We apply a proposal of Yuen and Tombesi for treating stochastic problems with negative diffusion to the analytically soluble problem of the single-mode anharmonic oscillator. We find that the associated stochastic realizations include divergent trajectories. It is possible, however, to solve the stochastic problem exactly, but the averaging must be performed with great care.

We show how one can use the anisotropic properties of a coherent medium to separate temporally the two polarization components of a linearly polarized pulse. This is achieved by applying a control field such that one component of the pulse becomes ultraslow while the other component’s group velocity is almost unaffected by the medium. We present analytical and numerical results to support the functioning of such a coherent medium as a polarization splitter of pulses.

A magnetometric technique is demonstrated that may be suitable for precision measurements of fields ranging from the submicrogauss level to above the earth field. It is based on resonant nonlinear magneto-optical rotation caused by atoms contained in a vapor cell with antirelaxation wall coating. Linearly polarized, frequency-modulated laser light is used for optical pumping and probing. If the time-dependent optical rotation is measured at the first harmonic of the modulation frequency, ultra-narrow (∼ a few hertz) resonances are observed at near-zero magnetic fields, and at fields where the Larmor frequency coincides with half the light modulation frequency. Upon optimization, the sensitivity of the technique is expected to exceed ${10}^{-11}\hspace{0.5em}G/\sqrt{\mathrm{Hz}}.$

We point out that the perturbative method of Qiong-gui Lin misses some exact solutions and some physical effects, which could be of interest for experimental areas.

Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states. The R-matrix method combined with a Lagrange basis, i.e., functions that vanish at all points of a mesh but one, leads to simple meshlike equations which also allow an accurate description of scattering. These methods are shown to be exactly equivalent for any basis size, with or without discretization. The comparison of their assumptions shows how to accurately derive poles of the scattering matrix in the R-matrix formalism and suggests how to extend the Siegert-pseudostate method to higher partial waves. The different concepts are illustrated with the Bargmann potential and with the centrifugal potential. A simplification of the R-matrix treatment can usefully be extended to the Siegert-pseudostate method.

Electron-nuclear-dynamics theory simulations have been performed with the aim to understand the dynamic aspects of triatomic molecules in pseudorotational motion. More specifically, the units ${\mathrm{H}}_3^{+}$ and ${\mathrm{Li}}_3^{+}$ are investigated close to the threshold of dissociation. For both species, the dynamic response of the electronic system to the nuclear motion is examined by the computation of electronic angular momentum expectation values. The respective results differ markedly for α- and β- spin orientations, reflecting the emergence of rapid spin oscillations. This phenomenon is investigated by a detailed analysis of the electronic excitation content in both molecules. This is achieved by projection of the dynamic wave function on adiabatic electronic states that are evaluated along the nuclear trajectories. From an examination of the phase relations between expansion coefficients for electronic excitations with α- and β-spin orientation, we conclude that the systems maximize the observed spin polarization effects.

We have investigated the structure and properties of small metal clusters using all-electron ab initio theoretical methods based on the Hartree-Fock approximation, density functional theory, and perturbation theory and compared the results of our calculations with the available experimental data and the results of other theoretical work. We have systematically calculated the optimized geometries of neutral and singly charged sodium clusters having up to 20 atoms, their multipole moments (dipole and quadrupole), static polarizabilities, binding energies per atom, ionization potentials, and frequencies of normal vibration modes. Our calculations demonstrate the important role of many-electron correlations in the formation of the electronic and ionic structure of small metal clusters and form a good basis for further detailed study of their dynamic properties, as well as the structure and properties of other atomic cluster systems.

We investigate the thermodynamical aspects of the Casimir effect in the case of plane parallel plates made of real metals. The thermal corrections to the Casimir force between real metals were recently computed by several authors using different approaches based on the Lifshitz formula with diverse results. Both the Drude and plasma models were used to describe a real metal. We calculate the entropy density of photons between metallic plates as a function of the surface separation and temperature. Some of these approaches are demonstrated to lead to negative values of entropy and to nonzero entropy at zero temperature depending on the parameters of the system. The conclusion is that these approaches are in contradiction with the third law of thermodynamics and must be rejected. It is shown that the plasma dielectric function in combination with the unmodified Lifshitz formula is in perfect agreement with the general principles of thermodynamics. As to the Drude dielectric function, the modification of the zero-frequency term of the Lifshitz formula is outlined, which does not violate the laws of thermodynamics.

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green’s functions. We especially focus on the description of the boson-fermion interaction. To do so we need to introduce the renormalized boson-fermion $T$ matrix, which we determine to second order in the boson-fermion $s$-wave scattering length. We also discuss how to incorporate the usual boson-boson $T$ matrix in mean field approximation to obtain the total ground-state properties of the system. The next-order term beyond mean field stems from the boson-fermion interaction and is proportional to $a_{\mathrm{BF}}{k}_{\mathrm{F}}.$ The total ground-state energy density to this order is the sum of the kinetic energy of the free fermions, the boson-boson mean-field interaction, the usual mean-field contribution to the boson-fermion interaction energy, and the first boson-fermion correction beyond mean field. We also compute the bosonic and the fermionic chemical potentials, the compressibilities, and the modification to the induced fermion-fermion interaction. We discuss the behavior of the total ground-state energy and the importance of the correction beyond mean field for various parameter regimes, in particular considering mixtures of ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ and of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}.$ Moreover, we determine the modification of the induced fermion-fermion interaction due to the effects beyond mean field. We show that there is no effect on the depletion of the Bose condensate to first order in the boson-fermion scattering length $a_{\mathrm{BF}}.$

Using the Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn, and Smith [Phys. Rev. Lett. 80, 2265, (1998)] for the ground states at angular momentum $L$ of $N$ harmonically trapped Bose atoms, interacting via weak attractive ${\delta }^2\mathrm{}\left(r\right)\mathrm{}$ forces, are valid for a broad class of predominantly attractive interactions $V\left(r\right),$ not necessarily attractive for any $r.\mathrm{}$ This class is described by sufficient conditions on the two-body matrix elements of the potential $V\left(r\right).$ It includes, in particular, the Gaussian attraction of arbitrary radius, $-1/r$-Coulomb and $\log \mathrm{}\left(r\right)\mathrm{}$-Coulomb forces, as well as all the short-range interactions satisfying inequality $\int d^2\overrightarrow{r}V\left(r\right)<0.\mathrm{}$ In the precollapse regime, the angular momentum $L$ is concentrated in the collective “center-of-mass” mode, and there is no condensation at high $L.\mathrm{}$

We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.

We show that each of two copies of the nonorthogonal states randomly selected from a certain set S can be probabilistically deleted by a general unitary-reduction operation if and only if the states are linearly independent. We derive a tight bound on the best possible deleting efficiencies. These results for $\overrightarrow{2}1$ probabilistic deleting are also generalized into the case of $\overrightarrow{N}M$ deleting (N,M positive integers and $N>M).\mathrm{}$

We demonstrate an efficient frequency up-conversion based on generation of large atomic coherence in a cascade system. Two infrared, low power laser fields tuned to the vicinity of the two-photon transition in Rb vapor were converted spontaneously into infrared and blue radiation. Extension of the technique into other spectral regions using highly excited states seems feasible.

Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off- diagonal) and in terms of the quantum-erasing phenomenon.

We propose a scalable design for a solid-state spin-based quantum computer. It uses endohedral fullerenes like $\mathrm{N}@{\mathrm{C}}_{60}$ or $\mathrm{P}@{\mathrm{C}}_{60},$ which can be positioned on Si surfaces with a scanning tunneling microscope. Each logical qubit is stored in two physical qubits, corresponding to the nuclear and electronic spins. We discuss the addressing of individual qubits by a magnetic field gradient, and the implementation of one- and two-qubit quantum gates by sequences of radio-frequency and microwave pulses.

The coupling to the continuum is studied in a one-dimensional problem that describes the interaction of a weakly bound composite object with a wall in a semiclassical approach. A transformed harmonic oscillator basis is introduced to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum. The convergence of the scattering magnitudes is investigated as the number of states in the basis is increased. The role of bound-to-continuum and continuum-to-continuum coupling is investigated.

One of the theories of the electronic stopping power S for fast light ions was derived by Bethe. The algorithm currently used for the calculation of S includes terms known as the mean excitation energy I, the shell correction, the Barkas correction, and the Bloch correction. These terms are described here. For the calculation of the shell corrections an atomic model is used, which is more realistic than the hydrogenic approximation used so far. A comparison is made with similar calculations in which the local plasma approximation is utilized. Close agreement with the experimental data for protons with energies from 0.3 to 10 MeV traversing Al and Si is found without the need for adjustable parameters for the shell corrections.

We have measured electron emission from ${\mathrm{C}}_{60}^{-}$ ions in a storage ring. The ions were produced at room temperature and excited by absorption of photons with a total energy of 14 eV. The observed lifetime $\left(\sim 0.6\hspace{0.5em}\mathrm{ms}\right)$ is consistent with detailed balance and a cross section of $42\hspace{0.5em}{\mathrm{\AA }}^2$ for electron attachment. The measurements also determine the thermal radiation intensity $I_r$ at a well-defined internal temperature T, $I_r=138\mathrm{}\pm 20\hspace{0.5em}\mathrm{eV}/\mathrm{s}$ at $T=1356\mathrm{}\hspace{0.5em}\mathrm{K}.$ The results are consistent with the scaling law $I_r\propto T^6$ and with the intensity, $I_r\sim 200\hspace{0.5em}\mathrm{eV}/\mathrm{s}$ at 1400 K, inferred from previous measurements of cooling in a storage ring of ${\mathrm{C}}_{60}^{-}$ ions injected from a hot source.

We explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration. If the system is prepared in a coherent superposition of two of the lower levels, we show that two incident resonant pulses can parametrically generate a third pulse in the medium. Over short distances, the propagation of this generated pulse can be partially controlled by varying the Rabi frequency of one of the driving fields. For a medium prepared in a coherent superposition of the three lower levels, we obtain a general expression for a three-photon Beer’s length. Under specific conditions, the medium can either become completely opaque or completely transparent to three incident resonant pulses. Moreover, a single incident pulse can be used to parametrically generate two additional pulses. Finally, a general relationship is found that links the amplitudes of the initial superposition of states and the amplitudes of the pulses at large distances in the medium, implying that the initial superposition can be used to engineer the amplitudes of the exiting pulses.