We demonstrate Bose-Einstein condensation of rubidium atoms in a simple low-power magnetic trap. This trap combines the quadrupole with the Ioffe configuration (QUIC trap) and consists of just three coils. Magneto-optically trapped ${}^{87}\mathrm{Rb}$ atoms are first loaded into the linear trapping potential of a magnetic quadrupole, which is then converted into the parabolic geometry of an Ioffe trap. During this process two spherical quadrupole traps with perpendicular axes merge and the trapped atomic cloud moves close to the magnetic field producing coils, resulting in tight confinement of the atoms while the power dissipation of the trap remains low. The magnetically trapped atoms are cooled to below the phase transition of Bose-Einstein condensation by rf-induced evaporation.

We measure the wavelengths of the Ni-like ${3d}^{9}4d{}^1{S}_0–{3d}^{9}4p{}^1{P}_1$ x-ray laser line in several low-Z Ni-like ions ranging from Y $\mathrm{}(Z=39\mathrm{})\mathrm{}$ to Cd $\mathrm{}(Z=48\mathrm{}).$ These wavelengths are compared with optimized level calculations using a multiconfiguration Dirac-Fock code. With the help of these results, we identify this line to very high accuracy in nonlasing plasmas from As $\mathrm{}(Z=33\mathrm{})\mathrm{}$ to Mo $\mathrm{}(Z=42\mathrm{}).$ Accurate values of these wavelengths are essential for performing plasma imaging and interferometry experiments with multilayer optics that use the x-ray laser to backlight other plasmas. These results also provide important atomic data that are currently missing about the energy of the $4d{}^1{S}_0$ level in the Ni I sequence.

We present a systematic investigation of the dynamical behavior of semiconductor lasers subject to external optical feedback dependent on the injection current and the optical feedback strength. We identify the regimes of low-frequency fluctuations (LFFs), fully developed coherence collapse, and a large regime of the coexistence of LFFs and stable emission on single high-gain external-cavity mode extending over more than one order of magnitude of optical feedback strengths. Thus, we provide experimental evidence for one major prediction of the theoretical model based on the Lang-Kobayashi equations, which proposes a deterministic mechanism underlying the LFFs.

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates.

We propose to pump semiconductor quantum dots with surface acoustic waves that deliver an alternating periodic sequence of electrons and holes. In combination with a good optical cavity such regular pumping could entail antibunching and sub-Poissonian photon statistics. In the bad-cavity limit a train of equally spaced photons would arise.

The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat reservoir, which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature $T$, and whose spectral density has a bandwidth that is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry’s phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electriclike forces appear as a consequence of geometrical effects. We also determine the average energy level shift produced in the fast system by this mechanism.

Motion of a nonrelativistic particle on a cone with a magnetic flux running through the cone axis (a “flux cone”) is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. The probability fluid (“quantum flow”) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial Aharonov-Bohm effects. For example, it is shown that, near the singularity, quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined, and the way it affects quantum flow is analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum flow. The connectivity of the configuration space is also discussed.

The ladder proof of nonlocality without inequalities for two spin-$\frac{1}{2}$ particles proposed by Hardy [in New Developments on Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1997)] and Hardy and co-workers [Phys. Rev. Lett. 79, 2755 (1997)] works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-$1$ particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-$s$ particles (with $s>~1)$.

Following the ideas of Popescu, the generic structure of any local hidden variable model for experiments involving sequences of measurements is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of “hidden nonlocality” is illustrated by an operational example.

A nonlinear stochastic Schrödinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (“Schrödinger cat”). Finally, our description of open systems is compatible with different positions of the “Heisenberg cut” between system and environment.

A path-integral formulation is developed for the dynamic Casimir effect. It allows us to study small deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency–wave-vector plane, using which a plethora of interesting phenomena can be studied. For a single corrugated plate we find a correction to mass at low frequencies and an effective shear viscosity at high frequencies that are both anisotropic. The anisotropy is set by the wave vector of the corrugation. For two plates, the mass renormalization is modified by a function of the ratio between the separation of the plates and the wavelength of corrugations. The dissipation rate is not modified for frequencies below the lowest optical mode of the cavity and there is a resonant dissipation for all frequencies greater than that. In this regime, a divergence in the response function implies that such high-frequency deformation modes of the cavity cannot be excited by any macroscopic external forces. This phenomenon is intimately related to resonant particle creation. For particular examples of two corrugated plates that are stationary, or moving uniformly in the lateral directions, Josephson-like effects are observed. For capillary waves on the surface of mercury a renormalization to surface tension and sound velocity is obtained.

We show how to determine (reconstruct) a master equation governing the time evolution of an open quantum system. We present a general algorithm for the reconstruction of the corresponding Liouvillian superoperators. The dynamics of a two-level atom in various environments is discussed in detail.

Mathematical methods are presented that give pairs of linearly independent solutions for an attractive ${1/r}^6$ potential. These solutions represent a different class of special functions that are important to the understanding of molecular vibration spectra near the dissociation threshold and slow atomic collisions.

Within the framework of the Milburn model of intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)], which is based on an assumption of an existence of the fundamental time step, we study the dynamics of open systems. We show that evolution of an open system governed by the Milburn equation can be significantly modified compared to the standard Schrödinger quantum mechanics. This modification is most pronounced when an open system is strongly coupled to its environment.

Whether the loss of visibility due to measurement in two-slit interference patterns can always be attributed to momentum transfer depends upon how one defines the last term. The momentum transfer to a quantum particle can be determined unambiguously if it was initially in a momentum eigenstate, but that is not the state relevant to a two-slit experiment. A sensible answer for the two-slit problem was obtained by Wiseman et al. [Phys. Rev. A 56, 944 (1997)] using the formalism of the Wigner function. Here I show that a more general answer can be obtained using the Bohmian formulation of quantum mechanics, in which particles have a definite position and momentum at all times. By following all possible trajectories of the particle it is possible to calculate the probability distribution $P_{\mathrm{total}}^B{(p}^{\prime })$ for it to receive a momentum transfer $p^{\prime }$ as a result of the measurement. Furthermore, the 1-norm of this distribution obeys the relation $〈|p^{\prime }|{〉}_{\mathrm{total}}^{B}d>~2ħ\left(1\mathrm{}-V\right)/\pi ,$ where $V$ is the visibility of the interference pattern and $d$ is the slit separation. This confirms that the momentum transfer in a welcher Weg (which path) experiment is in accord with the uncertainty principle. Like the Wignerian analysis, the Bohmian analysis clearly distinguishes between a local momentum transfer (which occurs even if the particle is localized at a single slit) and a nonlocal momentum transfer (which occurs only if the particle is delocalized, at both slits). In the Bohmian analysis the former occurs at the time of the measurement, while the latter occurs after the measurement, and is a consequence of Bohm’s “quantum potential.”

Various differential cross sections of high-energy photon splitting in the electric fields of heavy atoms are calculated exactly in the parameter $Z\alpha$. The consideration is based on the quasiclassical approach applicable for small angles between all photon momenta. The expressions obtained are valid for arbitrary transverse momenta of final photons. The detailed investigation of the process is performed taking into account the effect of screening. The exact cross section turns out to be noticeably smaller than the result obtained in the Born approximation.

General Hamiltonian systems related by linear canonical transformations, which are combinations of the scale and gauge transformations, are considered. Using path integrals, it is proven that each quantum Hamiltonian can be expressed by the classical Hamiltonian whose canonical variables are replaced by their corresponding quantum operators. The relation between the Schrödinger solution and the propagator for the transformed (new) and for the original (old) systems are evaluated by applying the unitary operator which describes the linear relationship between their quantum operators as the corresponding relations between their classical forms. It is shown that the uncertainty relations between the canonical position and momentum operator depend on the gauge function chosen, and satisfy Heisenberg’s uncertainty principle. The uncertainty relations between the canonical position and kinetic momentum operator (distinguished from the momentum operator) do not depend on the gauge function chosen, and may not satisfy Heisenberg’s uncertainty principle. By the gauge transformation, a single system has innumerable Schrödinger equations, but the quantum averages of the function of the position and kinetic momentum operators are invariant for all solutions, as for classical cases.

The many-particle time-dependent Schrödinger equation is derived using the principle of minimum Fisher information. This application of information theory leads to a physically well motivated derivation of the Schrödinger equation, which distinguishes between subjective and objective elements of the theory.

It is shown that the differential virial theorem and its time-dependent extension are equivalent to the Euler equation for a quantum fluid. In light of this, the connection between the differential virial theorem and density-functional theory is also explored.

A canonical formalism is presented that allows for investigations of quantum radiation induced by localized, smooth disturbances of classical background fields by means of a perturbation theory approach. For massless, nonself-interacting quantum fields at zero temperature, we demonstrate that the low-energy part of the spectrum of created particles exhibits a nonthermal character. Applied to QED in varying dielectrics, the response theory approach facilitates the study of two distinct processes contributing to the production of photons: the squeezing effect due to space-time varying properties of the medium and the velocity effect due to its motion. An alternative quantization method of the electromagnetic field in linear, inhomogeneous but nondispersive dynamical dielectrics is proposed. The generalization of this approach to finite temperatures as well as the relation to sonoluminescence is indicated.