The transmission spectrum of a high-finesse optical cavity containing an arbitrary number of trapped atoms is presented in the zero-temperature, low saturation limit. We take spatial and motional effects into account and show that in the limit of strong coupling, the important spectral features can be determined for an arbitrary number of atoms, $N$. We also show that these results have important ramifications in limiting our ability to determine the number of atoms in the cavity.

It is shown that any quantum operation that perfectly clones the entanglement of all maximally entangled qubit pairs cannot preserve separability. This “entanglement no-cloning” principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.

The need for spatial and spectral filtering in the generation of polarization entanglement is eliminated by combining two coherently driven type-II spontaneous parametric down-converters. The resulting ultrabright source emits photon pairs that are polarization entangled over the entire spatial cone and spectrum of emission. We detect a flux of $\sim \mathrm{12\hspace{0.17em}000}$ polarization-entangled pairs/s per mW of pump power at $90\%$ quantum-interference visibility, and the source can be temperature tuned for $5\text{nm}$ around frequency degeneracy. The output state is actively controlled by precisely adjusting the relative phase of the two coherent pumps.

We used the basis of the x-ray extended range technique to measure the lattice spacing of ${\text{LaB}}_6$ standard powder samples relative to silicon $640b$ standard powder samples with an accuracy of $5\times {10}^{-5}\mathrm{\AA }$. Measurements were not constrained to one energy but were carried out over a $5\text{keV}–20\text{keV}$ energy range. These measurements used powder diffraction to determine the synchrotron beam energy, to diagnose discrepancies in the nominal calibrated beam energies, and to determine beam energy bandwidths as a function of energy. More specifically, this technique is able to yield a result independent of certain energy-dependent systematics and to yield the most accurate determination of the lattice spacing of NIST SRM 660 ${\text{LaB}}_6$ standard powder so far undertaken. This has direct application to beam line energy calibration, structural evaluation, edge energy calibration, and lattice spacing determinations.

In contrast to the widespread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system. For any separable quantum state, we derive quantum analogs of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended Clauser-Horne-Shimony-Holt inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.

We describe an electrodynamic mechanism for coherent, quantum-mechanical coupling between spatially separated quantum dots on a microchip. The technique is based on capacitive interactions between the electron charge and a superconducting transmission line resonator, and is closely related to atomic cavity quantum electrodynamics. We investigate several potential applications of this technique which have varying degrees of complexity. In particular, we demonstrate that this mechanism allows design and investigation of an on-chip double-dot microscopic maser. Moreover, the interaction may be extended to couple spatially separated electron-spin states while only virtually populating fast-decaying superpositions of charge states. This represents an effective, controllable long-range interaction, which may facilitate implementation of quantum information processing with electron-spin qubits and potentially allow coupling to other quantum systems such as atomic or superconducting qubits.

We show that a network of ballistic electron waveguides can generate entangled Bell-like states from separable states when it is resonant. The network we study is grouped into individual qudits $\left(d=4\right)$ made up of pairs of waveguides. Rotation gates in the network produce coherent superpositions of qudit states. A Coulomb gate entangles the qudits. We construct a unitary matrix which characterizes the network dynamics and allows a more systematic study of that dynamics.

The long-time behavior of scattered wave packets $\psi \left(x,t\right)$ from a finite-range potential is investigated, by assuming $\psi \left(x,t\right)$ to be initially located outside the potential. It is then shown that $\psi \left(x,t\right)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi \left(x,t\right)$ exhibits the asymptotic behavior $t^{-3∕2}$, while another behavior like $t^{-5∕2}$ can also appear for another $\psi \left(x,t\right)$.

Inner and outer multiple ionization of clusters by a superintense ultrashort laser pulse is studied. The barrier-suppression mechanism governs inner field ionization in this case, while impact ionization can be neglected. Outer ionization produces a static Coulomb field inside the ionized cluster. This field increases the charge multiplicity of the atomic ions produced inside the cluster approximately by a factor of 1.5. Various models are suggested for the charge distribution inside the cluster.

We analyze the ground state of the two-component gas of trapped ultracold fermionic atoms. We neglect the forces between atoms in the same hyperfine state (the same component). For the case when the forces between distinguishable atoms (i.e., atoms in different hyperfine states) are repulsive (positive mutual scatteringlength), we find the existence of critical interaction strength above which one atomic fraction expels the other from the center of the trap. When atoms from different components attract each other (negative mutual scattering length) the ground state of the system dramatically changes its structure for strong enough attraction—the Cooper pairs built of atoms in different hyperfine states appear.

In this paper we explore the quantum behavior of a superconducting quantum-interference device (SQUID) ring which has a significant Josephson coupling energy. We show that the eigenfunctions of the Hamiltonian for the ring can be used to create macroscopic quantum superposition states of the ring. We also show that the ring potential may be utilized to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum-mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.

We investigate the effects of dimensional reduction in atomic Bose-Einstein condensates (BECs) induced by a strong harmonic confinement in the cylindric radial direction or in the cylindric axial direction. The former case corresponds to a transition from three dimensions (3D) to 1D in cigar-shaped BECs, while the latter case corresponds to a transition from 3D to 2D in disk-shaped BECs. We analyze the first sound velocity in axially homogeneous cigar-shaped BECs and in radially homogeneous disk-shaped BECs. We consider also the dimensional reduction in a BEC confined by a harmonic potential both in the radial direction and in the axial direction. By using a variational approach, we calculate monopole and quadrupole collective oscillations of the BEC. We find that the frequencies of these collective oscillations are related to the dimensionality and to the repulsive or attractive interatomic interaction.

The $X{}^1\sum ^{+}$ state of NaRb was studied by Fourier-transform spectroscopy. An accurate potential energy curve was derived from more than 8800 transitions in isotopomers ${}^{23}\mathrm{Na}{}^{85}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}{}^{87}\mathrm{Rb}$. This potential reproduces the experimental observations within their uncertainties of $0.003{\text{cm}}^{-1}–0.007{\text{cm}}^{-1}$. The outer classical turning point of the last observed energy level $\left(v^{″}=76,J^{″}=27\right)$ lies at $\approx 12.4\mathrm{\AA }$, leading to an energy of $4.5{\text{cm}}^{-1}$ below the ground-state asymptote.

The stability of the ground state of the $\mathrm{H}_2{}^{+}$ and ${\mathrm{H}}_2$ systems, where nuclei and electrons interact through a Yukawa potential $e^{-\lambda r}∕r$, has been studied for different values of the screening parameter $\lambda$ using quantum Monte Carlo techniques. Nonadiabatic calculations using explicitly correlated trial wave functions were carried out, obtaining exact results within the statistical errors. $\mathrm{H}_2{}^{+}$ and ${\mathrm{H}}_2$ appear to be stable species for values of $\lambda$ as large as 1.35 and $1.38{\text{bohr}}^{-1}$. So in the range $1.35⩽\lambda ⩽1.38{\text{bohr}}^{-1}$ ${\mathrm{H}}_2$ is stable, while all the possible fragments are unbound, that is, it shows Borromean binding.

We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernández-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering.

We present cross sections of electronic excitation of nitrogen molecule $\left({\mathrm{N}}_2\right)$ by positron impact using the Schwinger multichannel method. Our calculated cross sections are compared with the recent and the only available experimental data of Sullivan et al. [Phys. Rev. Lett. 87, 073201 (2001)]. Present theoretical results for excitation to the $a{}^1\Pi _g$ states do not reproduce the near-threshold structure observed in the experimental data.

Selective resonant excitations can be realized with a shaped ultrashort pulse in an optically dense collection of multilevel individual atoms, where the near dipole-dipole interactions induce intrinsic frequency shifts of the atomic resonance. A proper transform-limited pulse and modulation of excitation pulses can be controlled to establish constructive or destructive quantum interference between different excitation pathways towards a desired selective resonant excitation, even driven by pulses with broadband spectral components.

Here we report a set of converged cross-section results for double photoionization of helium atoms obtained in the hyperspherical partial wave theory for equal energy sharing kinematics at $6\text{eV}$ energy above threshold. The calculated cross section results are generally in excellent agreement with the absolute measured results of Dörner et al. [Phys. Rev. 57, 1074 (1998)].

There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their quantum numbers. In this work, focussing on the ground state of a nonlinear, coupled Hamiltonian system, we show that approximate eigenstates can be constructed within the framework of adiabatic theory. Using the adiabatic eigenstates, we estimate the information entropies and their sum as a function of the nonlinearity parameter. We also briefly look at the information entropies for the highly excited states in the system.

Relativistic nuclear recoil effects are studied for antiprotonic and muonic atoms. The generalization of the Breit-Pauli Hamiltonian including vacuum polarization is presented. Previous treatments are corrected, and the result for the $2S_{1∕2}\text{−}2P_{1∕2}$ splitting in muonic hydrogen is updated.