We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Quantum computation in molecular magnets is studied by solving the time-dependent Schrödinger equation numerically. Following Leuenberger and Loss [Nature (London) $410,$ 789 (2001)], an external alternating magnetic field is applied to populate and manipulate a superposition of single-spin states in molecular magnet ${\mathrm{Mn}}_{12}.$ The conditions to realize parallel recording and reading databases of Grover algorithms in molecular magnets are discussed in detail. It is found that an accurate time duration of the magnetic pulse as well as the discrete frequency spectrum and the amplitudes are required to design a quantum computing device.

Coherent spectroscopy of degenerate two-level systems of the Doppler-broadened $D_2$ cesium line has been performed in vacuum and in buffer gas cells. Subnatural-width (SNW) electromagnetically induced transparency and electromagnetically induced absorption (EIA) resonances have been observed with single-frequency laser excitation for different light polarizations and collision regimes. SNW-EIA resonances with linearly polarized excitation of the $F_g=4\mathrm{}$ level are observed, and they increase their contrast with power density increase and reach a contrast of 20% at $200\hspace{0.5em}\mathrm{mW}{\mathrm{cm}}^{-2}.$ A theoretical model has been elaborated, taking into account the Doppler broadening of the transitions, the linewidth of the laser light, and the experimental conditions for observation of the fluorescence. Here the theoretical results are in agreement with those of the experiment. In a buffer gas cell, the SNW resonances in the fluorescence, in degenerate two-level systems are observed for the first time and they are only obtained with circularly polarized light. A theoretical explanation of this result is proposed. At the expense of contrast, in the presence of a buffer gas the coherent resonances are significantly narrower than in a vacuum cell for the same power density. The observation of SNW resonances in buffer gas is significantly less sensitive to the laser frequency drift than in a vacuum cell, which could be advantageous for applications in metrology and in the measurement of weak magnetic fields.

Electron-ion recombination spectra of the Li-like ion ${\mathrm{F}}^{6+}$ in the energy range $0.0-0.6\hspace{0.5em}\mathrm{eV}$ from two different ion storage rings are presented, showing excellent agreement. The experimental results are compared with a calculated spectrum, obtained by combination of relativistic many-body methods and complex rotation, and the agreement is found to be very good. The recombination spectrum in the studied energy region is determined by the ${2p}_{j}6{\mathcal{l}}_{j^{\prime }}^{\prime }$ dielectronic recombination resonances. The lowest-energy resonances are found around 10 meV, and include one broad resonance overlapping the threshold. The recombination rate coefficients are, even in this region, very well accounted for by the calculation. It is further shown that the nonrelativistically allowed resonances contribute to less than 60% of the integrated rate coefficients in the specified energy range.

Detailed simulations of the interaction of energetic ${\mathrm{C}}_{60}$ beams with amorphous targets are presented here. The spatial evolution of the cluster components is calculated accounting for multiple scattering and Coulomb explosion by means of Monte Carlo and molecular dynamics, respectively. The charge states of the individual cluster components (atoms, atomic ions, fragment cluster ions) as a function of penetration depth are also calculated in tandem with the above calculations by means of the Monte Carlo method. The relative importance of scattering versus Coulomb repulsion is studied as a function of the ${\mathrm{C}}_{60}$ cluster energy. The effect of the neighboring cluster constituents on the average charge state of the cluster atoms is calculated as a function of the depth of penetration for a ${\mathrm{C}}_{60}$ cluster of 40 MeV. The calculation accounts for the increase in ionization energy of the atom due to the other constituents. Relative track radii are calculated as a function of penetration depth and good agreement with the experimental results is obtained for the interaction of a 30 MeV carbon cluster with silicon. Track splitting observed well into the target as measured by Dunlop et al. in yttrium iron garnet is obtained in the simulations described here for the case of amorphous carbon, provided the Coulomb repulsion is screened by the four valence electrons. Collective energy deposition enhancement is calculated for the 720 MeV cluster. Here the cluster constituents are nearly fully ionized, thereby minimizing the ambiguity related to the value of the ionic charge in the calculation.

We have obtained photoelectron spectra of mixed clusters $(\mathrm{NaI}{)}_n{\mathrm{Na}}_m{\mathrm{OH}}^{-}$ $(n=2,3,\hspace{0.5em}m=1,2,3)$ and $(\mathrm{NaI}{)}_n{\mathrm{H}}_2{\mathrm{O}}^{-}$ $\mathrm{}(n=3,4,6\mathrm{}).$ Comparison with results obtained for pure sodium iodide clusters provides a microscopic view of the initial stages of the solvation process. We find that an $(\mathrm{NaI}{)}_n{\mathrm{Na}}_m{\mathrm{OH}}^{-}$ cluster incorporates the ${\mathrm{OH}}^{-}$ ion in the same way it would an ${\mathrm{I}}^{-}$ ion, whereas an $(\mathrm{NaI}{)}_n{\mathrm{H}}_2{\mathrm{O}}^{-}$ cluster appears to accommodate its intact water molecule on the edge of its ionic lattice.

Three bosonic, spin-polarized atoms in a spherical oscillator potential constitutes the simplest nontrivial Bose-Einstein condensate (BEC). The present paper develops the tools needed to understand the nature of the complete $J=0\mathrm{}$ energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length $a_{\mathrm{sc}},$ which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states $N_b$ increases by 1, and $a_{\mathrm{sc}}$ switches from $-\infty$ to $+\infty .$ We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented.

A novel class of coherent nonlinear optical phenomena, involving induced transparency in semiconductor quantum wells, is considered in the context of a particular application to sensitive long-wavelength infrared detection. It is shown that the strongest decoherence mechanisms can be suppressed or mitigated, resulting in substantial enhancement of nonlinear optical effects in semiconductor quantum wells.

Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schrödinger-cat states.

For quantum mechanics on a lattice the position (“particle number”) operator and the quasimomentum (“phase”) operator obey canonical commutation relations (CCRs) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in a linear and a quadratic potential on the lattice with the expectations, when the CCRs are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions does this lead to reasonable results. In the long time limit the use of the CCRs can lead to a qualitatively wrong dynamics even if the initial state is in the dense set.

Recently Liu, Long, Tong, and Li [Phys. Rev. A 65, 022304 (2002)] proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits entanglement. We show that this scheme can be modified in order to allow more senders to benefit from the entanglement-enhanced information transmission.

The paper G. Brassard, R. Cleve, and A. Tapp, Phys. Rev. Lett. 83, 1874 (1999) begins thus: “Bell’s celebrated theorem shows that certain scenarios involving bipartite quantum measurements result in correlations that are impossible to simulate with a classical system if the measurement events are spacelike separated. If the measurement events are timelike separated, then classical simulation is possible, at the expense of some communication. Our goal is to quantify the required amount of communication.” In this note we tighten the bounds on the amount of communication required to simulate a von Neumann measurement on a Bell pair.

We develop and experimentally verify a theory of type II spontaneous parametric down-conversion (SPDC) in media with inhomogeneous distributions of second-order nonlinearity. As a special case, we explore interference effects from SPDC generated in a cascade of two bulk crystals separated by an air gap. The polarization quantum-interference pattern is found to vary strongly with the spacing between the two crystals. This is found to be a cooperative effect due to two mechanisms: the chromatic dispersion of the medium separating the crystals and spatiotemporal effects that arise from the inclusion of transverse wave vectors. These effects provide two concomitant avenues for controlling the quantum state generated in SPDC. We expect these results to be of interest for the development of quantum technologies and the generation of SPDC in periodically varying nonlinear materials.

Nonlinear circular dichroism is studied in a solution of ruthenium-tris(bipyridyl) salt in one-beam and pump-probe experiments by tuning the laser wavelength across the circular dichroism structure. The dispersion of the nonlinear circular dichroism is measured. This wavelength dependence is well accounted for by a model calculation where nonlocality is included in the optical response of a two-coupled-oscillator system. This calculation also allows us to address the question of the contribution of electric quadrupolarization to the nonlinear optical activity of an isotropic liquid of chiral molecules.

We investigate the validity conditions of the single-mode approximation (SMA) in a spinor-1 atomic condensate when effects due to residual magnetic fields are negligible. For atomic interactions of the ferromagnetic type, the SMA is shown to be exact, with a mode function different from what is commonly used. However, the quantitative deviation is small under current experimental conditions (for ${}^{87}\mathrm{Rb}$ atoms). For antiferromagnetic interactions, we find that the SMA becomes invalid in general. The differences among the mean-field mode functions for the three spin components are shown to depend strongly on the system magnetization. Our results can be important for studies of beyond mean-field quantum correlations, such as fragmentation, spin squeezing, and multipartite entanglement.

We analyze the implosion and subsequent explosion of a trapped condensate after the scattering length is switched to a negative value. Our results compare very well qualitatively and fairly well quantitatively with the results of recent experiments at JILA.

We present a simple multimode analysis of the Zeno and anti-Zeno effects in spontaneous parametric down-conversion. In this process the input vacuum is an unstable state decaying into a reservoir of down-converted modes by emitting a pair of photons. We show that the Zeno and the anti-Zeno effects are two particular examples of quantum propagation depending on the effective spectrum of down-converted modes. We show that this evolution can be easily tailored on demand and that these quantum phenomena admit a very simple explanation in terms of standard interference concepts.

The relativistic time-dependent density functional theory (RTDDFT) has been applied to the photoionization of mercury in the energy range from the threshold up to 300 eV, thus covering almost all the photon energy range for which experimental data are available. Partial cross sections and asymmetry parameter profiles for the $6s,$ $5d,$ $5p,$ and $4f$ subshells have been calculated and compared with earlier relativistic random-phase approximation and RTDDFT theoretical calculations and with the experimental results. A study of the spin polarization of photoelectrons from the outer subshells $6s$ and $5d$ at RTDDFT level is also presented. The use of the LB94 exchange-correlation potential together with an implementation of the RTDDFT equations in a B-spline basis set based on a noniterative procedure for the calculation of the induced response potential has permitted the study, at RTDDFT level, of the autoionization resonances converging to the ${5d}_{3/2,5/2}$ and ${5p}_{1/2,3/2}$ thresholds. Comparison of the RTDDFT results with the other theoretical and experimental data available confirms the effectiveness of the method in the description of correlation and relativistic effects in the photoionization of such a heavy system.

The dynamics of the elastic and inelastic scattering of helium atoms in collisions with oxygen atoms in different fine-structure levels $\mathrm{O}{(}^3{P}_j)$ at cold and ultracold temperatures is investigated using two sets of interaction potentials of the molecule HeO in the ground Σ and Π states. Scattering resonances occur in the collisions at low energies. The positions and shapes of the resonance peaks in the inelastic channels do not always mirror those in the elastic channels. The real parts of the scattering lengths are all positive with values in the range 2.5–4.2 Å. The rate coefficients for the quenching of the ${}^3{P}_0$ and ${}^3{P}_1$ fine-structure levels decrease almost by one order of magnitude as the temperature decreases from 1 to 0 K and their zero temperature values are, respectively, $3.09\times {10}^{-12}$ and $3.27\times {10}^{-12}$ ${\mathrm{cm}}^3{\sec }^{-1}.$

We present precise double- to single-photoionization ratios and partial cross sections of lithium in the energy range from 81 to 110 eV. We compare our data with those of ground-state and metastable helium and find a remarkable similarity in the photon energy dependence of the double- to single-photoionization ratio of ground-state He when the energy axis is scaled in units of the energy difference between the double- and single-ionization threshold. We also present a simple explanation for this scaling behavior.