We demonstrate experimentally the effect of a three-photon electromagnetically induced transparency in hot ${}^{85}\mathrm{Rb}$ atomic vapor driven by two coherent electromagnetic fields. The narrow transparency window is observed on the background of high-contrast Doppler-free subnatural absorption resonance. Our analytical calculations and numerical simulations are in good agreement with the experimental data. Both the transparency and the absorption resonances can find applications in high-precision metrology.

We present a scheme to reconstruct a two-mode entangled state in a high-$Q$ cavity from the spontaneous emission spectrum in a driven four-level atomic system. The two modes of the cavity field drive the upper three levels of the atom and thus the spontaneous emission spectrum contains the information about the photon statistics of the cavity field. Wigner function of the driving field is recovered from the photon statistics in a straightforward manner.

Absolute cross sections for the production of ${\mathrm{H}}^{-}+{\mathrm{D}}^{+}$ in the collision of cold ${\mathrm{HD}}^{+}$ with electrons have been measured in the storage ring CRYRING at Manne Siegbahn Laboratory, Stockholm University in Stockholm. The magnitude of this cross section $(\sim 3\times {10}^{-19}\hspace{0.5em}{\mathrm{cm}}^2$ above threshold), as well as its interference pattern (14 peaks in the interaction energy region 0–16 eV) were found to be identical to that observed for the production of ${\mathrm{D}}^{-}+{\mathrm{H}}^{+},$ which was measured earlier in CRYRING.

A much simpler method is proposed for the evaluation of the exact finite-temperature particle and energy densities for noninteracting Bose and Fermi gases in d-dimensional anisotropic harmonic traps. For the Bose gas in the whole range of temperature, the exact results are obtained. For the Fermi gas with chemical potential less than the single-particle ground-state energy, the exact results are obtained.

A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle qubits that are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.

so(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb, and Mörse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the oscillator potential by point canonical transformations. We call this class the “oscillator class.” A nontrivial graded extension of so(2,1) is defined and its realization by two-dimensional matrices of differential operators acting in spinor space is given. It turns out that this graded algebra is the supersymmetry algebra for a class of relativistic potentials that includes the Dirac-Oscillator, Dirac-Coulomb, and Dirac-Mörse potentials. This class is, in fact, the relativistic extension of the oscillator class. An extended point canonical transformation, which is compatible with the relativistic problem, is formulated. It maps all of these relativistic potentials into the Dirac-Oscillator potential.

We study the remote implementation of a unitary transformation on the state of a qubit. We show the existence of nontrivial protocols (i.e., using less resources than bidirectional state teleportation) that allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a nontrivial protocol: Arbitrary rotations around a fixed direction $\overrightarrow{n}$ and a $\pi$ rotation about an arbitrary direction lying in a plane orthogonal to $\overrightarrow{n}.$ The former operations effectively constitute the teleportation of arbitrary angles. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is known, a priori, in which of the two teleportable subsets the transformation belongs. If it is known, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If it is not known in which subset the transformation belongs, two e-bits of entanglement need to be consumed and the classical channel becomes asymmetric with two c-bits being conveyed from Alice to Bob but only one from Bob to Alice.

It was recently shown (e-print quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether already the interactions between the qubits introduced with the intention to operate the quantum computer may lead to quantum chaos. The analysis focuses on two well-known quantum algorithms, namely, Grover’s search algorithm and the quantum Fourier transform. I show that in both cases the same very unusual combination of signatures from chaotic and from integrable dynamics arises.

The effect of autoionizing resonances on ionization has been studied since the historic work of Fano. In the autoionization problem, it is not possible to distinguish electrons, that have been directly ejected from the atom, from those that were first excited to an autoionizing resonance level because of the extremely short lifetime. As a result, these two processes will interfere. Furthermore if the energy difference between the resonances is not larger than the width of the resonances, the resonances will also interfere with each other. In this paper, we examine electron-impact ionization $\mathrm{}(e,2e)\mathrm{}$ for cadmium in the energy range where the autoionizing resonances overlap and interfere. First-order distorted-wave results will be compared with recent measurements and previous calculations.

The convergent close-coupling method widely used now for calculations of charged particles scattering amplitudes is considered from the point of view of the rigorous many-body Coulomb scattering theory. It is shown that an approximate scattering amplitude calculated within the frame of the method does not converge to a solution of the corresponding Lippmann-Schwinger equation.

A theoretical investigation on low-energy electron scattering of vibrationally excited ${\mathrm{H}}_2$ molecules is reported. Cross sections for elastic and inelastic collisional processes calculated for the four lowest-vibrational-state targets are presented in the 1–10-eV energy range. The body-frame vibrational close-coupling approach which accounts for exactly the vibrational effects is used to solve the scattering equations. An optical potential, composed by the exact static-exchange and parameter-free correlation-polarization contributions, is used to represent the collisional dynamics. The calculated integral cross sections for both elastic and $\Delta v=1\mathrm{}$ excitation processes show resonance features for initial states with $v>~2.$ These structures are associated to the ${}^2{\Sigma }_u^{+}$ shape resonance. Also in general, the scattering cross sections for excited targets are larger than those for ground-state target. Their magnitudes at the maxima can be roughly related with the size of the target at each vibrational level.

Internal dielectronic excitation (IDE) is a correlated atomic physics process that takes place when the deexcitation of a Rydberg electron is accompanied by the excitation of a more tightly bound electron, resulting in a doubly excited inner-shell configuration. Subsequent x-ray emission involving an electron transition to a shell that initially contained no vacancies identifies the IDE process. IDE is mediated by the electron-electron interaction in a manner similar to a time-reversed Auger transition, and can occur during the neutralization of a slow highly charged ion interacting with a solid where there are many Rydberg levels that can give rise to correlated transitions to degenerate energy states. We have investigated IDE for a wide range of projectiles and solid targets by measuring the resulting x-ray emission. The characteristic features of the x-ray spectra suggest that IDE occurs above the surface of the solid.

We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage. Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level that will be populated in STIRAP process in $\Lambda$ or V systems by the choice of the peak amplitudes or the pulse sequence.

Using femtosecond pulse-shaping techniques, we are able to control several useful parameters of coherent anti-Stokes Raman spectroscopy (CARS). By shaping both the pump and the Stokes pulses with an appropriate spectral phase function, we eliminated the nonresonant CARS background. In addition, we designed pulses which selectively excite one of two neighboring Raman levels, even when both are well within the excitation spectrum. High-resolution CARS spectra were recorded in spite of the broad femtosecond pulse spectrum.

Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent nonpolynomial nonlinear Schrödinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D nonpolynomial Schrödinger equation (2D NPSE) that models disk-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schrödinger-like equations with different polynomial nonlinearities.

We make a comparative study of quadrature squeezing, photon-number distribution, and Wigner function in a decayed quantum system. Specifically, for a field mode prepared initially the Schrödinger cat states interacting with a zero-temperature environment, we show that the rate of reduction of the nonclassical effects in this system is proportional to the occurrence of the decoherence process.

As a development of our previous work, this paper is concerned with the Greenberger-Horne-Zeilinger (GHZ) nonlocality for continuous-variable cases. The discussion is based on the introduction of a pseudospin operator, which has the same algebra as the Pauli operator, for each of the N modes of a light field. Then the Bell-Clauser-Horne-Shimony-Holt inequality is presented for the N modes, each of which has a continuous degree of freedom. Following Mermin’s argument, it is demonstrated that for N-mode parity-entangled GHZ states (in an infinite-dimensional Hilbert space) of the light field, the contradictions between quantum mechanics and local realism grow exponentially with N, similarly to the usual N-spin cases.

The quantum time-of-arrival problem is discussed within the standard formulation of nonrelativistic quantum mechanics with parametric time. It is shown that a general class of arrival-time probability distributions results from the assumption that the arrival process of a quantum particle is similar in nature to other time-dependent arrival-type processes occurring, e.g., in population biology or queue theory. A simple but illustrative example related to the well-known Wigner discussion of the time-energy uncertainty relation is given and the numerical results obtained are compared with Kijowski’s distribution [Rep. Math. Phys. 6, 362 (1974)] of arrival times for a free quantum particle.

Quantum computing gates are proposed to apply on trapped ions in decoherence-free states. As the phase changes due to time evolution of components with different eigenenergies of quantum superposition are completely frozen, quantum computing based on this model would be perfect. Possible applications of our scheme in future ion-trap quantum computers is discussed.

In this paper we investigate the decoherence dynamics of nonclassical vibronic states of a trapped ion. We assume that the origin of decoherence is the coupling of the vibrational modes with classical stochastic electric fields and the finite lifetime of the electronic levels. We show that these interactions lead to a dispersivelike decoherence dynamics. The theoretical results agree with the measurements reported by Meekhof et al. [Phys. Rev. Lett. 76, 1796 (1996)].