Joint, or simultaneous, measurements of noncommuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin-$1∕2$ particle along any two directions. Starting from an operational locality principle, it is shown how to obtain a bound on how sharp the joint measurement can be. We give a direct interpretation of this bound in terms of an uncertainty relation.

The viscous and thermal relaxation rates of an interacting fermion gas are calculated as functions of temperature and scattering length, using a many-body scattering matrix which incorporates medium effects due to Fermi blocking of intermediate states. These effects are demonstrated to be large close to the transition temperature $T_c$ to the superfluid state. For a homogeneous gas in the unitarity limit, the relaxation rates are increased by nearly an order of magnitude compared to their value obtained in the absence of medium effects due to the Cooper instability at $T_c$. For trapped gases the corresponding ratio is found to be about three due to the averaging over the inhomogeneous density distribution. The effect of superfluidity below $T_c$ is considered to leading order in the ratio between the energy gap and the transition temperature.

In a previous work [Opt. Commun. 138, 71 (1997)] a scheme was proposed to create traveling fields in the Fock state $\mid 2^J⟩$. Here we show how to extend this result to arbitrary Fock states. The procedure combines one-photon states impinging on a sequence of distinct beam splitters, each one associated with a (zero detection) single-photon photodetector, with optimization of the success probability to get the desired state. Advantages and disadvantages of this scheme are discussed.

We have measured with high resolution the full vector momenta of the doubly charged recoil ions produced when Ar and Ne atomic targets are ionized by intense circularly polarized few-cycle $(\sim 8\mathrm{fs})$ laser pulses in the sequential ionization region. The momentum spectra of the ions were found to exhibit structure which is characteristic of the relative binding energies of the two electrons and the sequential nature of the emission process. We demonstrate that the measured spectra can be used to extract subcycle time information regarding the sequential release of the two electrons.

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems prepared in an arbitrary isotropic state. It maximizes the entanglement of formation contained in the two copies of any maximally entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of isotropic states. For large $d$, the entanglement of formation of each clone tends to one-half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one-fourth the input entanglement in the large-$d$ limit.

We present the quantum theory for creation of collective atomic memory and generation of nonclassically correlated photon pairs from an ensemble via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The temporal evolution of photon numbers, photon statistics, and cross-correlation between the Stokes and anti-Stokes fields is found by solving the equation of motion for atomic spin-wave excitations. We consider a low-finesse cavity model with collectively enhanced signal-to-noise ratio, which remains still considerably large in the free-space limit. Our results describe analytically the dependence of quantum correlations on spin decoherence time and time delay between the write and read lasers and reproduce the observed data very well including the generated pulse shapes, strong violation of Cauchy-Schwarz inequality and conditional generation of anti-Stokes single-photon pulse. The approach we developed may be used also for quantum description of storage and retrieval of quantum information, especially when the statistical properties of nonclassical pulses are studied.

We study numerically and analytically the role of the combined effect of self-focusing, geometrical focusing, and the plasma defocusing in the formation of the fluorescence signal during the filamentation of a Ti:sapphire laser pulse in nitrogen molecular gas. Results of numerical simulations are used to estimate the number of excited ions in the focal volume, which is proportional to the fluorescence signal. We find good agreement between the theoretical results and the experimental data, showing that such data can be used to get further insight into the effective focal volume during filamentation of femtosecond laser pulses in transparent media.

Practically applicable criteria for the nonclassicality of quantum states are formulated in terms of different types of moments. For this purpose the moments of the creation and annihilation operators, of two quadratures, and of a quadrature and the photon number operator turn out to be useful. It is shown that all the required moments can be determined by homodyne correlation measurements. An example of a nonclassical effect that is easily characterized by our methods is amplitude-squared squeezing.

We studied dissociative ionization of oxygen by intense femtosecond laser pulses with central wavelengths between 550 and 1800 nm. We measured kinetic energy release spectra and angular distributions of fragments resulting from symmetric dissociation of doubly charged molecular ions (${\mathrm{O}}_2^{2+}\to {\mathrm{O}}^{+}+{\mathrm{O}}^{+}$ channel). In the kinetic energy release spectra we identified a number of distinct excited states of the molecular ion. Angular distributions for all but one of those states were consistent with recollision excitation following single ionization of ${\mathrm{O}}_2$. For the remaining $\left(B{}^3\Pi _{\mathbf{g}}\right)$ excited state we observed a characteristic resonant dependence of its relative yield on the central optical frequency of the pulse, with the yield peaking at around 890 nm. This presents unambiguous evidence in support of importance of resonant excitation channels in strong field ionization of molecules.

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the energy density of the free Fermi gas with a proportionality constant $\xi$. The author uses a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employs Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi =0.42$ and a rather large effective mass. The form of the density functional is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.

The Aharonov-Bohm scattering of relativistic spin-$1∕2$ particles with an anomalous magnetic moment are studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. It is somewhat unexpected that the results are in general the same as those for particles without an anomalous magnetic moment. However, when the incident energy takes some special values, the cross section for polarized particles is dramatically changed. In these cases the helicity of scattered particles is not conserved. In particular, the helicity of particles scattered in the backward direction is all reversed. In the nonrelativistic limit, a very simple relation between the polarized directions of the incident and scattered particles is found, for both general and special incident energies. For particles without an anomalous magnetic moment this relation can be drawn from previous results but it appears to be unnoticed.

A scheme for the numerical evaluation of the one-loop self-energy correction to all orders in $Z\alpha$ is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a partial-wave expansion that converges more rapidly than in the other methods reported in the literature.

We have carried out a coincidence experiment between energy-resolved resonant Auger electrons and mass-resolved ions on ${\mathrm{CH}}_3\mathrm{F}$ molecules following F $1s$ and C $1s$ excitation to the lowest unoccupied C–F antibonding molecular orbital ${\sigma }_{\mathrm{CF}}^{*}$. We found a strong enhancement of the ${\mathrm{F}}^{+}$ or ${\mathrm{CH}}^{+}$ ion production in coincidence with the F $KVV$ and C $KVV$ spectator Auger electrons, respectively, in the wide binding energy range of 28–36 eV. This site-selective ion production is interpreted as a consequence of the resonant Auger emission taking place in the transient region where the C–F elongation caused by the core excitation transforms the molecular valence orbitals gradually into nonoverlapping valence orbitals of each fragment.

Total cross sections (TCSs) for $0.2–1000\mathrm{eV}$ positrons and $0.4–1000\mathrm{eV}$ electrons colliding with normal hexane and cyclohexane molecules are reported. For positron scattering, low-lying peaks at $0.8\mathrm{eV}$ for normal hexane and $1.6\mathrm{eV}$ for cyclohexane are observed. For both molecules, positron TCSs are larger than electron TCSs below $2.8\mathrm{eV}$; for electron scattering, the main resonance peak in the TCS curve is at $7.5\mathrm{eV}$, followed by a shoulder at about $22\mathrm{eV}$. TCSs for normal hexane are larger than those for cyclohexane for both positrons and electrons over all the energy range. Striking similarities, more pronounced for electron impact, have been observed between $c$-hexane and benzene TCSs and are attributed to the similarity in molecular structure between these two molecules, whereby each has a hexagonal ring based on the six C atoms.

The $3d$ photoionization and subsequent normal Auger decay processes in atomic strontium have been investigated. To understand the electron spectra following photoionization of a $3d$ electron, a series of ab initio computations, based on the multiconfiguration Dirac-Fock method, were performed. From the calculated photoionization and Auger decay amplitudes the relative photoionization cross sections were derived, together with the total and partial Auger decay widths and relative Auger intensities. Emphasis was placed on the effects of electron-electron correlations in the $3d$ hole state. The theoretical predictions were compared to the high-resolution synchrotron radiation-induced photoelectron and Auger electron spectra.

We derive scaling laws for the spin decoherence of neutral atoms trapped near conducting and superconducting plane surfaces. A result for thin films sheds light on the measurement of Y. J. Lin, I. Teper, C. Chin, and V. Vuletić [Phys. Rev. Lett. 92, 050404 (2004)]. Our calculation is based on a quantum-theoretical treatment of electromagnetic radiation near metallic bodies [P. K. Rekdal, S. Scheel, P. L. Knight, and E. A. Hinds, Phys. Rev. A 70, 013811 (2004)]. We show that there is a critical atom-surface distance that maximizes the spin relaxation rate and we show how this depends on the skin depth and thickness of the metal surface. In the light of this impedance-matching effect we discuss the spin relaxation to be expected above a thin superconducting niobium layer.

Effect of relativistic reversal of the ponderomotive force (PF), reported earlier for a collinear configuration of electron and laser standing wave [A. E. Kaplan and A. L. Pokrovsky, Phys. Rev. Lett., 95, 053601 (2005)], is studied here theoretically for various types of polarizations of the laser beam. We demonstrated that the collinear configuration, in which the laser wave is linearly polarized with electric field $\vec{E}$ parallel to the initial electron momentum ${\vec{p}}_0$, is the optimal configuration for the relativistic reversal. In that case, the transverse PF reverses its direction when the incident momentum is $p_0=mc$. The reversal effect vanishes in the cases of circular and linear with $\vec{E}\perp {\vec{p}}_0$ polarizations. We have discovered, however, that the counter-rotating circularly polarized standing waves develop attraction and repulsion areas along the axis of laser, in the laser field whose intensity is homogeneous in that axis, i.e., has no field gradient.

Two-photon interference and “ghost” imaging with entangled light have attracted much attention since the last century because of features such as nonlocality and subwavelength effects. Recently, it has been found that pseudothermal light can mimic certain effects of entangled light. We report here the first observation of two-photon interference with true thermal light.

The semiclassical propagation of spin-coherent states is considered in complex phase space. For two time-independent systems, we find the appropriate classical trajectories and show that their combined contributions are able to describe quantum interference with great accuracy. Not only the modulus but also the phase of the quantum propagator, both dynamical and geometric terms combined, are accurately reproduced.

In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a “maximally” mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e., how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.