A general analytical formalism is described for the design of the excitation pulse (in the weak-field limit) that will excite a specified target wave packet. These analytical formulas (accurate to third order in the phase) provide multiple solutions for a class of target wave packets and provide a basis for choosing between these solutions. In addition, the possibility of independent compensation of the second- and third-order phase terms offers flexibility in the creation of exotic wave packets. A concrete design example is given for the generation of a well-localized Rydberg atomic wave packet at a specific target time.

Quantized adiabatic particle transport (QAPT) is considered and verified in a one-dimensional system using numerical simulation. More importantly, suggestions are given for ways to observe QAPT phenomena in atoms manipulated by laser beams. Although QAPT was originally considered for electrons in periodic substrate potentials, the optical systems provide a cleaner and experimentally feasible way to physically realize QAPT. The results in this paper serve as a model for the design of these experiments.

We study the formation of hexagonal patterns and the roll-hexagon transition in an active nonlinear optical system, namely a two-level laser with an injected signal, which displays distinctive and noteworthy features from the most commonly encountered pattern-forming systems with broken inversion symmetry, such as convective hydrodynamic systems and passive nonlinear optical systems. With respect to these systems, we show here that the roll-hexagon transition is accompanied in the Fourier space by a spontaneous breaking of the inversion symmetry $\overrightarrow{\mathrm{k}}$-k, which is a signature of the different physical mechanisms involved in the elementary process of pattern formation.

Using a self-consistent model that solves both the three-dimensional Schrödinger equation and the wave equation ab initio, we study the propagation of subfemtosecond pulses produced by high harmonic generation in a gas. The presence of a plasma shortens the coherence length for the harmonics. However, for the case of very short pump pulses, ionization is suppressed, and the coherence length can approach that of a neutral gas. Thus, the combination of enhanced single-atom harmonic generation for short pulses and improved phase matching allows for efficient amplification of attosecond x-ray pulses, resulting in 100 times higher output intensity for 5 fs compared to 10-fs pump pulses.

We report a fourth-order interference experiment in which pairs of photons produced in parametric down-conversion pumped by short optical pulses interfere in a Hong-Ou-Mandel interferometer. The visibility of the interference pattern is reduced for larger pump bandwidths. This effect can be understood in terms of the spectral distinguishability of the photon pairs. The interference can be restored by blocking the distinguishing information with a spectral filter.

We report measurements of cavity-QED effects for the radiative coupling of atoms in a dilute vapor to the external evanescent field of a whispering-gallery mode (WGM) in a fused silica microsphere. The high $Q$ $(5\mathrm{}\times {10}^7)$, small mode volume (10${}^{-8}$ cm${}^3)$, and unusual symmetry of the microcavity evanescent field enable velocity-selective interactions between fields with photon number of order unity in the WGM and $N_T\sim 1$ atoms in the surrounding vapor.

The usual formulation of the quantum Zeno effect (QZE) uses a sequence of rapid observations to prevent change. The same effect can be achieved with continuous observation. For partial inhibition of change we provide a quantitative relation between pulsed (at intervals $\delta t$) and continuous (with response time ${\tau }_O$) observations: the slowdown is the same for $\delta t=4\mathrm{}{\tau }_O.$ Including the continuous observer in the Hamiltonian gives an alternative view of the QZE, showing the appropriateness of the name “dominated time evolution.” Finally, the variation on the QZE in which a nonconstant sequence of projections can force change is also shown to be achievable by time-varying continuous observation.

We obtained the dispersion relation which the ground-state eigenvalue of a two-electron atom, considered as a function of the nucleus charge $Z,$ is to satisfy. With the help of this dispersion relation, we were able to obtain some information about the nature of the singular point of the ground state of a two-electron atom as a function of $Z.\mathrm{}$

The exact analytical values of the position and momentum information entropies are calculated for the single-slit and double-slit diffraction experiments. In both cases, the product of the exponentials of the entropies is strictly greater than the lower bound $\pi eħ$ given by the optimal entropic uncertainty relation for position and momentum, which implies that the single-slit and double-slit configurations are not minimum-uncertainty states. The results obtained show that the position-momentum entropic uncertainty relation provides a rigorous quantitative expression for the uncertainty principle in these experiments, unlike the Heisenberg inequality for standard deviations. However, it is also shown that, in the double-slit experiment, wave-particle duality cannot be derived from the entropic uncertainty relation.

In this work we present a theoretical study of the hydrogen atom in quantum phase space. A coordinate transformation is used that maps the hydrogen atom into a four-dimensional harmonic oscillator and the Wigner distribution function for the hydrogen atom is then obtained. This exactly soluble model can shed some light on finite-size features of Wigner’s distribution, which will be a vital experience for various dynamic problems.

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.

Semiclassical expansions for traces involving Green’s functions receive two contributions, one from the periodic or recurrent orbits of the classical system and one from the phase space volume, i.e., the paths of infinitesimal length. Quantitative calculations require the control of both terms. Here we discuss the contribution from paths of zero length with an emphasis on the application to Franck-Condon transitions. The expansion in the energy representation is asymptotic and a critical parameter is identified. In the time domain, a series expansion of the logarithm of the propagator gives very good results. The expansions are illustrated for transitions onto a linear potential and onto a harmonic oscillator.

Two-loop self-energy contributions to the fourth-order Lamb shift of ground-state hydrogenic ions are treated to all orders in $Z\alpha$ by using exact Dirac-Coulomb propagators. A rearrangement of the calculation into four ultraviolet finite parts, the $M,\hspace{0.5em}P,\hspace{0.5em}F$, and perturbed orbital (PO) terms, is made. Reference-state singularities present in the $M$ and $P$ terms are shown to cancel. The most computationally intensive part of the calculation, the $M$ term, is evaluated for hydrogenlike uranium and bismuth, the $F$ term is evaluated for a range of $Z$ values, but the $P$ term is left for a future calculation. For hydrogenlike uranium, previous calculations of the PO term give $-0.971$ eV: the contributions from the $M$ and $F$ terms calculated here sum to $-0.325$ eV.

We show that a quantum system may be associated with a backward stochastic process in complex configuration space when the so-called weak value of the position operator is interpreted as a conditional expectation value. The quantum-mechanical expectation values of the position, momentum, angular momentum, and energy are shown to be the weighted averages of the corresponding quantities for the stochastic process. Moreover, the stochastic trajectory is shown to reduce to the correct classical trajectory in the limit where the de Broglie wavelength vanishes.

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a very natural consistency constraint: if there are two different ways to compute the amplitude for a given process, the two answers must agree. This constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrödinger equation must be linear; i.e., nonlinear variants of quantum mechanics are inconsistent. The physical interpretation of the theory is given in terms of a single natural rule. This rule, which does not itself involve any probabilities, is used to obtain a proof of Born’s statistical postulate: we show that the probability of a certain outcome in an experiment is given by the square of the modulus of the corresponding amplitude. Thus, consistency leads to indeterminism.

An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)], is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the ratio between these two quantities is obtained.

The failure of conventional perturbation theory due to secularity is considered with renormalization-group tecniques in two operator problems. Specifically, some results concerning the quantum anharmonic oscillator and quantum parametric resonance are obtained with a rather modest effort in comparison to other methods.

The contribution of vacuum fluctuations and the radiation reaction to the energy-level shifts of a hydrogen atom, moving with uniform acceleration and interacting with the electromagnetic field, is considered. It is found that the reaction field contribution is not affected by the acceleration, whereas the vacuum fluctuations’ contribution depends on the acceleration. The differences with previous results for an accelerated two-level atom interacting with a scalar field are discussed in detail; in particular, it is shown that the effect of electromagnetic vacuum fluctuations on atomic level shifts, contrarily to the scalar field case, is not totally equivalent to that of a thermal field. It is argued that this lack of equivalence should be observable.

The precision with which the amplitude of the free electromagnetic field can be measured locally in QED is evaluated by analyzing a well-known gedanken experiment originally proposed by Bohr and Rosenfeld (BR). The analysis is performed by applying standard theoretical techniques familiar in quantum optics. The main result obtained for the precision is significantly different from the generally accepted Bohr-Rosenfeld result. This leads to questioning the widely accepted notion of the compensating field, fostered by these authors. A misconception at the origin of this notion is pointed out by a careful investigation of the self-force acting on the apparatus designed to measure the field. The correct expression for this self-force is found to be at variance with that proposed by Bohr and Rosenfeld and generally accepted. It is argued that, as a consequence of this new expression and in contrast with the generally accepted view, no compensating force of nonelectromagnetic nature is required in order to perform measurements of the quantum field amplitude with any desired accuracy. It is shown that the only limitations to the precision of the measurement, in the BR gedanken experiment, arise from the time-energy uncertainty principle, as well as from the finite dimensions of the measuring apparatus.

In consistent-history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories that it contains. It is argued that the framework is chosen by the physicist constructing a description of a quantum system on the basis of questions he wishes to address, in a manner analogous to choosing a coarse-graining of the phase space in classical statistical mechanics. The choice of framework is not determined by some law of nature, though it is limited by quantum incompatibility, a concept that is discussed using a two-dimensional Hilbert space (spin half particle). Thus certain questions of physical interest can only be addressed using frameworks in which they make (quantum-mechanical) sense. The physicist’s choice does not influence reality, nor does the presence of choices render the theory subjective. On the contrary, predictions of the theory can, in principle, be verified by experimental measurements. These considerations are used to address various criticisms and possible misunderstandings of the consistent-history approach, including its predictive power, whether it requires a new logic, whether it can be interpreted realistically, the nature of “quasiclassicality,” and the possibility of “contrary” inferences.