the presence of nonidentical decay constants in beam single-foil experiment in contrast to the growth structures in beam–two-foil measurements at different beam energies. Analysis of such data has not only confirmed the satellite blending problem of the $M2\mathrm{}$ line ${1s}^2{}^1{S}_0–1s2p{}^3{P}_2^o,$ but has also led to the mean lifetime measurement of the partially autoionizing satellite level of the $1s2s2p{}^4{P}_{5/2}^o$ line in lithiumlike vanadium. The lifetime so measured is compared with theoretical calculations.

Rates and line strengths are calculated for the ${2s}^2{2p}^5{3l3l}^{\prime }-{2s}^2{2p}^6{3l}^{″}$ and ${2s2p}^6{3l3l}^{\prime }-{2s}^2{2p}^6{3l}^{″}$ electric-dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transitions in Na-like ions with nuclear charges ranging from $Z=14\mathrm{}$ to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a ${1s}^2{2s}^2{2p}^6$ Dirac-Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. A detailed discussion of the various contributions to dipole matrix elements is given for sodiumlike copper $\mathrm{}(Z=29\mathrm{}).$ Transition energies used in the calculation of transition rates are from second-order RMBPT. Trends of transition rates as functions of Z are shown graphically for selected transitions.

The interaction between slow, heavy pointlike charges and a classical electron harmonically bound to a heavy nucleus was studied by means of computer simulations. It is found that the equation of motion governing the interaction between a charge and classical harmonic oscillator can be conveniently scaled up so that the number of independent parameters is significantly reduced. Therefore, the stopping cross section S appears to be a universal function of Bohr’s ξ parameter, the sign of the ion charge, and, with less significance, the scaled initial amplitude of the harmonic oscillator. Strikingly however, the stopping cross section of positive charges appears to be larger than that of negative ions at the same ξ. Moreover, S is found to be a linear function of the ion velocity for positive ions, whereas it is a nearly quadratic function for negative charges. It turns out that the mechanism responsible for the energy loss of positive ions is completely different from that of negative charges and, in both cases, different from those assumed in previous models of stopping of low-energy ions.

We describe an original approach for the accurate description of alkali-metal Rydberg states exposed to intense electromagnetic fields. Our method combines Floquet and R-matrix theory, complex dilation of the Hamiltonian, a Sturmian basis set to describe the atomic degrees of freedom (including the continuum), and, last but not least, an efficient parallel implementation of the Lanczos algorithm on some of the most powerful supercomputers currently available. Without adjustable parameters, this ab initio approach opens a route to the comprehensive understanding of an abundance of laboratory data on the microwave ionization of one-electron Rydberg states. The versatility of our theoretical/numerical machinery is illustrated in the specific case of microwave driven lithium, faithfully mimicking every single step of the laboratory experiment.

Using a set of general methods developed by Krotov [A. I. Konnov and V. A. Krotov, Automation and Remote Control 60, 1427 (1999)], we extend the capabilities of optimal control theory to the nonlinear Schrödinger equation (NLSE). The paper begins with a general review of the Krotov approach to optimization. Although the linearized version of the method is sufficient for the linear Schrödinger equation, the full flexibility of the general method is required for treatment of the nonlinear Schrödinger equation. Formal equations for the optimization of the NLSE, as well as a concrete algorithm are presented. As an illustration, we consider a Bose-Einstein condensate (BEC) initially at rest in a harmonic trap. A phase develops across the BEC when an optical lattice potential is turned on. The goal is to counter this effect and keep the phase flat by adjusting the trap strength. The problem is formulated in the language of optimal control theory (OCT) and solved using the above methodology. To our knowledge, this is the first rigorous application of OCT to the nonlinear Schrödinger equation, a capability that is bound to have numerous other applications.

It has been proposed that the adiabatic loading of a Bose-Einstein condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a nonstationary BEC in a harmonic trap.

We study the transverse-mode dynamics of vertical-cavity surface-emitting lasers with weak optical feedback. We use a model that takes into account the spatial dependence of the transverse modes and of two carrier density profiles, associated with confined carriers in the quantum well region of the laser and unconfined carriers in the barrier region. Optical feedback is included as in the Lang-Kobayashi model. We find that for adequate parameter values antiphase dynamics occurs. As the injection current varies, the antiphase dynamics is destroyed through a sequence of periodic mixed states leading to in-phase dynamics. In these mixed states there are time intervals in which the modes are in phase, followed by time intervals in which they are in antiphase. We study the origin of the antiphase dynamics, assessing the role of the different spatial profiles. We show that the competition between the different profiles leads to the observed antiphase behavior.

We consider three- and four-level atomic lasers that are either incoherently (unidirectionally) or coherently (bidirectionally) pumped, the single-mode cavity being resonant with the laser transition. The intracavity Fano factor and the photocurrent spectral density are evaluated on the basis of rate equations. According to that approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is simple. Whenever a comparison is made, the expressions obtained coincide with the previous results. The conditions under which the output light exhibits sub-Poissonian statistics are considered in detail. Analytical results, based on linearization, are verified by comparison with Monte Carlo simulations. An essentially exhaustive investigation of sub-Poissonian light generation by three- and four-level lasers has been performed. Only special forms were reported earlier.

The targeting method recently proposed by Lippi et al. to shorten lengthy transients in separable systems has been experimentally implemented in the particular case of a solid-state laser. It allows to reduce the intensity transient of a ${\mathrm{Nd}}^{3+}:{\mathrm{YVO}}_4$ laser by a factor of 60 and its duration by a factor in excess of 10 without altering the system. This process is extremely sensitive to targeting parameters due to the stiffness of the system. Internal noise sets a practical limit on the achievable squeezing of transients.

Closely packed vertical-cavity-surface emitting laser arrays support collective modes via nearest-neighbor interactions. Nonlinear cavity-lattice dynamic equations are introduced through the derivation of intercavity coupling coefficients based on microscopic transition probabilities and the tight-binding approximation for lattice eigenstates. Ultrafast numerical simulations show array relaxation to phase-locked steady-state configurations, of fixed phase difference among nearest neighbors. Linear stability analysis derives the dispersion relation of the collective modes excited over the cavity lattice, their stability regimes, and transitions to limit cycles and chaotic behavior at high coupling strengths. Spontaneous phase selection is also analyzed.

We examine the stimulated light scattering onto the propagation modes of a dissipative optical lattice. We show that two different pump-probe configurations may lead to the excitation, via different mechanisms, of the same mode. We found that in one configuration the scattering on the propagation mode results in a resonance in the probe transmission spectrum while in the other configuration no modification of the scattering spectrum occurs, i.e., the mode is dark. A theoretical explanation of this behavior is provided.

It is known that in phase-covariant quantum cloning, the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite z component of spin. It is shown that once we know the z component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states that give rise to a separable density matrix for the outputs.

It is shown that every zero-temperature Bose-Einstein condensate is a highly entangled state, as a consequence of the fact that the particles in a condensate are distributed over space in a coherent way. In particular, any two regions within a condensate of finite particle number are entangled. This entanglement does not depend on the distance between the two regions. Criteria for the presence of entanglement are derived in the context of interference experiments. For separable states there is a trade-off between fluctuations in particle number and interference visibility.

Using a semiclassical rescattering model, the momentum distributions of recoil ions from laser induced single and double ionization are obtained. Not only in the case of double ionization but also in the case of single ionization, the distributions of the momentum parallel to the polarization direction of the laser field show a double-hump structure as a consequence of the rescattering. By comparing with experimental data we find that, as the intensity of the laser decreases, the rescattering ionization mechanism of the second electron as calculated within our model does not dominate the process. In addition, the correlated emission of the electrons in the double ionization is discussed and the effect of the repulsion between the emitted electrons is shown.

In this work we investigate scattering of ultrashort light pulses from two coupled neutral atomic Bose-Einstein condensates corresponding to two different ground hyperfine sublevels. Two counterpropagating ${\sigma }_{+}$ and ${\sigma }_{-}$ light waves are employed to excite the atomic condensates. We find that the spectrum of scattered light is determined by the initial preparation of the atomic condensate. The spectrum is found to be a mirror image of the population distribution. The scattered light probes the population distribution between the two condensates. In particular, we find that, when the population is equally distributed between the two ground states, the quantum fluctuations in the spectrum are suppressed due to destructive quantum interference.