We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive-operator-valued measure corresponding to the multiple-phase estimation. In particular, we discuss the explicit case of the optimal detection of double phase for a system of identical qutrits and generalize these results to optimal multiple-phase detection for d-dimensional quantum states.

The nonrelativistic energies of the hydrogen molecular ions ${\mathrm{H}}_2^{+},$ ${\mathrm{D}}_2^{+},$ ${\mathrm{T}}_2^{+},$ ${\mathrm{HD}}^{+},$ ${\mathrm{HT}}^{+},$ and ${\mathrm{DT}}^{+}$ are evaluated for the ground and the first-excited P states, using variational wave functions in Hylleraas coordinates. The dipole polarizabilities of the ground states of the ions are determined precisely. Our results for the dipole polarizabilities represent the most accurate calculations reported so far. For ${\mathrm{H}}_2^{+},$ for example, the dipole polarizability is $3.168725802{67\left(1\right)a}_0^3,$ with the uncertainty of three parts in ${10}^{12}.$

We report sympathetic cooling and compression of a few thousand positrons by laser-cooled ${}^9{\mathrm{Be}}^{+}$ ions in a Penning ion trap. The observed centrifugal separation of the two species implies approximate rigid rotation of the positrons and ${}^9{\mathrm{Be}}^{+}$ ions, and a positron density comparable to the ${}^9{\mathrm{Be}}^{+}$ ion density of $\gtrsim 4\times {10}^9{\mathrm{cm}}^{-3}.$ We use the sharpness of the separation to place a 5-K upper limit on the positron temperature of motion parallel to the magnetic field. The positron lifetime is greater than two weeks in our room-temperature Penning trap.

Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.

A theoretical possibility of shock wave formation in a high-density Bose-Einstein condensate with strong repulsive interaction is reported. A mechanism of transformation of sound waves into shock waves is described. The speed of shock waves as well as relationships between jumps of velocity and density at the front of the surface of discontinuity are derived. The theory is illustrated by the analytical solution for shock wave propagation in a dense condensate cloud.

For a transition $F_e=0\mathrm{}\leftrightarrow F_g=1\mathrm{}$ driven by a linearly polarized light and probed by a transverse light, which has two equal circular components and is orthogonal to the linear polarization of the drive field and magnetic field, quantum coherence effects are investigated. Due to the coupling between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating with a pump-probe detuning in the steady state. At the zero pump-probe detuning, the subluminal and superluminal light propagations are predicted. Finally, there exist the large population fluctuations when we vary the pump-probe detuning.

It is shown that the mean value of any observable with a bounded spectrum can be uniquely determined from binary statistics of the measurement performed on a single-qubit ancilla coupled to a given system. The corresponding positive operator-valued measure fully encodes the observable structure. The method is generalized to the case of distant-laboratory paradigm and is considered in the context of entanglement detection with few local measurements. The results are also discussed in the context of quantum programming.

The surface-impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics that are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates (or the Casimir force acting between a plate and a sphere) are performed at different separations and temperatures specific for the regions of the anomalous skin effect and infrared optics. The results are in good agreement with those obtained by the use of the tabulated optical data for the complex refraction index and plasma model. It is argued that the surface impedance approach lays a reliable theoretical framework for the future measurements of the thermal Casimir force.

A diode-laser-based technique has been developed for absolute line strength measurements with high precision and accuracy, combining a spectroscopic determination of the integrated absorbance with an optical measurement of the absorption path length by means of a Michelson interferometer. This method has been applied to several ${}^{12}{\mathrm{C}}^{16}{\mathrm{O}}_2$ vibrorotational transitions belonging to the ${\nu }_1+2\mathrm{}{\nu }_2^0+{\nu }_3$ combination band, in the spectral region around 2 μm. The 1σ overall accuracy in line strength determination ranges between $0.4\%$ and $0.7\%,$ while the experimental reproducibility is estimated to be around $0.1\%.$ To our knowledge, these levels are the highest ever reached before. The pressure-broadening coefficients for the same transitions are also reported.

We discuss the relation between attractive singular potentials $-{\alpha }_s{/r}^s,$ $s>~2,$ and inelasticity. We show that attractive singular potentials can be regularized by an infinitesimal imaginary addition to the interaction strength ${\alpha }_s=\mathrm{Re}{\alpha }_s\pm i0.\mathrm{}$ Such a procedure enables the unique definition of the scattering observables and is equal to an absorption (creation) of the particles in the origin. It is shown that the suggested regularization is an analytical continuation of the scattering amplitudes of a repulsive singular potential as a function of the interaction strength ${\alpha }_s.$ Thus a regularized singular potential has no bound states. The near-threshold properties of the regularized singular potential are examined. We obtain expressions for the scattering lengths, which turn to be complex even for an infinitesimal imaginary part of the interaction strength. The problem of the perturbation of the near-threshold spectrum of a regular potential by a singular one is treated, the expressions for the level shifts and widths are obtained. The physical sense of the suggested regularization is that the scattering observables are insensitive to any details of the short-range modification of a singular potential if there exists sufficiently strong inelastic short-range interaction. In this case, the scattering observables are determined by the solutions of the Schrödinger equation with the regularized potential $-({\alpha }_s\pm {i0)/r}^s.$ Possible applications of the developed formalism to the systems with a short-range annihilation are discussed.

The solution of the many-electron many-photon (MEMP) problem for strong fields is facilitated if the corresponding theory entails a computational methodology that combines economy with accuracy and generality, as regards electronic structure and the incorporation of the continuous spectrum. By applying the nonperturbative MEMP theory (MEMPT) to the prototypical ${\mathrm{Li}}^{-}{}^{1}S$ state, where both radial and angular correlations in the initial state and interchannel couplings in the final scattering states cannot be ignored, we computed frequency-dependent widths Γ(ω) of multiphoton detachment, as well as energy shifts Δ(ω), for intensities $1\times {10}^9–1\times {10}^{11}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ using one- as well as two-color fields. Even though the ${1s}^{2}2p{}^2{P}^o$ threshold is kept energetically closed, its coupling to the open channel ${1s}^{2}2s{}^{2}S$ cannot be ignored. For the two-color MEMP problem, the present application of the MEMPT provides results for a four-electron system, whereby the self-consistent field, electron correlation, and interchannel coupling are taken into account. The results for (ω, 3ω) laser fields exhibit the recently predicted [Th. Mercouris and C.A. Nicolaides, Phys. Rev. A 63, 013411 (2001)] linear dependence of the rate on $\cos \phi ,$ where φ is the phase difference of the two weak fields. Based on this and on lowest-order perturbation theory (LOPT), we obtain a quantity characteristic of the system atom plus fields, which we name the “interference generalized cross section.” For the one-color system, comparison is made with our previous conclusions [C.A. Nicolaides and Th. Mercouris, Chem. Phys. Lett. 159, 45 (1989); J. Opt. Soc. Am. B 7, 494 (1990)] and with results from recent calculations of the two- and three-photon detachment rates by Glass et al. [J. Phys. B 31, L667 (1998)], who implemented R-matrix Floquet theory, and by Telnov and Chu [Phys. Rev. A 66, 043417 (2002)], who implemented time-dependent density-functional theory in the Floquet formulation via exterior complex scaling. Similarities as well as discrepancies are observed. Our results for Γ(ω) and Δ(ω) involve a dense set of values as a function of ω and provide a clear picture of the physics below, at, and above the $\overrightarrow{3}2$ photon threshold.

The kinetic-energy distribution of ${\mathrm{D}}^{+}$ fragments obtained from the ionization of ${\mathrm{D}}_2$ molecules with intense 20-fs pulses includes a high-energy component extending up to ∼10 eV. These fragments are only present for linearly, or slightly elliptically, polarized light. Both the maximum kinetic-energy and the ellipticity dependence are consistent with nonsequential double ionization caused by recollision.

We record angle-resolved electron-momentum distributions from 800-nm short-pulse laser ionization of argon and compare our data with numerical solutions of the time-dependent Schrödinger equation. A model potential of argon and the single active electron approximation are used. The calculation shows quantitative agreement in all dominant features of the experimental results. The energy and angular distributions of the photoelectrons, together with numerical simulations, allow us to identify the multiple processes involved during the interaction, such as channel switching, multiphoton resonant and nonresonant ionization, and ac Stark splitting.

We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to the decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case, four-wave mixing can persist for much longer times compared to the case of negligible back action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.

We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\Lambda$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.

We theoretically study the collision-induced constructive quantum interference in an open four-level system with the density-matrix approach based on the experimental observation of constructive quantum interference between two transition pathways ${3P}_{1/2}-5S$ (or $4D)$ and ${3P}_{3/2}-5S$ (or $4D)$ via equal-frequency hybrid excitation in the ${\mathrm{Na}}_2-\mathrm{Na}$ system. The effects of the collision-induced coherent and incoherent decay rates and the ratio of the two transition dipole moments on the interference are analyzed. It is shown that through the incoherent process (collision), the coherence between a widely separated doublet and subsequent constructive quantum interference can be realized. The physical origin of the constructive interference can be seen clearly in the dressed-atom picture. The theoretical results can also be used to qualitatively explain the dependence of quantum interference on the experimental buffer gas pressure and sample temperature.

We discuss conditional measurements as probes of quantum dynamics and show that they provide different ways to characterize quantum fluctuations. We illustrate this by considering the light from a subthreshold degenerate parametric oscillator. Analytic results and curves are presented to illustrate the behavior.

Within the framework of non-Markovian stochastic Schrödinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.