We study some aspects of the quantum theory of a charged particle moving in a time-independent, unidirectional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and momentum eigenstates with the diamagnetism of a free electron gas as an example. When the field is nonuniform but weakly varying, we discuss both perturbative and nonperturbative methods for studying a quantum mechanical system. As an application, we derive the quantized energy levels of a charged particle in a Helmholtz coil, which go over to the usual Landau levels in the limit of a uniform field.

We propose a realistic scheme to create motionally entangled states of a few bosonic atoms. It can experimentally be realized with a gas of ultracold bosonic atoms trapped in a deep optical lattice potential. By simultaneously deforming and rotating the trapping potential on each lattice site it is feasible to adiabatically create a variety of entangled states on each lattice well. We fully address the case of $N=2$ and 4 atoms per well and identify a sequence of fractional quantum Hall states: the Pfaffian state, the $1∕2$-Laughlin quasiparticle, and the $1∕2$-Laughlin state. Exact knowledge of the spectrum has allowed us to design adiabatic paths to these states, with all times and parameters well within the reach of current experimental setups. We further discuss the detection of these states by measuring different properties as their density profile, angular momentum, or correlation functions.

We further elaborate the theory of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSEL’s), developed by [Hermier et al. Phys. Rev. A 65, 053825 (2002)]. In particular, we introduce quantum Stokes parameters to describe the quantum self-correlations and cross correlations between two polarization components of the electromagnetic field generated by this type of laser. We calculate analytically the fluctuation spectra of these parameters and discuss experiments in which they can be measured. We demonstrate that in certain situations VCSEL’s can exhibit polarization squeezing over some range of spectral frequencies. This polarization squeezing has its origin in sub-Poissonian pumping statistics of the active laser medium.

Using a model potential representation combined with a variationally stable method, we present a precise calculation of the electric dipole polarizabilities of the sodium negative ion $\left({\mathrm{Na}}^{-}\right)$. The effective two-electron eigensolutions for ${\mathrm{Na}}^{-}$ are obtained from a hyperspherical coupled-channel calculation. This approach allows efficient error control and insight into the system’s properties through one-dimensional potential curves. Our result of $1018.3\mathrm{a.u.}$ for the static dipole polarizability is in agreement with previous calculations and supports our results for the dynamic polarizability, which has scarcely been investigated hitherto.

In the presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds of external influences on quantal interference. The concept of mixed-state phase and concomitant gauge invariance is extended to dissipative internal motion. The resulting complex-valued mixed-state interference effects lead to well-known results in the unitary limit and in the case of dissipative motion of pure quantal states. Dissipative interferometry is applied to fault-tolerant geometric quantum computation.

Recently spherical codes were introduced as potentially more capable ensembles for quantum key distribution. Here we develop specific key-creation protocols for the two qubit-based spherical codes, the trine and tetrahedron, and analyze them in the context of a suitably tailored intercept/resend attack, both in standard form, and in a “gentler” version whose back action on the quantum state is weaker. When compared to the standard unbiased basis protocols, Bennett-Brassard 1984 (BB84) and six-state, two distinct advantages are found. First, they offer improved tolerance of eavesdropping, the trine besting its counterpart BB84 and the tetrahedron the six-state protocol. Second, the key error rate may be computed from the sift rate of the protocol itself, removing the need to sacrifice key bits for this purpose. This simplifies the protocol and improves the overall key rate.

We have measured the near-threshold cross sections for the photodetachment of ${\mathrm{Li}}^{-}$ into the $e^{-}(ks,d)\text{−}\mathrm{Li}\left(2p_{1∕2}\right)$, $e^{-}(ks,d)\text{−}\mathrm{Li}\left(3p\right)$, $e^{-}\left(kp\right)\text{−}\mathrm{Li}\left(3s\right)$, and $e^{-}\left(kp\right)\text{−}\mathrm{Li}\left(4s\right)$ continuum channels and the photodetachment of ${\mathrm{K}}^{-}$ into the $e^{-}(ks,d)\text{−}\mathrm{K}\left(4p_{3∕2}\right)$ continuum channel. The data was analyzed using both a top-of-barrier model and a modified effective range theory. Both approaches explicitly take into account the significant polarization potential in the final continuum channels. The study involving both experiment and theory enabled us to investigate the effect of the polarization on near-threshold photodetachment. Furthermore, since photodetachment and electron scattering are related in the half-collision concept, we were able to determine low-energy electron scattering quantities such as phase shifts, elastic cross sections, and $s$ wave scattering lengths for electron scattering on excited Li and K atoms. The results allowed us to predict a virtual state in the $e^{-}\left(ks\right)\text{−}\mathrm{Li}\left(3p\right)$ system.

This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a constant frequency. A very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and amplitude of the probability oscillations, for the excitation profile and excitation linewidth. The linewidth, in particular, shows a weak, logarithmic power broadening.

In this paper, the quantum interference of a mode-locked two-photon state, which is a new phenomenon that has recently been experimentally observed, is analyzed. We show some interference fringes that will be observed in an unbalanced Mach-Zehnder interferometer.

We previously suggested that photon exchange interactions could be used to produce nonlinear effects at the two-photon level, and similar effects have been experimentally observed by Resch et al. (e-print quant-ph/0306198). Here we note that photon exchange interactions are not useful for quantum information processing because they require the presence of substantial photon loss. This dependence on loss is somewhat analogous to the postselection required in the linear optics approach to quantum computing suggested by Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)].

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic $S$ states. The corresponding level shift is of the order of ${(\alpha ∕\pi )}^2{\left(Z\alpha \right)}^6{m}_{\mathrm{e}}{c}^2$ and may be ascribed to a two-loop generalization of the Bethe logarithm. For $1S$ and $2S$ states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. 91, 113005 (2003)]. Here, we generalize the approach to higher excited $S$ states, which in contrast to the $1S$ and $2S$ states can decay to $P$ states via the electric-dipole $\left(E1\right)$ channel. The more complex structure of the excited-state wave functions and the necessity to subtract $P$-state poles lead to additional calculational problems. In addition to the calculation of the excited-state two-loop energy shift, we investigate the ambiguity in the energy level definition due to squared decay rates.

We present a comprehensive set of theoretical results for differential, total, and momentum transfer cross sections and Sherman functions for the elastic scattering of electrons by barium and strontium atoms, for the entire angular range and energies below 1 keV. This study extends our method of calculations, already employed for inert gases, to other atoms with closed subshells and provides insight into the electron scattering from these two atoms, particularly for strontium where there is a serious lack of both experimental and prior theoretical works. Our relatively simple semiempirical approach, with a single adjustable parameter, produces a satisfactory agreement with the measured values and convergent close-coupling calculations for barium, for the limited number of energies and angles at which they are available. Based on this success, we provide a recommended set of values of cross sections and scattering phase shifts for both atoms and for future applications.

The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously treated to recover unitarity for the non-Hermitian Hamiltonians. In contrast to other models of parametrized scatterers we assemble explicit potentials profiles in the form of delta arrays, Pöschl-Teller holes, and complex Scarf potentials. The techniques developed provide analytical expressions for the scattering and absorption probabilities of arbitrarily long wires. The approach presented is suitable for modeling molecular aggregate potentials and also supports new models of continuous disordered systems. The results obtained also suggest the possibility of using these complex potentials within disordered wires to study the loss of coherence in the electronic localization regime due to phase-breaking inelastic processes.

We consider the effect of using necessarily inexact target wave functions in a Kohn variational calculation of the $\mathrm{Ps}\mathrm{He}$ scattering length. We use the simplest closed-shell or one-term Hylleraas function in the static-exchange approximation and examine two plausible ways of handling such an inexact function. Both of these methods have been employed in the past, and our results are compared with these previous calculations. Significant differences are found which may persist in more elaborate calculations.

We interpret the results of a molecular fragmentation learning control experiment. We show that in the case of a system where control can be related to the structure of the optimal pulse matching the vibrational dynamics of the molecule, a simple change of pulse-shape basis in which the learning algorithm performs the search can reduce the dimensionality of the search space to one or two degrees of freedom.

A “gaseous droplet”—a stable gas that coheres by itself in free space—is shown to be produced with a Bose-Einstein condensate. Collapse and expansion of the droplet are suppressed by rapid oscillations of the interatomic interaction between attractive and repulsive through, e.g., the Feshbach resonance. Energy dissipation, which is present in realistic situations, is found to play a crucial role in suppressing dynamical instabilities that destabilize the droplet.

The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is $1∕2$ (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.

Modulation features in the frequency domain can be transferred from an amplitude-modulated laser field to a nonmodulated one by a strong Raman coupling, which is based on refractive index control with a strong Raman coherence established with two sufficiently intense laser fields slightly off the two-photon Raman resonance of a selected Raman mode. Numerical simulations show that modulation transfers between the driving lasers, such as transfers from ultraviolet to extreme ultraviolet and from infrared to middle infrared lasers, can be realized in gaseous Raman media. This provides an efficient way to extend the optical modulation range beyond the transparent ranges of commercial modulators. Modulation features can also be transferred from a low-intensity driving laser to a high-intensity one, which ensures a direct application to modulate lasers with high intensities beyond the damage thresholds of standard modulators.

A method to study the rotational dynamics of a molecule interacting with a single short laser pulse or a train of pulses is proposed. The method is based on the observation that for such pulses the time propagator, in the $(t,t^{\prime })$ formalism, can be expressed as a function of approximate Floquet states given by eigenstates of the one-period time-averaged rotational Hamiltonian multiplied by appropriate Fourier functions for the $t^{\prime }$ coordinate. Each zeroth-order eigenstate can be improved by diagonalizing a small configuration-interaction matrix formed from virtual Hartree-type wave functions. The resulting approximate propagators are more efficient than the usual sudden propagator as they allow one to obtain, in a single step, the propagated wave function at the end of the last pulse of a pulse train.

Thermal (or pseudothermal) radiation has been recently proposed for imaging and interference types of experiments to simulate entangled states. We report an experimental study on the momentum correlation properties of a pseudothermal field in the photon counting regime. The characterization and understanding of such a light source in the context of two-photon physics, especially its similarities and differences compared to entangled two-photon states, is useful in gaining knowledge of entanglement and may help us to assess the real potential of applications of chaotic light in this context.