The emergence of conformal states is established for any problem involving a domain of scales where the long-range SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs is in place, this renormalization mechanism is capable of producing binding in the strong-coupling regime. A realization of this phenomenon, in the form of dipole-bound anions, is discussed.

Local quantum operations and classical communication (LOCC) put considerable constraints on many quantum information processing tasks such as cloning and discrimination. Surprisingly, however, discrimination of any two pure states survives such constraints in some sense. We show that cloning is not that lucky; namely, probabilistic LOCC cloning of two product states is strictly less efficient than global cloning. We prove our result by giving explicitly the efficiency formula of local cloning of any two product states.

A comparative study of charge transfer in collisions of ground-state ${\mathrm{S}}^{2+}$ ions with He has been performed within fully quantal and semiclassical molecular-orbit close-coupling approaches. The processes for capture into ${\mathrm{S}}^{+}({}^{4}S^0,{}^{2}D^0,{}^{2}P^0)+{\mathrm{He}}^{+}$ are taken into account. Quantal and semiclassical cross sections were evaluated, respectively, in the diabatic and adiabatic representations and found to be in good agreement. The calculations show that at collision energies below about $40\mathrm{eV}∕\mathrm{u}$, the charge-transfer processes are dominated by ${\mathrm{S}}^{2+}\left({}^{3}P\right)+\mathrm{He}\to {\mathrm{S}}^{+}\left({}^{2}D^0\right)+{\mathrm{He}}^{+}$, and capture into the ${}^{2}P^0$ and ${}^{4}S^0$ states becomes comparable with that into the ${}^{2}D^0$ state above $40\mathrm{eV}∕\mathrm{u}$ and $600\mathrm{eV}∕\mathrm{u}$, respectively. The multireference single- and double-excitation configuration-interaction method was utilized to obtain adiabatic potentials and nonadiabatic coupling matrix elements. A detailed comparison of quantal and semiclassical transition probabilities is discussed. State-selective and total rate coefficients are presented with temperatures between $10000\mathrm{K}$ and $5.0\times {10}^6\mathrm{K}$.

General selection rules for differential cross sections for laser-assisted electron-atom scattering are derived for the geometry in which the linearly polarized laser field is perpendicular to the scattering plane. Numerical calculations using the $R$-matrix Floquet theory are presented for electron-helium scattering in order to discuss the possibility of observing these selection rules experimentally.

We report on our recent progress in the manipulation and cooling of a magnetically guided, high-flux beam of ${}^{87}\mathrm{Rb}$ atoms. Typically, $7\times {10}^9\text{atoms}\text{per}\text{second}$ propagate in a magnetic guide providing a transverse gradient of $800\mathrm{G}∕\mathrm{cm}$, with a temperature $\sim 550\mu \mathrm{K}$, at an initial velocity of $90\mathrm{cm}∕\mathrm{s}$. The atoms are subsequently slowed down to $\sim 60\mathrm{cm}∕\mathrm{s}$ using an upward slope. The relatively high collision rate $\left(5{\mathrm{s}}^{-1}\right)$ allows us to start forced evaporative cooling of the beam, leading to a reduction of the beam temperature by a factor of 4, and a tenfold increase of the on-axis phase-space density.

The strong field approximation is used to investigate the harmonic generation of aligned ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules. It is shown that the angular dependence of the yields of high-order harmonic generation from ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules are different, which can be attributed to the orbital symmetry of the outmost electrons. The theory is applied to study the angular dependence of harmonic generation from recent pump-probe experiments where the pump pulse was used to produce the time-dependent partial alignment of molecules and the probe pulse was used to generate high-order harmonics. Good agreement with the experiments was found.

We theoretically investigate the high-order harmonic generation from a neon atom irradiated by an intense two-color femtosecond laser pulse, in which the fundamental field and its second harmonic are linearly polarized and orthogonal to each other. In contrast to usual high-harmonic generation with linearly polarized fundamental field alone, a very strong and clean high-harmonic spectrum, consisting of both odd and even orders of harmonics, can be generated in the orthogonally polarized two-color laser field with proper selection of the relative phase between the fundamental and second-harmonic fields. In time domain, this results in a strong and regular attosecond pulse train. The origin of these behaviors is elucidated by analyzing semiclassical electron paths and by simulating high-harmonic generation quantum mechanically.

We suggest two types of experiments, NMR and macroscopic magnetometry, with solid $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ to search for the nuclear Schiff moment of ${}^{207}\mathrm{Pb}$. Both kinds of experiments promise substantial improvement over the presently achieved sensitivities. Statistical considerations show that the improvement of the current sensitivity can be up to ten orders of magnitude for the magnetometry experiment and up to seven orders of magnitude for the NMR experiment. Such significant enhancement is due to the strong internal electric field of the ferroelectric, as well as due to the possibility to cool the nuclear-spin subsystem in the compound down to nanokelvin temperatures.

The electron-impact double ionization of two isomers of ${\mathrm{C}}_3{\mathrm{H}}_4$ (allene and propyne) between 25 and 1000 eV has been investigated using time-of-flight mass spectrometry. Unambiguous differences in the partial double-ionization spectra of these isomers are observed over the entire energy range. These isomer effects have been observed in ${\mathrm{C}}_3{\mathrm{H}}_4$ through the recording of target product channels and, in particular, when hard collisions involving the transfer of a large amount of energy is involved. Measurements of double-ionization events which fragment through Coulomb explosion are also reported. Coincidences between the charged fragment ions and protons were measured and shown to only exhibit isomer effects in the channel involving production of ${\mathrm{H}}^{+}+{\mathrm{CH}}_2^{+}$.

We investigate the security bounds of quantum-cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the Bennett-Brassard 1984 quantum-key-distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum-cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.

We discuss the potential of quantum key distribution (QKD) for long-distance communication by proposing an analysis of the errors caused by dark counts. We give sufficient conditions for a considerable improvement of the key generation rates and the security thresholds of well-known QKD protocols such as the Bennett-Brassard 1984, Phoenix-Barnett-Chefles 2000, and six-state protocols. This analysis is applicable to other QKD protocols like the Bennett 1992 protocol. We examine two scenarios: a sender using a perfect single-photon source and a sender using a Poissonian source.

We show that for an $m$-qubit quantum system, there is a ball of radius asymptotically approaching $\kappa 2^{-\gamma m}$ in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices, for an exponent $\gamma =0.5(\ln 3∕\ln 2-1)\approx 0.29248125$ much smaller in magnitude than the best previously known exponent, from our earlier work, of $1∕2$. For normalized $m$-qubit states, we get a separable ball of radius $\sqrt{3^{m+1}∕(3^m+3)}\times 2^{-(1+\gamma )m}\equiv \sqrt{3^{m+1}∕(3^m+3)}\times 6^{-m∕2}$ (note that $\kappa =\sqrt{3}$), compared to the previous $2\times 2^{-3m∕2}$. This implies that with parameters realistic for current experiments, nuclear magnetic resonance (NMR) with standard pseudopure-state preparation techniques can access only unentangled states if 36 qubits or fewer are used (compared to 23 qubits via our earlier results). We also obtain an improved exponent for $m$-partite systems of fixed local dimension $d_0$, although approaching our earlier exponent as $d_0\to \infty$.

We study a quantum cellular automaton (QCA) whose time evolution is defined using the global transition function of a classical cellular automaton (CA). In order to investigate natural transformations from CAs to QCAs, the present QCA includes the CA with Wolfram’s rules 150 and 105 as special cases. We first compute the time evolution of the QCA and examine its statistical properties. As a basic statistical value, the probability of finding an active cell averaged over spatial-temporal space is introduced, and the difference between the CA and QCA is considered. In addition, it is shown that statistical properties in QCAs are related to the classical trajectory in configuration space.

Fine structure resolved $4p$ photoemission studies have been performed on free rubidium atoms in the ground state and after excitation into the $\left[\mathrm{Kr}\right]5p{}^{2}P_{1∕2}$ and ${}^{2}P_{3∕2}$ states. The $4p^{5}5p$ final states have been excited in the $4p^{6}5s\to 4p^{5}5p$ conjugate shakeup process from ground state atoms as well as by direct photoemission from laser excited atoms. The relative intensities differ considerably in these three excitation schemes. The differences in the laser excited spectra could be described well using calculations based on the pure $jK$-coupling scheme. Thereby it was possible to specify the character of the various final states. Furthermore it has been possible to resolve two of the final states whose energy separation is smaller than the experimental resolution by selectively exciting them in a two step scheme, where the laser selects the spin-orbit coupling in the intermediate state and determines the final state coupling after x-ray photoemission.

We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunneling leads to a residual sensitivity to the atom dynamics hence requiring large depths [$\left(50\text{–}100\right)E_r$ for Sr] to avoid any frequency shift or line broadening of the atomic transition at the ${10}^{-17}\text{–}{10}^{-18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g., higher-order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunneling. We show that using the Earth’s gravity, much shallower traps (down to $5E_r$ for Sr) can be used for the same accuracy goal.

Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In particular, we study the entanglement between the atoms in the condensate as well as that between the two modes. The nature of the enhanced quantum correlations in TBEC is clarified by considering squeezing and entanglement both with and without the nonlinear interaction turned on; it is found that entanglement approaching maximal value can be achieved with the nonlinear interactions present. Somewhat counterintuitively, greater squeezing is found in the absence of nonlinear interactions. This is due to the collapses and revivals of the TBEC quantum state induced by the nonlinear interactions. In addition, results involving the self-trapping phase state of TBEC indicate potential for creating a dynamically stable, macroscopic entangled quantum state which is relatively robust with respect to atom number fluctuations.

It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.

We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing wave generated by a high-finesse optical cavity, which is an atomic version of the well-known “kicked rotor.” We show that the classical phase-space map can be “reconstructed” by monitoring the transmission of the cavity. We also studied the effect of spontaneous emission on the reconstruction and put limits to the maximum acceptable spontaneous emission rate.

Using a resonant interaction between atoms and the field in a high-quality cavity, we show how to realize quantum random walks as proposed by Aharonov et al. [Phys. Rev. A 48, 1687 (1993)]. The atoms are driven strongly by a classical field. Under conditions of strong driving we could realize an effective interaction of the form $i{S}^x(a-a^{†})$ in terms of the spin operator associated with the two-level atom and the field operators. This effective interaction generates displacement in the field’s wave function depending on the state of the two-level atom. Measurements of the state of the two-level atom would then generate an effective state of the field. Using a homodyne technique, the state of the quantum random walker can be monitored.

Distinctive optical forces and torques arise between nanoparticles irradiated by intense laser radiation. These forces, associated with a pairwise process of stimulated scattering, prove to enable the possibility of producing significant modifications to both the form and magnitude of interparticle forces, with additional contributions arising in the case of dipolar materials. Moreover, such forces have the capacity to generate unusual patterns of nanoscale response, entirely controlled by the input beam characteristics—principally the optical frequency, intensity, and polarization. Based on quantum electrodynamical theory, a general result is secured for the laser-induced force under arbitrary conditions, incorporating both static and dynamic coupling mechanisms. Specific features of the results are identified for pairs of particles with prolate cylindrical symmetry, e.g., carbon nanotubes, where it is shown that the laser-induced forces and torques are sensitive functions of the pair spacing and orientation, and the laser beam geometry; significantly, they can be either repulsive or attractive according to conditions. For nanoparticles trapped in a Laguerre-Gaussian laser beam the results also reveal additional and highly distinctive torques that suggest further possibilities for nanomanipulation with light. The paper concludes with a discussion on several potential applications of such forces.