We present a formalism for studying the behavior of quantum systems coupled to nonequilibrium environments exhibiting non-Gaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations, as well as non-Markovian effects in both weak and strong-coupling limits. We also discuss the differences between the influences of classical and quantum environments. As examples of the application of this formalism we study the dephasing and relaxation of a charge qubit coupled to nonequilibrium electron transport through single and double quantum dots.

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum-information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.

We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. A tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities of three qubits reduced from those of three qudits are also studied.

The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest separable state, is obtained. Analysis of the formula for a large class of entangled states strongly suggests that a compact analytical solution of the original problem, which corresponds to finding the closest separable state for a given entangled state, can be given only in some special cases. A few applications of the compact-form formula are given to show additivity of the REE, to relate the REE with the Rains upper bound for distillable entanglement, and to show that a Bell state does not have a unique closest separable state.

Calculations using multiconfiguration Breit-Pauli and multiconfiguration Dirac-Fock methodologies have revealed that the radiative and Auger rates, and the associated fluorescence yields, of the six electron $1s2s^{2}2p^3$ $K$-shell vacancy isoelectronic sequence exhibit nonmonotonic behavior as a function of nuclear charge $Z$. This behavior is explained in terms of an accidental degeneracy, an avoided crossing of two nearly degenerate spin-orbit coupled levels. The results also demonstrate the importance of including both electron-electron correlation and spin-orbit effects even at low $Z$.

The dielectronic recombination of high-$Z$ hydrogenlike ions is studied within the framework of the density matrix theory. Emphasis is placed on the alignment of the doubly excited ions and the non-electric-dipole $\left(E1\right)$ contributions to the subsequent characteristic x-ray emission. Multiconfiguration Dirac-Fock calculations have been carried out in order to investigate the multipole mixing effects on the radiative decay of the doubly excited resonances of heliumlike uranium, following the $K\text{−}LL$ dielectronic recombination of hydrogenlike ${\mathrm{U}}^{91+}$ ions. In particular, the angular distribution of the $K{\alpha }_1$ hypersatellites is notably modified by the interference between the leading $E1$ and the magnetic-quadrupole $\left(M2\right)$ transitions. The results are compared with measurements and previous computations available.

We have experimentally investigated the anisotropy-dependent circular polarization spectra of the ${}^{133}\mathrm{Cs}$ $6s{}^{2}S_{1∕2}\to 6p{}^{2}P_{3∕2}\to 10s{}^{2}S_{1∕2}$ double-resonance transition in the presence of Ar. Satisfaction of double-resonance condition, achieved by use of a two-photon two-color pulse laser excitation scheme, was monitored by measurement of the intensity of the $9p{}^{2}P_{1∕2}\to 6s{}^{2}S_{1∕2}$ cascade fluorescence at $361.73\mathrm{nm}$. In the experiment anisotropies, namely, alignment and orientation in the $6p{}^{2}P_{3∕2}$ level, were produced from circularly polarized light with positive helicity. Then, a circular polarization degree was measured when both lasers were circularly polarized with positive helicities, and alternately positive and negative helicities for the $6p{}^{2}P_{3∕2}\to 10s{}^{2}S_{1∕2}$ transition. From the measurement, we obtained the orientation-dependent depolarization cross section in the $6p{}^{2}P_{3∕2}$ level due to collisions with ground-level argon atoms. A disorientation cross section value of 151 $\left(42\right){\mathrm{\AA }}^2$ is reported.

The Floquet problem for the interaction of an atom with a monochromatic laser field of frequency $\omega$ was studied long ago for the case of high $\omega$ and arbitrary intensity using the ‘‘high-frequency Floquet theory’’ (HFFT). The two parameters of the theory are the frequency $\omega$ and the classical excursion parameter ${\alpha }_0\equiv E_0{\omega }^{-2}$, where $E_0$ is the electric field strength. HFFT solves the Floquet system by successive iterations. Convergence of the iteration procedure was shown to be ensured by the condition that $\omega$ be suffiently large with respect to some typical atomic excitation energy. We now establish that the same iteration procedure is capable of handling the case of low frequency at sufficiently high intensity. This leads to the conclusion that in this case the ionization rates display quasistationary stabilization also at low $\omega$. The concept is thus not exclusively related to high frequencies, as widely assumed. In addition, it suggests that a more appropriate designation for the theory should be ‘‘high-intensity, high-frequency Floquet theory’’ (HIHFFT). Our general results are applied to a frequently used one-dimensional (1D) soft-core potential model, for which explicit analytic results can be obtained for the quasienergies and wave functions from the general HIHFFT formulas. The relevance of these quasistationary results for the case of laser pulses is pointed out.

In the preceding paper we have shown, based on the high-intensity, high-frequency Floquet theory (HIHFFT), that atomic quasistationary stabilization (QS) and dichotomy are not necessarily high-frequency phenomena as widely believed, but can occur also at photon energies small with respect to the unperturbed ground state binding energy, provided that the field is strong enough. In this paper we approach the issue from the point of view of accurate numerical Floquet computations. We have made a comprehensive determination of the Floquet quasienergies for a one-dimensional (1D) atomic model with a soft-core Coulomb potential (ground state energy $W_0=-0.500\mathrm{a.u.}$) in a laser field of constant amplitude $E_0$ and frequency $\omega$. The excursion parameter ${\alpha }_0=E_0∕{\omega }^2$ was varied over the range $0<{\alpha }_0<100$, at two low frequencies $\omega =0.12$ and $0.24\mathrm{a.u.}$ $(\omega <\mid W_0\mid )$; the lowest-lying 18 states were computed. We present graphs for the ${\alpha }_0$ dependence of the energies of the states in the field, $W\left({\alpha }_0\right)=\mathrm{Re}E$ (“Floquet maps”), and their ionization rates $\Gamma \left({\alpha }_0\right)$. An intricate behavior of $W\left({\alpha }_0\right)$ was revealed at low ${\alpha }_0$, with many crossings, avoided crossings (ACs), and Floquet states materializing or disappearing at multiples of $\omega$ energy thresholds. At large ${\alpha }_0$, however, the uneventful pattern encountered at high frequencies is regained, in which the levels tend monotonically to zero modulo $\omega$ (i.e., the binding energies of all states vanish). Also $\Gamma \left({\alpha }_0\right)$ varies substantially at low ${\alpha }_0$, attaining sometimes large values, but at large ${\alpha }_0$ it decreases to zero in an oscillatory manner (QS). The form of the components of the Floquet wave function was also followed from low to large ${\alpha }_0$, and abrupt changes were found in most cases at ACs. The Floquet results were then compared to a computation of the HIHFFT formulas for the quasienergies and good agreement was found (to within the expected accuracy of HIHFFT). This confirms that HIHFFT is fully capable of describing the low-frequency regime at large enough ${\alpha }_0$, and in particular the existence of QS and dichotomy.

We derive a controlled expansion into mean field plus fluctuations for the extended Bose-Hubbard model, involving interactions with many neighbors on an arbitrary periodic lattice, and study the superfluid-supersolid phase transition. Near the critical point, the impact of (thermal and quantum) fluctuations on top of the mean field grows, which entails striking effects, such as negative superfluid densities and thermodynamical instability of the superfluid phase—earlier as expected from mean-field dynamics. We also predict the existence of long-lived “supercooled” states with anomalously large quantum fluctuations.

Light storage in atomic ensembles has been implemented successfully, but the retrieval efficiency can be low. We propose to improve this efficiency with appropriately phase-matched backward propagating retrieval. This method allows for easy spatial filtering of the retrieved light; in addition, multiple optical modes can be stored in the transverse momentum of the ensemble. We model walk-off effects with a full numerical simulation, and confirm the applicability of the scheme.

We have experimentally and theoretically studied the scheme of all-optical switching based on stored light pulses. In the scheme, a probe pulse is stored in the medium by the effect of electromagnetically induced transparency and a switching pulse is applied during the storage in order to turn off the probe transmission in the retrieval process. Our study takes into account the attenuation of the switching pulse induced by the stored probe pulse. The consistency between the experimental data and the theoretical predictions from the numerical calculation is satisfactory. We further derive the analytical expressions of energy losses of the probe and switching pulses. The results from the analytical expressions are in good agreement with those from the numerical calculation. Using the analytical expressions, we investigated the switching efficiency with the consideration of the Gaussian beam profile of the photon pulses and explored the feasibility of switching a single photon by another.

Long-living entanglement between the emitter and the field of a photonic-crystal reservoir near the band edge is suggested for implementation of an effective single-photon generator. It can be efficiently driven by incoherent excitation, is highly controllable, allows no two-photon generation, and provides for a high extraction probability of the emitted photon into a well-defined mode.

The Cooper problem for interacting fermions is solved in a lattice. It is found that the binding energy of the Cooper problem can behave qualitatively differently from the gap parameter of the BCS theory and that pairs of nonzero center-of-mass momentum are favored in systems with unequal Fermi energies.

A generalization of the Hohenberg-Kohn theorem for finite systems proves the existence of a density functional (DF) for a symmetry violating intrinsic state, out of which a physical state with good quantum numbers can be projected.

We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\times {10}^{-17}$ and below. In particular, we focused on ac polarizabilities of the $5s^2$ ${}^{1}S_0$ and $5s5p$ ${}^{3}P_0^o$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the ${}^{1}S_0\text{−}{}^{3}P_0^o$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the ${}^{3}P_0^o$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the ${}^{3}P_0^o$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\times {10}^{-17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.

We analyze the effects of partial coherence of ground-state preparation on two-pulse propagation in a three-level $\Lambda$ medium, in contrast to previous treatments that have considered the cases of media whose ground states are characterized by probabilities (level populations) or by probability amplitudes (coherent pure states). We present analytic solutions of the Maxwell-Bloch equations, and we extend our analysis with numerical solutions to the same equations. We interpret these solutions in the bright and dark dressed-state basis, and show that they describe a population transfer between the bright and dark state. For mixed-state $\Lambda$ media with partial ground-state phase coherence the dark state can never be fully populated. This has implications for phase-coherent effects such as pulse matching, coherent population trapping, and electromagnetically induced transparency (EIT). We show that for partially phase-coherent three-level media, self-induced transparency dominates EIT and our results suggest a corresponding three-level area theorem.

The influence of air turbulence on femtosecond laser filamentation is studied experimentally and numerically for laser powers of a few critical powers. Air turbulence in the path of the beam prior to filamentation induces a large pointing and formation instability attributed to an increase of the self-focusing distance and higher modulational instability in the presence of turbulence. By contrast, previously formed filaments are robust both in terms of beam pointing accuracy and survival when crossing turbulent air.

We explain the rotational Doppler effect associated with light beams carrying with orbital angular momentum in left-handed materials (LHMs). We demonstrate that the rotational Doppler effect in LHMs is unreversed, which is significantly different from the axial Doppler effect. The physics underlying this intriguing effect is the combined contributions of negative phase velocity and the inverse screw of the wave front. We find that the additional Doppler effect caused by Gouy phase and wave-front curvature should be reversed, because of the negative index. In the normal dispersion region, the rotational Doppler effect induces an upstream energy flow but a downstream momentum flow. In the anomalous dispersion region, however, the rotational Doppler effect produces a downstream energy flow but an upstream momentum flow. We theoretically predict that the rotational Doppler effect can induce a transfer of angular momentum of the LHM to orbital angular momentum of the beam.

We propose an ion-trap implementation of Grover’s quantum search algorithm for an unstructured database of arbitrary length $N$. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward construction, in a single interaction step and without a multitude of Hadamard transforms, of the reflection operator, which is the engine of the Grover algorithm. Consequently, a dramatic reduction in the number of the required physical steps takes place, to just $O\left(\sqrt{N}\right)$, the same as the number of mathematical steps. The proposed setup allows for demonstration of both the original (probabilistic) Grover search and its deterministic variation, and is remarkably robust to imperfections in the register initialization.