In this paper initial steps in an analysis of cyclic networks of quantum logic gates will be given. Cyclic networks are those in which the qubit lines are loops. In our investigations of cyclic networks of quantum gates we have studied one- and two-qubit systems plus two-qubit systems connected to another qubit on an acyclic line. The analysis includes classifying networks into groups, the dynamics of the qubits in the cyclic network, and the perturbation effects of an acyclic qubit acting on a cyclic network of quantum gates. This will be followed by a discussion on quantum algorithms and quantum information processing with cyclic networks of quantum gates. An implementation of a cyclic network quantum memory and quantum sensors via cyclic networks will also be discussed.

We report a proof-of-principle demonstration of a probabilistic controlled-NOT gate for single photons. Single-photon control and target qubits were mixed with a single ancilla photon in a device constructed using only linear optical elements. The successful operation of the controlled-NOT gate relied on post-selected three-photon interference effects, which required the detection of the photons in the output modes.

The hyperfine structure of ns and nd Rydberg states of ${}^{83}\mathrm{Kr}$ has been measured in the range $n=30\mathrm{}–190$ below the ${}^2{P}_{3/2}$ ionization threshold by pulsed-field ionization following single-photon excitation from the ${}^1{S}_0$ ground state using a narrow-bandwidth vacuum-ultraviolet laser system. A multichannel quantum defect theory (MQDT) treatment of the hyperfine structure in Rydberg states of the rare-gas atoms has been developed that quantitatively accounts for the effects of the nuclear spin on the spectral structures over the entire range of principal quantum number investigated. The model allows the parametrization of the hyperfine structure of the Rydberg states in terms of the ionic hyperfine structure and relies on the assumption that the interaction with the nuclear spin is negligible in the close-coupling region of the electron-ion collision, an assumption that is also expected to be valid in other atomic and molecular systems. Improved eigen quantum defects for the ns and nd Rydberg series with $J=1\mathrm{}$ and 2 have been derived from the MQDT analysis, and the hyperfine structure of the two ${}^2{P}_{3/2}$ and ${}^2{P}_{1/2}$ spin-orbit components of the ground state of ${}^{83}{\mathrm{Kr}}^{+}$ has been determined.

The energy-level shift of a ground-state atom in front of a nondispersive dielectric half-space is calculated by quantizing the electric field by means of a normal-mode expansion and applying second-order perturbation theory to the electric-dipole Hamiltonian $\mathit{\mu }\cdot \mathbf{E}.$ It is shown that the contributions to this shift coming from traveling and from evanescent waves can be combined into a single expression which lends itself readily to asymptotic analysis for large atom-surface separations, while in the opposite asymptotic regime when the atom is close to the surface the combined expression is less convenient. Employing a Green’s-function formalism instead of the normal-mode expansion leads directly to the combined formula, and in that case it is advantageous to be able to apply the same transformation backwards and split the energy shift into a sum of distinct contributions corresponding to different physical processes. The analysis serves to shed light on common sources of error in the literature and paves the way for the study of more complicated models in cavity quantum electrodynamics.

We have made a nonlinear dynamics study of a parametrically driven magneto-optical trap. When the trapping potential is modulated at around twice the trap frequency above a threshold, the limit cycle is manifested as two separate collective atomic packets oscillating with opposite phases and finite amplitudes, determined by the balance of the nonlinearity and the damping of the trap. In particular, we directly observe in situ the subcritical Hopf bifurcation, which suddenly converts the combined motions of a limit cycle and a stable attractor into a limit cycle motion. The experimental results are in quantitative agreement with the numerical results based on the simple Doppler cooling theory.

We report the discovery of unexpected instabilities of a trapped charged particle in the dynamic Kingdon trap. A detailed phase-space analysis shows that these instabilities are caused by the collapse of the primary trapping island. A resonance condition accurately predicts the locations of the instabilities. Avoiding these instabilities is essential for successfully operating the dynamic Kingdon trap.

Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling $I_s$ cannot lead to a FM phase transition unless it is larger than a threshold value $I_0.$ The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.

We present a study of the influence of the constant uniform electric field and spin-orbit interaction on the doubly excited ${2l2l}^{\prime }$ resonance states of helium-like ions. The calculation is performed in the framework of the complex coordinate rotation method allowing one to obtain results both for real part of the energy (position of the resonance) and for imaginary part of the energy (related to the width of the resonance). Singlet and triplet states with angular momenta from $L=0\mathrm{}$ to $L=4\mathrm{}$ have been included in the calculation. Results are given for the $M=0\mathrm{}$ Stark components of the Feshbach ${}^1{S}^e\mathrm{}\left(1\right),$ ${}^1{P}^o,$ ${}^1{D}^e$ ${}^3{P}^e,$ ${}^3{P}^o$ resonances. We show that though spin-orbit interaction generally produces only a minor effect, in a situation where real parts of energies of singlet and triplet levels cross, the spin-orbit interaction can dramatically modify behavior of the widths of these states.

The plateaus in laser-assisted recombination and high-order harmonic generation are investigated in the frequency domain. It is found that the probability amplitude of finding an electron with a given energy is given by a generalized Bessel function, which can be represented as a coherent superposition of contributions from a few electronic quantum trajectories. This concept is illustrated by comparing the spectral density of the electron with the laser-assisted recombination spectrum. On the other hand, the plateau of high-order harmonic generation reflects the spectral density of the electron at the location of the nucleus after above-threshold ionization.

We study numerically the excitations of off-centered vortices in a Bose-Einstein condensate. The displacement of a single vortex and the separation of a doubly quantized vortex are considered. We find that the core-localized excitations of the precessing vortices continue to feature the property which implies that the vortices are unstable. The core-localized, dipolar, and quadrupolar excitations are found to deform continuously as functions of vortex displacements and intervortex separation.

We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach [Phys. Rev. E 62, 1646 (2000)] where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and noncondensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the usual coupled Gross-Pitaevskiĭ equations when the time scale of the pair dynamics is short compared to that of the individual dynamics. Such time scales are discussed in the case of typical photoassociation experiments with cw lasers. We show that the individual dynamics plays a minor role, demonstrating the validity of the rates predicted by the usual models describing photoassociation in a nondegenerate gas.

Recently the influence of dielectric and geometrical properties on the Casimir force between dispersing and absorbing multilayered plates in the zero-temperature limit has been studied within a one-dimensional (1D) quantization scheme for the electromagnetic field in the presence of causal media [R. Esquivel-Sirvent, C. Villarreal, and G.H. Cocoletzi, Phys. Rev. Lett. $64,$ 052108 (2001)]. In the present paper a rigorous 3D analysis is given, which shows that for complex heterostructures the 1D theory only roughly reflects the dependence of the Casimir force on the plate separation in general. Further, an extension of the very recently derived formula for the Casimir force at zero temperature [M.S. Tomaš, Phys. Rev. A $66,$ 052103 (2002)] to finite temperatures is given, and analytical expressions for specific distance laws in the zero-temperature limit are derived. In particular, it is shown that the Casimir force between two single-slab plates behaves asymptotically like $d^{-6}$ instead of $d^{-4}$ $(d,$ plate separation).

We present a comprehensive experimental characterization of the dynamics of semiconductor lasers subject to polarization-rotated optical feedback. We find oscillatory instabilities appearing for large feedback levels and disappearing at large injection currents, which we classify in contrast to the well-known conventional optical-feedback-induced dynamics. In addition, we compare our experiments to theoretical results of a single-mode model assuming incoherence of the optical feedback, and we identify differences concerning the average power of the laser. Hence, we develop an alternative model accounting for both polarizations, where the emission of the dominant TE mode is injected with delay into the TM mode of the laser. Numerical simulations using this model show good qualitative agreement with our experimental results, correctly reproducing the parameter dependences of the dynamics. Finally, we discuss the application of polarization-rotated-feedback induced instabilities in chaotic carrier communication systems.

Via the Richards-Wolf vector diffraction theory, we analyze the three-dimensional intensity distribution of the focal volume that is produced by a strongly focused 750-nm beam of ultrafast, Gaussian-shaped optical pulses ${(10\mathrm{}}^{-9}\mathrm{s}>~$ pulse width $\tau >~1\mathrm{fs}{=10\mathrm{}}^{-15}\mathrm{s}).\mathrm{}$ Knowledge of the three-dimensional distribution near focus is essential in determining the diffraction-limited resolution of an optical microscope. The optical spectrum of a short pulse is characterized by side frequencies about the carrier frequency. The effect of spectral broadening on the focused intensity distribution is evaluated via the Linfoot’s criteria of fidelity, structural content, and correlation quality and with reference to a 750-nm cw focused beam. Different values are considered for $\tau$ and numerical aperture of the focusing lens $(0.1\mathrm{}<~X_{\mathrm{NA}}<~1.2).$ At $X_{\mathrm{NA}}=0.8,$ rapid deterioration of the focused intensity distribution is observed at $\tau =1.2\mathrm{}\mathrm{fs}.$ This happens because a 750-nm optical pulse with $\tau =1.2\mathrm{}\mathrm{fs}$ has an associated coherence length of 359.7 nm which is less than the Nyquist sampling interval of 375 nm that is required to sample 750 nm sinusoid without loss of information. The ill-effects of spectral broadening is weaker in two-photon excitation microscope than in its single-photon counterpart for the same focusing lens and light source.

We investigate the class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely, that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.

A two-dimensional spin 1 three-boson system trapped by a parabolic confinement and interacting with hard-core repulsion has been investigated. The spectrum has been analyzed in detail, in particular, the existence of breathing bands has been confirmed. Two density functions associated with the oscillations of breathing and deformation, respectively, have been defined to study the structure of low-lying states. The inherent nodal structure of wave functions is found to play a decisive role. The effect of rotation on the ground-state property has also been studied. Not only the angular momentum, the permutation symmetry will also transit in accord with the increase of the speed of rotation.

The ionization probabilities of hydrogenic Rydberg states in intense fields are calculated using a trajectory method, which was previously shown to be accurate for ionization of the ground-state hydrogen atom [J. S. Cohen, Phys. Rev. A 64, 043412 (2001)]. It is found that the ionization probability approaches the classical over-the-barrier probability for sufficiently large n quantum numbers, but that tunneling still significantly decreases the onset field strengths at surprisingly high n. Calculations are done for ns, ${\mathrm{np}}_0,$ and ${\mathrm{np}}_{\pm }$ targets, subjected to sudden and adiabatically ramped pulses in the long-wavelength limit. The dependence on the angular-momentum projection m along the field axis is also examined for circular orbits.

A fully quantal calculation of the ${}^{1}S$ three-body wave function is performed for the Wannier model of electron-hydrogen scattering in the near-ionization threshold region using an exterior complex scaling method. The region of configuration space of the wave function that provides the dominant contribution to the total ionization cross section is demonstrated to be $r_1\approx r_2$ in accord with the argument of Rau [Phys. Rev. A 4, 207 (1971)], but only in the so-called Coulomb zone. The work confirms to a high precision ${(E}^{1.128\pm 0.004})$ the Wannier threshold law for the total ionization cross section, which is strictly valid only at the threshold. A threshold law for the ${}^{3}S$ total ionization cross section is determined to be $E^{3.37\pm 0.02},$ in agreement with the semiclassical calculations of Peterkop [J. Phys. B 16, L587 (1983)].

We show that the photoassociation of an atomic Bose-Einstein condensate to form condensed molecules is a chemical process which not only does not obey the Arrhenius rules for chemical reactions, but that it can also depend on the quantum statistics of the reactants. Comparing the predictions of a truncated Wigner representation for different initial quantum states, we find that, even when the quantum prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other quantum states may result in very different dynamics.

Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a nonlocal superposition will lead to rapid decoherence. However, it is also known that quantum counterparts of classically chaotic systems lose exponential sensitivity to initial conditions, so this expectation of enhanced decoherence is by no means obvious. We analyze decoherence due to a “toy” quantum environment that is analytically solvable, yet displays the crucial phenomenon of exponential sensitivity to perturbations. We show that such an environment, with a single degree of freedom, can be far more effective at destroying quantum coherence than a heat bath with infinitely many degrees of freedom. This also means that the standard “quantum Brownian motion” model for a decohering environment may not be as universally applicable as it once was conjectured to be.