We analyze the long-time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a given syndrome history and the associated residual decoherence encoded in the reduced density matrix. Systems with nonzero gate times (“long gates”) are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.

We analyze the angular momentum distribution of electrons near threshold in atomic ionization by short laser pulses. The radial fanlike pattern in the two-dimensional momentum distribution observed in experiments is controlled by the dominance of a few angular momenta of the order $l_0$. We find a semiclassical expression for $l_0$ strongly dependent on the quiver amplitude of the detached electron but independent of the atomic species. The value of $l_0$ can be also related to the minimum number of absorbed photons needed to reach the threshold. The strongly peaked sub-Poissonian angular distribution precludes a description by a stochastic random walk model in angular momentum.

We investigate theoretically the energy levels of two identical fermions in a harmonic potential trap under a $p$-wave Feshbach resonance. The magnetic fields needed to affect the energy levels differ strongly among the levels, and they can be at values far from the free-space resonant field.

A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium (${\chi }^{\left(3\right)}$ nonlinearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are discussed. We provide examples of quantum interference, sub-Planck phase space structures, and Gaussian vs non-Gaussian dynamical evolution of the state. The results also apply to the description of a nanomechanical resonator with an intrinsic Duffing nonlinearity.

Linear Thomson scattering of relativistic electrons with few-cycle laser pulses is theoretically analyzed, and the radiated energy spectra of electrons show that attosecond x-ray pulses can be supported. The influences of the carrier-envelope phase offset ${\varphi }_{\text{CE}}$ of the incident laser pulses and of the initial phase as the electrons enter the field, ${\varphi }_{\text{in}}$, on the radiated x-ray pulses are studied, and the results demonstrate that a single attosecond pulse can be produced in linear Thomson scattering by using either a single-cycle laser pulse with fixed carrier-envelope phase offset ${\varphi }_{\text{CE}}=0$, or a few-cycle laser pulse with controlled initial phase at the electron entrance to the field ${\varphi }_{\text{in}}$.

We present a scheme for single-photon transistors based on the strong interaction of a three-level atom with a microtoroidal resonator, where the presence (absence) of a single “gate” photon is sufficient to block (allow) the propagation of a “signal” photon. Considering its robustness against major experimental errors and high efficiency for coupling single photons into and out of the resonator through a fiber taper, this scheme may be a promising candidate for single-photon transistors.

We study theoretically the mode structure of few-mode helical core optical fibers with small (up to a wavelength order) values of the helix pitch. We demonstrate that in such fibers, at certain values of pitch the fundamental $H{E}_{11}$ mode strongly hybridizes with $l=1$ optical vortices and the forbidden zone appears in the spectra of such hybrid modes, which results in their attenuation. We have shown that within the spectrum gap, the only forward-propagating guiding modes are represented by two circularly polarized optical vortices with opposite polarization and the same topological charge so that upon excitation of such a fiber with a circularly polarized beam, only a solitary optical vortex could be excited in it. Such “monovortex” fibers are found to be analogous to conventional monomode fibers that maintain the propagation of the $H{E}_{11}$ mode.

In this paper, tripartite entanglement among the two pump fields and the second-order harmonic field is established in the process of type-II second-order harmonic generation (SHG) with a triply resonant optical cavity below threshold. A sufficient inseparability criterion for continuous-variable tripartite entanglement proposed by van Loock and Furusawa is used to evaluate the degree of the quadrature–phase-amplitude correlations between the three modes. The dependence of the entanglement on the pump parameter and analysis frequency is also discussed. It is shown that the best entanglement appears at the appropriate pump power and analysis frequency. These three entangled states with different frequencies generated directly from a simple SHG process make the scheme useful for the application in quantum communication and network.

We analyze quantitatively the generation of a continuous beam of atoms by the periodic injection of individual packets in a guide, followed by their overlapping. We show that slowing the packets using a moving mirror before their overlapping enables an optimal gain on the phase space density of the generated beam. This is interpreted as a Maxwell’s demon type strategy as the experimentalist exploits the information on the position and velocity of the center of mass of each packet.

We propose a method for completely controlling a nuclear spin subsystem using only microwave irradiation of resolved anisotropic hyperfine interactions with a single electron spin. This paradigm of control has important applications for spin based solid-state quantum information processing. In particular we argue that indirect addressing of the nuclear spins via an electron spin acting as a spin actuator allows for nuclear spin quantum logic gates whose operational times are significantly faster than either gates based on rf fields resonant with nuclear spin flips or nuclear-nuclear dipolar interactions. We demonstrate experimental aspects of this method with one electron and one nuclear spin of a single crystal of irradiated malonic acid.

Transverse entanglement between pairs of photons can be detected through intensity correlation measurements in the near and far fields. We show theoretically and experimentally that at intermediate zones, it is also possible to detect transverse entanglement performing only intensity correlation measurements. Our results are applicable to a number of physical systems.

Self-pulsed lasing in the form of a coherent solitary wave train from a periodically amplifying Bragg structure is proposed. It is shown both analytically and numerically that the generated pulse train propagates in the periodically amplifying Bragg structure chip with superluminal group velocity. Its stability and coherence are in contrast with the inherent instability and chaoticity of self-pulsing from a uniform gain medium embedded in a Bragg reflector. Bragg-periodic semiconductor quantum-well heterostructures are candidates for realizing the required periodically amplifying Bragg structure.

The prime number decomposition of a finite-dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger’s quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space that characterizes the Hilbert space and specifies the simultaneous definitions of both (modular) positions and (modular) momenta. The area in phase space for each quantum state in each of these quantum degrees of freedom, is shown to be exactly $h$, Planck’s constant.

Suppose we want to identify an input state with one of two unknown reference states, where the input state is guaranteed to be equal to one of the reference states. We assume that no classical knowledge of the reference states is given, but a certain number of copies of them are available instead. Two reference states are independently and randomly chosen from the state space in a unitary invariant way. This is called the quantum state identification problem, and the task is to optimize the mean identification success probability. In this paper, we consider the case where each reference state is pure and bipartite, and generally entangled. The question is whether the maximum mean identification success probability can be attained by means of a local operations and classical communication (LOCC) measurement scheme. Two types of identification problem are considered when a single copy of each reference state is available. We show that a LOCC scheme attains the globally achievable identification probability in the minimum-error identification problem. In the unambiguous identification problem, however, the maximal success probability by means of LOCC is shown to be less than the globally achievable identification probability.

Few-cycle pulses of 800 nm light cause ionization and dissociation of ${\text{CS}}_2$ in the intensity and temporal regime where, by contemporary wisdom, rescattering is expected to dominate laser-molecule interactions. However, our experiments indicate that in the case of laser-${\text{CS}}_2$ interactions in the strong-field regime, the wave packet of the rescattered electron destructively interferes with the antibonding $\pi$ orbital of $\text{CS}_2{}^{+}$ such that rescattering is essentially “switched off.” Consequently, dissociation becomes an almost nonexistent channel; long-lived singly, doubly, and triply charged molecular ions dominate the mass spectrum in the few-cycle regime, revealing the importance of molecular symmetry in strong-field ionization. Comparison with ${\text{CS}}_2$ ionization spectra that we measure in the 700 attosecond domain using fast, highly charged ions corroborates that rescattering is not of importance when ${\text{CS}}_2$ ionization is caused by intense laser light. Direct signature of enhanced ionization being “switched off” in the few-cycle domain is also obtained in our measurements.

Motivated by recent proposals of “collisionally inhomogeneous” Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a “stitching” approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.

We show that a few-cycle pulse launched in a quadratic medium may result in a half-cycle soliton in the form of a single hump, with no oscillating tail. The analysis involves the derivation of a Korteweg-de Vries (KdV) equation from both a classical and a quantum mechanical simple model of matter-radiation interaction. The sign of the electric field in the half-cycle KdV soliton is fully determined by the properties of the material, which definitely breaks the phase invariance.

We study the photonic interactions between two distant atoms which are coupled by an optical element (a lens or an optical fiber) focusing part of their emitted radiation onto each other. Two regimes are distinguished depending on the ratio between the radiative lifetime of the atomic excited state and the propagation time of a photon between the two atoms. In the two regimes, well below saturation the dynamics exhibit either typical features of a bad resonator, where the atoms act as the mirrors, or typical characteristics of dipole-dipole interaction. We study the coherence properties of the emitted light and show that it carries signatures of the multiple scattering processes between the atoms. The model predictions are compared with the experimental results of Eschner et al. [Nature (London) 413, 495 (2001)].

In an ordinary electromagnetically-induced-transparency (EIT) experiment using a hot sodium vapor, we have observed a probe gain up to 32 in the presence of a coupling beam in an otherwise totally opaque (transmissivity $\sim {10}^{-5}$) situation, increasing the transmissivity by 6 orders of magnitude. This gain is attributable to parametric amplification (PA), accompanying the Stokes (or anti-Stokes) wave with similar output intensity, and is critically dependent upon the atomic density and the coupling beam power. Experimental and theoretical analyses have revealed that, while the EIT picture is valid for relatively low atomic densities, the PA picture becomes dominant for high atomic densities and high coupling powers. We have also found that the parametric coupling between the probe and Stokes waves can be nullified by the proper choice of the coupling detuning frequency, due to destructive interference of two elementary processes.

The correlation potential, determined recently by Ginzburg [Theor. Math. Phys. 146, 275 (2006)] in the region far outside a finite many-electron system, differs significantly from the potential determined previously by Almbladh and von Barth (AvB) [Phys. Rev. B 31, 3231 (1985)]—the two versions sum to zero. We demonstrate that the arguments of Ginzburg for accepting his result (rather than that of AvB) as the correct one are inconsistent. We also find an error in the derivation of Ginzburg (some terms are omitted without explanation). After our correction, the Ginzburg result becomes identical with that of AvB.