The interaction of the permanent electric dipole moment of a polar molecule with a strong static electric field can create oriented rotational wave packets, which are termed pendular states. Molecules traveling in a molecular beam experience a fringing field due to the edges of the conducting plates which create the electric field as a slowly varying time-dependent perturbation. Since Stark energies of some asymmetric-top molecules present numerous avoided crossings as a function of field strength, the time evolution of rotational wave functions for molecules entering the field is complex. We have studied, by solving the time-dependent Schrödinger equation, the dynamics caused by selected avoided crossings, and the time evolution of the orientation corresponding to 24 rotational wave functions, for the near-prolate asymmetric-top iodobenzene. Implications for the population distribution of molecules in the electric field and for experimental schemes to decelerate molecules are discussed.

We investigate the quantum localization of the one-dimensional Rydberg atom subject to a unidirectional periodic train of impulses. For high frequencies of the train the classical system becomes chaotic and leads to fast ionization. By contrast, the quantum system is found to be remarkably stable. We identify for this system the coexistence of different localization mechanisms associated with resonant and nonresonant diffusion. We find for the suppression of nonresonant diffusion an exponential localization whose localization length can be related to the classical dynamics in terms of the “scars” of the unstable periodic orbits. We show that the localization length is determined by the energy excursion along the periodic orbits. The suppression of resonant diffusion along the sequence of photonic peaks is found to be nonexponential due to the presence of high harmonics in the driving force.

We study tunneling dynamics of atomic pairs in Bose-Einstein condensates with Feshbach resonances. It is shown that the tunneling of the atomic pairs depends on not only the tunneling coupling between the atomic condensate and the molecular condensate, but also the interatomic nonlinear interactions and the initial number of atoms in these condensates. It is found that in addition to oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic-pair tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of decoherence induced by noncondensate atoms on the tunneling dynamics is investigated. It is shown that decoherence suppresses atomic-pair tunneling.

A grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation with fields for occupied and unoccupied sites, an effective field theory is derived in which a complex field corresponds with the order parameter of the condensate and a real field with the total density of bosons. Near the boundary between the normal and the superfluid phase, we obtain the Ginzburg-Landau functional for the superfluid order parameter. A mean-field calculation shows that the critical temperature $T_c$ increases with increasing density up to a maximum and decreases with further increasing density.

We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential, the one-dimensional δ-kicked harmonic oscillator, and its semiclassical limit, discovering in the process an interesting interference effect, where increasing the strength of the repulsive nonlinearity promotes localization of the wave function. We explore the feasibility of an experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion.

We study the quantum coherent tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slow and rapid varying in the time trap potential are considered. In the case of a slowly varying trap, we study the nonlinear resonances and chaos in the oscillations of the relative atomic population. Using the Melnikov function approach, we find the conditions for chaotic macroscopic quantum-tunneling phenomena to exist. Criteria for the onset of chaos are also given. We find the values of frequency and modulation amplitude which lead to chaos on oscillations in the relative population, for any given damping and the nonlinear atomic interaction. In the case of a rapidly varying trap, we use the multiscale expansion method in the parameter $\varepsilon =1/\Omega ,$ where Ω is the frequency of modulations, and we derive the averaged system of equations for the modes. The analysis of this system shows that new macroscopic quantum self-trapping regions, in comparison with the constant trap case, exist.

The energy bandwidths of high-order harmonics of a Ti:sapphire ultrafast laser are extracted from electron kinetic-energy measurements of the photoionization of gas-phase atoms and molecules. High-order harmonics of the 70 fs, 800 nm laser are produced by focusing $\approx 2.5\hspace{0.5em}\mathrm{mJ}$ pulses into a jet of neon gas and are frequency-separated by a grazing-incidence grating. Photoelectrons resulting from the ionization of gaseous samples are energy-analyzed with a magnetic bottle time-of-flight spectrometer. Energy broadening of the photoelectron peaks at low kinetic energies are a direct result of the energy bandwidths of the harmonics. The energy bandwidths of the harmonics are found to increase from $0.11(\pm 0.03)\hspace{0.5em}\mathrm{eV}$ (7th harmonic) to $0.37(\pm 0.03)\hspace{0.5em}\mathrm{eV}$ (45th harmonic) in a gradual manner. The higher-order harmonics (47th–55th) appear to reach a plateau at a value of $\approx 0.43\hspace{0.5em}\mathrm{eV}.$ Though a full theoretical treatment of bandwidths of the harmonics for the 70 fs driving pulse regime does not exist, the theories developed for shorter pulses $(<~30\hspace{0.5em}\mathrm{fs})$ can give insight into the observed results.

The bright Einsten-Podolsky-Rosen (EPR) beams with the quantum correlations between the quadrature-phase amplitudes of the spatially separated signal and idler beams have been experimentally generated from a cw nondegenerate optical parametric amplifier injected by seed waves with degenerate frequency but orthogonal polarization. The correlation degree of $0.853\pm 0.004$ between the quadrature-phase amplitudes of the output entangled beams is directly inferred from the measured quadrature-phase squeezing of the output vacuum squeezed-state light field formed from superposition of the original signal and idler modes. Our theoretical calculation and experimental measurements provide a reliable method to confirm the quadrature phase-squeezing and EPR correlation of bright light field.

In this paper we investigate how excess noise behaves in a two-mode laser below and above threshold. In both cases the mode correlations of the stationary state modify the noise essentially. Our two-mode model relates directly to experimental situations.

We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze different schemes of phase-shift estimation. Finally, the absolute estimation of the quantum efficiency of both linear and avalanche photodetectors is studied. In all the considered applications, the Gaussian bound on statistical errors is attained with a few thousand data.

This paper discusses the generation of high-order optical harmonics from solid targets using laser pulses of 35 and 120 femtoseconds. Harmonics up to the 35th order were observed. High conversion efficiency has been achieved, e.g., ${10}^{-6}$ to the $10\mathrm{th}$ harmonic. It is demonstrated that the harmonic emission is highly directional and that the harmonic efficiency decreases rapidly with increasing plasma scale length.

In a recent paper Marburger and Das [J. H. Marburger III and K. K. Das, Phys. Rev. A 59, 2213 (1999)] considered an interference visibility experiment involving two weakly interacting Bose-Einstein condensates. It was shown that condensate eigenstates of the Hermitian relative phase operator do not give interference fringes with unit visibility in a Young’s double slit type of experiment. The authors concluded that “… these states are not especially well suited to describe weakly interacting multiply occupied coherent bosonic systems.” In this work we suggest a criterion for states with a well-defined relative phase. Subsequently we show that the relative phase operator eigenstates satisfy this criterion. This suggests that the concept of interference visibility can, and should, be generalized, since it is widely believed that interference visibility is a measure of the relative phase properties. We therefore propose a broader, but still operational, definition of interference visibility, which we call generalized visibility, and prove that the relative phase operator eigenstates indeed can show unit generalized visibility. We also derive a simple, but general, criterion for states which can display a unit generalized visibility. Somewhat surprisingly, this criterion is weaker than the criterion for a well-defined relative phase. Finally, we discuss which two-mode states can display unit (ordinary) visibility.

We study a composite system consisting of N three-level Λ-type atoms and a degenerate optical parametric oscillator (DOPO). The standard DOPO threshold is modified by the presence of the three-level atoms. Bistability (in the intracavity field intensity versus pumping intensity for the DOPO) appears for certain atomic detunings and coupling field strengths between the intracavity field and one of the atomic transitions. The effects of the coupling field (for the auxiliary transition in the three-level atomic system) are discussed. The susceptibility of the three-level atoms is calculated for the lower and upper branches of the bistable curve. Both analytical (for certain special cases) and numerical (for more general cases) results are presented.

Deflection of an inverted two-state atom by a standing-wave cavity vacuum is analyzed. It is shown that clean vacuum Rabi oscillations occur at a frequency of $g_0/2\mathrm{}$ between the initial atom-field state and the state with the atomic transverse momentum displaced by $ħk$ if the cavity is tuned to the Doppler shift associated with the atomic motion along the cavity axis, given that the shift is much larger than the optimum atom-cavity coupling constant $g_0.$ Consequently, the atom can be deflected by the cavity, the direction of which is precisely controlled by the atom-cavity detuning.

The concept of the half density matrix is proposed. It unifies the quantum states that are described by density matrices and physical processes that are described by completely positive maps. With the help of the half-density-matrix representation of the Hermitian linear map, we show that every positive map that is not completely positive is a difference of two completely positive maps. A necessary and sufficient condition for a positive map that is not completely positive is also presented, which is illustrated by some examples.

It is shown that in the complex plane of the total angular momentum, an atom-diatom S-matrix element may have complex zeros as well as resonance poles. The zeros close to the real axis correlate with interference minima of the partial reaction probability. With the help of the Padé approximation we estimate positions of both poles and zeros, and construct a uniform semiclassical model for the angular distributions. Examples include $\mathrm{C}\mathrm{l}+\mathrm{H}\mathrm{C}\overrightarrow{l}\mathrm{C}\mathrm{l}\mathrm{H}+\mathrm{C}\mathrm{l}$ and $\mathrm{F}+\mathrm{H}\overrightarrow{D}\mathrm{F}\mathrm{H}+\mathrm{D}$ reactive scattering.

We investigate how the nonlinear Zeeman shift affects the dynamics of rf field-induced evaporative cooling in magnetic traps. We demonstrate for the ${}^{87}\mathrm{Rb}$ $F=2\mathrm{}$ trapping state with wave-packet simulations how the cooling stops when the rf field frequency goes below a certain limit. We examine the applicability of semiclassical models for the strong-field case as an extension of our previous work [Phys. Rev. A 58, 3983 (1998)]. Our results verify many of the aspects observed in a recent ${}^{87}\mathrm{Rb}$ experiment [Phys. Rev. A 60, R1759 (1999)].

We present a selective vibronic interaction for manipulating motional states in two trapped ions, acting resonantly on a previously chosen vibronic subspace and dispersively on all others. The generation of Fock states and entanglement in the ionic collective motional degrees of freedom, among other applications, is discussed.

The decay rate of an excited atom is described using Fermi’s golden rule. Welton’s interpretation of the Lamb shift is extended by introducing a damping term in the Heisenberg equation of motion associated with the fluctuation in the position of the electron. These expressions are related to the imaginary part of the vector potential Green function through the fluctuation dissipation theorem and Kubo’s formula. The results are applied to the calculation of the radiative properties of an atom in the vicinity of a perfect mirror.

Causal “superluminal” effects have recently been observed and discussed in various contexts. The question arises whether such effects could be observed with extremely weak pulses, and what would prevent the observation of an “optical tachyon.” Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett. 81, 2190 (1998)] have argued that quantum noise will preclude the observation of a superluminal group velocity when the pulse consists of one or a few photons. In this paper we reconsider this question both in a general framework and in the specific example, suggested by Chiao, Kozhekin, and Kurizki (CKK) [Phys. Rev. 77, 1254 (1996)], of off-resonant, short-pulse propagation in an optical amplifier. We derive in the case of the amplifier a signal-to-noise ratio that is consistent with the general ARS conclusions when we impose their criteria for distinguishing between superluminal propagation and propagation at the speed c. However, results consistent with the semiclassical arguments of CKK are obtained if weaker criteria are imposed, in which case the signal can exceed the noise without being “exponentially large.” We show that the quantum fluctuations of the field considered by ARS are closely related to superfluorescence noise. More generally, we consider the implications of unitarity for superluminal propagation and quantum noise and study, in addition to the complete and truncated wave packets considered by ARS, the residual wave packet formed by their difference. This leads to the conclusion that the noise is mostly luminal and delayed with respect to the superluminal signal. In the limit of a very weak incident signal pulse, the superluminal signal will be dominated by the noise part, and the signal-to-noise ratio will therefore be very small.