Using the Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the entanglement follows different scalings with the size, just as an order parameter does. This fact reveals the subtle role played by the entanglement in QPT as a fungible physical resource.

The photoionization of $\mathrm{Ar}2p_{3∕2}$ has been investigated by Auger electron–photoelectron coincidence experiments. The results have shown that the basic quantities that define the photoionization, i.e., the dipole matrix elements, can be extracted from these experiments and all the observables of the process, apart from the sign of the circular dichroism, can be predicted. The analysis also proved that a description of the process in terms of LSJ approximation is satisfactory.

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply and singly quantized vortex states. We also show that states of different circulation can be metastable and, as a result, the gas can exhibit hysteresis as the angular frequency of rotation of the trap is varied. The simplicity of the picture that emerges for small coupling strengths suggests that this system may be attractive for studies of phase transitions.

We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude damping. The effects of the non-Markovian decoherence are compared to the Markovian decoherence.

The standard theoretical treatment of the Kapitza-Dirac effect—that is, the scattering of an electron passing through a standing-wave laser field—is extended here through the use of the Pauli equation to account for the interaction of the electron spin with the magnetic field of the standing wave. Prescriptions for determining unitarity-preserving approximations for the transition probabilities for scattering both with and without rotation of the electron spin direction are provided. This formalism is used to develop a perturbation theory for the spin-flip probability which, in the strong-field limit of interest here, reduces to a fairly simple relation between $S$-matrix elements for scattering with and without change in spin orientation, each expressed in terms of a Bessel function. A similar perturbative procedure is applied to estimate corrections to the standard theory for scattering in the absence of spin-flip processes, in which interactions that change the net number of photons in the field are ignored.

We approach the problem of $N$ atoms in a magneto-optical trap through a hierarchical tree method, using an algorithm originally developed by Barnes and Hut (BH) in the astrophysical context. Such an algorithm numerically takes care of the particle-particle interaction by controlling the approximation level in a way that offers more physical fidelity than the mean-field treatment and considerably less time consumption ($\tau \sim N{\log }_{10}N$ in the hierarchical BH method, in contrast with the $\tau \sim N^2$ and $\tau \sim N^{3∕2}$ dependences found in direct and mean-field approaches, respectively). Our results reproduce the experimentally reported single-ring orbital mode for $N\lesssim {10}^6$ atoms and also find indication of a double-ring structure for $N\sim {10}^7$, a situation mimicked by a $N={10}^6$ system with enhanced radiative force, in agreement with experimental observations. We stress that this high-density regime is not accessed by direct integration of the equations of motion, due to the enormous computing times required, and is not suitably described through mean-field approaches, due to the rather unphysical enhancement of the particle-particle interactions and the presence of a spurious numerical grid dependence.

We solve the exact three-dimensional time-dependent Schrödinger equation for ${{\mathrm{H}}_2}^{+}$ (with fixed nuclei) interacting with an intense laser pulse with an arbitrary oriented linear polarization. We find that at equilibrium internuclear distance, the ionization probability of ${{\mathrm{H}}_2}^{+}$ is maximum for the parallel orientation of the molecule with respect to the laser polarization, and is minimum for the perpendicular orientation. The contribution of each nucleus to the harmonic spectrum is evaluated, so that interference effects between the two contributions are assessed unambiguously. We show that every half-cycle, high order harmonics are emitted by each nucleus when the electron wave packet returns for a recollision with both nuclei, and that the resulting harmonic emission is predominant for the nucleus that experiences the first recollision. In general, each nucleus emits both even and odd harmonics, but even harmonics are destroyed by interferences between contributions from each nucleus. In general, this destructive interference occurs over a large spread of harmonic orders, which depends on the angle between the molecular axis and the laser polarization.

The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.

We investigate the physical implementation of Shor’s factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits are available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor’s algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.

We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one and two qubits gates. Our method is analytical and is not based on numerical search in the space of all loops.

A Cs referenced optical frequency comb system has been used to measure the center frequency of the $5s{}^{2}S_{1∕2}–4d{}^{2}D_{5∕2}$ transition at $445\mathrm{THz}$ in a single, trapped, and laser-cooled ${}^{88}\mathrm{Sr}^{+}$ ion. The transition frequency ${\nu }_{SD}=\mathrm{444\hspace{0.17em}779\hspace{0.17em}044\hspace{0.17em}095\hspace{0.17em}510}\mathrm{Hz}\pm 50\mathrm{Hz}\left(1\sigma \right)$ is obtained, when corrected for systematic shifts. A detailed calculation of the estimated systematic shifts is presented which yields improved values for the various shift parameters including blackbody and electric quadrupole moment shifts.

We examine in this paper the spectral characteristics of a coherent population trapping (CPT) maser in order to evaluate the frequency stability achievable by this kind of passive frequency standard. The peculiar features of the coherent microwave emission associated with the coherent population trapping phenomenon are theoretically examined taking into account the impact of the various noise contributions on the physical principle of operation. The theoretical predictions are then compared with the experimental results obtained with a laboratory prototype of ${}^{87}\mathrm{R}\mathrm{b}$ CPT maser. The measured frequency stability is mainly limited in the short term by the system thermal noise and in the medium term by the thermal drift and turns out to be in agreement with the computations within a factor of 2.

Variational ab initio $R$-matrix theory is combined with generalized multichannel quantum defect theory, implemented in spheroidal coordinates, to calculate clamped-nuclei ${}^1\Sigma _g^{+}$, ${}^1\prod _g$, and ${}^1\Delta _g^{+}$ electron-ion scattering phase shift matrices for ${\mathrm{H}}_2$. The calculations cover the bound state region below $\mathrm{H}_2{}^{+}1{\sigma }_g$, the resonance region between $\mathrm{H}_2{}^{+}1{\sigma }_g$ and $\mathrm{H}_2{}^{+}1{\sigma }_u$, and they extend beyond the $\mathrm{H}_2{}^{+}1{\sigma }_u$ threshold. They span the range of internuclear distances $1⩽R⩽5\mathrm{a.u.}$ The use of spheroidal instead of spherical coordinates allows a restricted partial wave expansion to be used, thus yielding a compact set of interaction parameters pertaining to the electron-ion scattering dynamics in ${\mathrm{H}}_2$. The accuracy of our fixed-nuclei quantum defects is generally of the order of about 0.02. At the same time the quantum defect matrices obtained here exhibit a smooth behavior across the ionization thresholds and their elements also vary rather smoothly with internuclear distance. These results represent a step toward the goal of constructing a unfied theoretical description of ionization and dissociation fragmentation dynamics of ${\mathrm{H}}_2$.

To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads in the saddle point approximation to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schrödinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derive an approximate analytical expression for the oscillation frequency of the center of mass in an external harmonic potential. In both the weak and intermediate coupling regimes, the detection of the Josephson oscillations described by our path integral formalism constitutes experimental evidence for the fermionic superfluid regime.

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.

We investigate the propagation of attosecond pulse in a dense two-level medium by using an iterative predictor-corrector finite-difference time-domain method. We find when attosecond pulse is considered, that the standard area theorem will break down even for small area pulses: ideal self-induced transparency cannot occur even for a $2\pi$ pulse, while the pulses whose areas are not integer multiples of $2\pi$, such as $1.8\pi$ and $2.2\pi$ pulses, cannot evolve to $2\pi$ pulses as predicted by the standard area theorem. Significantly higher spectra components can occur on all these small area propagating pulses due to strong carrier reshaping. Furthermore, these higher spectral components dependent sensitively on the pulse area: the larger the pulse area is, the more evident are these higher spectral components.

In a recent paper Geyer, Klimchitskaya, and Mostepanenko [Phys. Rev. A 67, 062102 (2003)] proposed the final solution of the problem of temperature correction to the Casimir force between real metals. The basic idea was that one cannot use the dielectric permittivity in the frequency region where a real current may arise leading to Joule heating of the metal. Instead, the surface impedance approach is proposed as a solution of all contradictions. The purpose of this comment is to show that (i) the main idea contradicts to the fluctuation dissipation theorem, (ii) the proposed method to calculate the force gives the wrong value of the temperature correction since the contribution of low frequency fluctuations is calculated with the impedance which is not applicable at low frequencies.

The preceding Comment discusses in detail the main idea of our paper [Phys. Rev. A 67, 062102 (2003)], namely that one cannot substitute the Drude dielectric function into the Lifshitz formula for the thermal Casimir force in the frequency region where a real current of conduction electrons leads to Joule heating in the metal. In that Comment, it is claimed that this idea would be in contradiction to the fluctuation-dissipation theorem. In this Reply we present an explicit explanation why there is no contradiction. In the second part of the Comment an alternative method is suggested, different from the one used in our paper, to calculate the thermal Casimir force in the framework of the impedance approach. This method is in support of a previous prediction by Svetovoy and Lokhanin, criticized by us, that there exists a relatively large thermal correction to the Casimir force between real metals at small separations. Here we present strong quantitative arguments in favor of the statement that the method of the Comment is in violation of the Nernst heat theorem. We also demonstrate that it is in contradiction with experiment. The approach of our paper is shown to be in agreement with both thermodynamics and experimental data.

Interference between dipole and quadrupole transition amplitudes in photo-double-ionization of He by an elliptically polarized vuv photon is shown to induce circular dichroism in the case of equal energy sharing. The magnitude of this retardation-induced dichroic effect is estimated and its impact on the nondipole asymmetries of the triply differential cross section is demonstrated.