Difference-phase (or Hanbury Brown–Twiss type) intensity interference of classical light is considered in higher orders in the intensity. It is shown that, while the visibility of sum-phase (NOON-type) interference for classical sources drops with the order of interference, the visibility of difference-phase interference has opposite behavior. For three-photon and four-photon interference of two coherent sources, the visibility can be as high as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon interference of space-time and polarization types has been observed in experiment, for both coherent and pseudothermal light.

We show that a longitudinal (Goos-Hänchen) and a transverse (Imbert-Fedorov) beam displacement can be observed upon total internal reflection at two-dimensional photonic crystal slabs. By inspecting only the dispersion relation of the photonic crystal we derive qualitative criteria for the direction of the beam shift. Furthermore, it will be shown that the beam shift can be strongly enhanced at particular angles of incidence where Fabry-Pérot resonances of the slab are excited. The Renard model, which predicts the strength of the shifts based on the Poynting vector in the totally reflecting medium, has been adapted to quantitatively analyze the beam shift.

We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.

A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wave function for the pointer is real, the mean displacement of the pointer is proportional to the so-called weak value of the observable being measured. This gives an intuitively direct way of understanding weak measurement. However, if the initial pointer wave function takes complex values, the relationship between pointer displacement and weak value is not quite so simple, as pointed out recently by Jozsa [R. Jozsa, Phys. Rev. A 76, 044103 (2007)]. This is even more striking in the case of sequential weak measurements [G. Mitchison, R. Jozsa, and S. Popescu, Phys. Rev. A 76, 062105 (2007)]. These are carried out by coupling several pointers at different stages of the evolution of the system, and the relationship between the products of the measured pointer positions and the sequential weak values can become extremely complicated for an arbitrary initial pointer wave function. Surprisingly, all this complication vanishes when one calculates the cumulants of pointer positions. These are directly proportional to the cumulants of sequential weak values. This suggests that cumulants have a fundamental physical significance for weak measurement.

We propose a method to generate entanglement measures systematically by using the irreducible decomposition of some copies of a state under the local unitary (LU) transformations. It is applicable to general multipartite systems. We show that there are entanglement monotones corresponding to singlet representations of the LU group. They can be evaluated efficiently in an algebraic way, and experimentally measurable by local projective measurements of the copies of the state. Nonsinglet representations are also shown to be useful to classify entanglement. Our method reproduces many well-known measures in a unified way.

A relativistic $R$-matrix close-coupling method based on effective many-body Hamiltonians is employed to calculate the electron-impact excitations of intercombination transitions in the ${\text{Kr}}^{6+}$ ion as benchmarks in the quest for accurate representation of the target and collisional states in multivalence-electron ions. The effective Hamiltonian in relativistic multireference many-body perturbation theory accurately accounts for short-range many-body interactions unaccounted for by limited configuration-interaction representations of the basis states. The $R$-matrix method is successfully applied to the near-threshold electron impact excitation of the $4s^2{}^{1}S\to 4s4p{}^{3}P$ intercombination transition in the zinclike krypton $\left({\text{Kr}}^{6+}\right)$ ion, where the observed disagreement between the experimental absolute total cross sections dominated by dielectronic resonances and those predicted by using the Breit-Pauli and Dirac $R$-matrix methods reveals an inadequacy of the extant $R$-matrix close-coupling calculations in compact configuration-interaction representation of target states.

There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.

We present a detailed analysis of decoherence free subspaces and develop a rigorous theory that provides necessary and sufficient conditions for dynamically stable decoherence free subspaces. This allows us to identify a special class of decoherence free states which rely on incoherent generation of coherences. We provide examples of physical systems that support such states. Our approach employs Markovian master equations and applies primarily to finite-dimensional quantum systems.

We introduce a partial state fidelity approach to quantum phase transitions. We consider a superconducting lattice with a magnetic impurity inserted at its center, and look at the fidelity between partial (either one-site or two-site) quantum states. In the vicinity of the point of the quantum phase transition, we observe a sudden drop of the fidelity between two one-site partial states corresponding either to the impurity location or its close vicinity. This enables us to identify the on-site magnetization as the order parameter for the phase transition studied. In the case of two-site states, the fidelity reveals the transition point as long as one of the two electron sites is located at the impurity, while the other lies elsewhere in the lattice. We also determine the Uhlmann mixed state geometric phase, recently introduced in the study of the structural change of the system state eigenvectors in the vicinity of the lines of thermal phase transitions, and find it to be trivial, both for one- and two-site partial states, except when an electron site is at the impurity. This means that the system partial state eigenvectors do not contribute significantly to the enhanced state distinguishability around the point of this quantum phase transition. Finally, we use the fidelity to analyze the total amount of correlations contained within a composite system, showing that, even for the smallest one-site states, it features an abrupt quantitative change in the vicinity of the point of the quantum phase transition.

The methodology of optimal control theory is applied to the problem of implementing quantum gates in continuous-variable (CV) systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for CV gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete-variable and continuous-variable quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, but can be routinely achieved for all the major classes of computing primitives. The exact-time controllability of CV systems, hitherto largely ignored in the design of information processing models, is shown to play an important role in determining the maximal achievable gate fidelity. Moreover, the ability to control interactions between qunits can be exploited to delimit the total control fluence. Future experimental model systems should carefully tune these parameters so as to enable the implementation of CV quantum information processing with optimal fidelity.

We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary $2$-designs.

Many promising schemes for quantum information processing (QIP) rely on few-photon interference effects. In these proposals, the photons are treated as being indistinguishable particles. However, single photon sources are typically subject to variation from device to device. Thus the photons emitted from different sources will not be perfectly identical, and there will be some variation in their frequencies. Here, we analyze the effect of this frequency mismatch on QIP schemes. As examples, we consider the distributed QIP protocol proposed by Barrett and Kok [Phys. Rev. A 71, 060310 (2005)], and Hong-Ou-Mandel interference which lies at the heart of many linear optical schemes for quantum computing [E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) 409, 46 (2001); P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007)]. In the distributed QIP protocol, we find that the fidelity of entangled qubit states depends crucially on the time resolution of single photon detectors. In particular, There is no reduction in the fidelity when an ideal detector model is assumed, while reduced fidelities may be encountered when using realistic detectors with a finite response time. We obtain similar results in the case of Hong-Ou-Mandel interference—with perfect detectors, a modified version of quantum interference is seen, and the visibility of the interference pattern is reduced as the detector time resolution is reduced. Our findings indicate that problems due to frequency mismatch can be overcome, provided sufficiently fast detectors are available.

Phase matching has been studied for the Grover algorithm as a way of enhancing the efficiency of the quantum search. Recently Li and Li found that a particular form of phase matching yields, with a single Grover operation, a success probability greater than $25/27$ for finding the equal-amplitude superposition of marked states when the fraction of the marked states stored in a database state is greater than $1/3$. Although this single operation eliminates the oscillations of the success probability that occur with multiple Grover operations, the latter oscillations reappear with multiple iterations of Li and Li’s phase matching. In this paper we introduce a multiphase matching subject to a certain matching rule by which we can obtain a multiple Grover operation that with only a few iterations yields a success probability that is almost constant and unity over a wide range of the fraction of marked items. As an example we show that a multiphase operation with six iterations yields a success probability between 99.8 and $100\%$ for a fraction of marked states of $1/10$ or larger.

We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method based on the algebraic properties of octonions. Since the protocol does not use any post-selection, it can be proven secure against arbitrary collective attacks by using well-established theorems on the optimality of Gaussian attacks. By using this coding scheme with an appropriate signal-to-noise ratio, the distance for a secure continuous-variable quantum key distribution can be significantly extended.

Detailed analysis of spectral line broadening and variations in relative intensities of hyperfine spectral components due to optical pumping is presented. Hyperfine levels of sodium $3p_{1/2}$ and $3p_{3/2}$ levels are selectively excited in a supersonic beam at various laser intensities under the conditions when optical pumping time is shorter than transit time of atoms through the laser beam. The excitation spectra exhibit significant line broadening at laser intensities well below the saturation intensity, and redistribution of intensities of hyperfine spectral components is observed, which in some cases is contradicting with intuitive expectations. Theoretical analysis of the dynamics of optical pumping shows that spectral line broadening sensitively depends on the branching coefficient of the laser-driven transition. Analytical expressions for branching ratio dependent critical Rabi frequency and critical laser intensity are derived, which give the threshold for onset of noticeable line broadening by optical pumping. The critical laser intensity has its smallest value for transitions with branching coefficient equal to 0.5, and it can be much smaller than the saturation intensity. Transitions with larger and smaller branching coefficients are relatively less affected. The theoretical excitation spectra were calculated numerically by solving density matrix equations of motion using the split propagation technique, and they well-reproduce the observed effects of line broadening and peak intensity variations. The calculations also show that presence of dark (i.e., not laser coupled) Zeeman sublevels in the lower state results in effective branching coefficients which vary with laser intensity and differ from those implied by the sum rules, and this can lead to peculiar changes in peak ratios of hyperfine components of the spectra.

We study the process of low-energy electron capture by the ${\text{SF}}_6$ molecule. Our approach is based on the model of Gauyacq and Herzenberg [J. P. Gauyacq and A. Herzenberg, J. Phys. B 17, 1155 (1984)] in which the electron motion is coupled to the fully symmetric vibrational mode through a weakly bound or virtual $s$ state. By tuning the two free parameters of the model, we achieve an accurate description of the measured electron attachment cross section and good agreement with vibrational excitation cross sections of the fully symmetric mode. An extension of the model provides a limit on the characteristic time of intramolecular vibrational relaxation in highly excited $\text{SF}_6{}^{-}$. By evaluating the total vibrational spectrum density of $\text{SF}_6{}^{-}$, we estimate the widths of the vibrational Feshbach resonances of the long-lived negative ion. We also analyze the possible distribution of the widths and its effect on the lifetime measurements, and investigate nonexponential decay features in metastable $\text{SF}_6{}^{-}$.

We calculate the position distribution of an ensemble of cold thermal atoms in the vicinity of a dielectric surface. We find that the profile of the position distribution exhibits spatial oscillations resulting from the quantum nature of the atomic center-of-mass motion and the interference between the incident and reflected matter waves. When the temperature of the atoms is in the nanokelvin range, the position distribution density becomes negligible in a broad spatial region due to the combined action of the classical acceleration of the atoms, the interference between the incident and reflected waves, and the quantum reflection of the atoms from the slope of the surface-induced potential.

We investigate the quantum signature scheme proposed by and Zeng and Keitel [Phys. Rev. A 65, 042312 (2002)]. It uses Greenberger-Horne-Zeilinger states and the availability of a trusted arbitrator. However, in our opinion the protocol is not clearly operationally defined and several steps are ambiguous. Moreover, we argue that the security statements claimed by the authors are incorrect.

We experimentally investigate nonlinear couplings between individual quanta of the vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions’ Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian $H=\hslash \chi {\widehat{n}}_r{\widehat{n}}_s$, where ${\widehat{n}}_r$, ${\widehat{n}}_s$ are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment over a range of trap frequencies. With $2.97\mathrm{MHz}$ stretch mode and $3.61\mathrm{MHz}$ rocking mode frequencies, we observed a coupling of $20.5\mathrm{Hz}∕\mathrm{phonon}$. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.

An investigation of the lifetime of the $3d^{9}4s{{}^{3}D}_3$ level along a part of the nickel-like isoelectronic sequence has been performed. The focus of this work has been to evaluate the importance of the hyperfine induced electric quadrupole channel of the $3d^{10}{{}^{1}S}_0-3d^{9}4s{{}^{3}D}_3$ transition for isotopes with nuclear spin. Comparisons between the magnetic octupole transition rate and the hyperfine-induced electric quadrupole transition rate shows that the hyperfine quenching is of importance along the whole isoelectronic sequence. At the low-$Z$ end the hyperfine induced electric quadrupole transition channel dominates, being several orders of magnitude larger than the rate for the magnetic octupole transition channel, while for higher $Z$ the two rates are of comparable size.