Scully and coworkers [M. O. Scully, E. S. Fry, C. H. R. Oii, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006)] demonstrated that there is directional, phase-matched emission following the excitation of an ensemble of atoms by a single-photon pulse. While the phase-matched emission intensity is proportional to the the number of atoms, for optically thin samples the total energy emitted in the phase-matched direction is much less than that radiated in other directions. Moreover, even for optically thin samples, it is necessary to take into account effects related to cooperative decay if energy is to be conserved in the overall emission process. An analytic calculation is presented to show explicitly how cooperative decay reduces the incoherent emission and restores energy conservation in this low-density limit.

We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

We propose a high-efficiency scheme to tomographically reconstruct an unknown quantum state by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the stationary transmissions through a driven dispersively coupled resonator. It is shown that only one kind of QND measurement is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining nondiagonal elements can be similarly determined by transferring them to the diagonal locations after a series of unitary operations. Compared with the tomographic reconstructions based on the usual destructive projective measurements (wherein one such measurement can determine only one diagonal element of the density matrix), the present reconstructive approach exhibits significantly high efficiency. Specifically, our generic proposal is demonstrated by the experimental circuit quantum electrodynamics systems with a few Josephson charge qubits.

Four types of photon counters are discussed in terms of information, fidelity, and physical reversibility: conventional photon counter, quantum counter, and their quantum nondemolition (QND) versions. It is shown that when a photon field to be measured is in an arbitrary superposition of vacuum and one-photon states, the quantum counter is the most reversible, the QND version of conventional photon counter provides the most information, and the QND version of the quantum counter causes the smallest state change. Our results suggest that the physical reversibility of a counter tends to decrease the amount of information obtained by the counter.

It is generally assumed that sources randomly sending two particles to one or two different observers, random destination sources (RDSs), cannot be used for genuine quantum nonlocality tests because of the postselection loophole. We demonstrate that Bell experiments not affected by the postselection loophole may be performed with (i) an RDS and local postselection using perfect detectors, (ii) an RDS, local postselection, and fair sampling assumption with any detection efficiency, and (iii) an RDS and a threshold detection efficiency required to avoid the detection loophole. These results allow the adoption of RDS setups which are simpler and more efficient for long-distance free-space Bell tests, and extend the range of physical systems which can be used for loophole-free Bell tests.

We derive a family of entanglement criteria for continuous-variable systems based on the Rényi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order moments, as well as previous tests involving the Shannon entropy [Phys. Rev. Lett. 103, 160505 (2009)]. We extend our results to include the case of discrete sampling. We provide several numerical results which show that our criteria can be used to identify entanglement in a number of experimentally relevant quantum states.

A quasi-one-dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one-dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In Fishman et al. [Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a ${\varphi }^4$ model. We propose a mapping of the ${\varphi }^4$ field theory to the well-known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures $T$. We focus in particular on a trapped-ion system and estimate the implied limitations on $T$ and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is, in principle, accessible.

We develop connections between generalized notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli directions. By considering restricted measurements one can (by considering the dual positive operators) construct single-particle-state spaces that are different to the usual quantum-state space. This leads to a modified notion of entanglement that can be very different to the quantum version (for example, Bell states can become separable). We use this approach to develop alternative methods of classical simulation that have strong connections to the study of nonlocal correlations: we construct noisy quantum computers that admit operations outside the Clifford set and can generate some forms of multiparty quantum entanglement, but are otherwise classical in that they can be efficiently simulated classically and cannot generate nonlocal statistics. Although the approach provides new regimes of noisy quantum evolution that can be efficiently simulated classically, it does not appear to lead to significant reductions of existing upper bounds to fault tolerance thresholds for common noise models.

We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations obtained by exploiting the mapping of an $N$-electron system in $d$ dimensions onto a single electron in $N\times d$ dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.

As yet there is no experimental determination of the binding energy of a positron to any neutral atom. However, quantum calculations have given positron binding energies for 12 atoms (including positronium) and have shown that 14 atoms do not bind a positron. We find that the known binding energies can be fitted to a simple expression involving only the polarizabilities, ionization potentials, and the numbers of valence $s$ electrons of the atoms, and we use this relationship to predict positron-atom binding energies for other atoms. Positronium-atom binding is not treated here.

We performed nuclear dynamics calculations on HCN and DCN to study the isotope effect in dissociative electron attachment. Our previous calculations at 333 K led to a ratio ${\sigma }^{({\mathrm{CN}}^{-}/\mathrm{HCN})}/{\sigma }^{({\mathrm{CN}}^{-}/\mathrm{DCN})}$ of about 13, which is significantly higher than recent experimental findings. This discrepancy is attributed to the neglect of correlation and polarization effects in the scattering calculation performed. We carried out a relaxed–self-consistent field calculation to determine the variation of the resonance parameters under these effects. We observe a shift in the positions of the shape resonance as well as a narrowing of the autoionization widths resulting in an isotope ratio of 3.2 at $T=333$ K; in closer agreement with the measured value.

We present a theoretical approach for the simulation of time-resolved harmonic spectra, including the effect of nuclear dynamics, which is applicable to complex systems involving many nuclear degrees of freedom. The method is based on the combination of our semiclassical field-induced surface hopping approach for the treatment of laser-induced nuclear dynamics with the time-dependent density functional theory for electron dynamics. We apply our method to the simulation of ultrafast nonadiabatic dynamics and time-resolved harmonic spectra in small silver clusters (Ag${}_2$ and Ag${}_8$), which exhibit discrete molecularlike electronic transitions. We demonstrate that the harmonic signal is highly sensitive to the nuclear dynamics and thus can be used as a probe of coupled electron-nuclear dynamics, which is complementary to common pump-probe methods such as time-resolved photoelectron spectroscopy. Our simulations allowed us also to determine the mechanism and the time scale of nonradiative relaxation in the “magic” Ag${}_8$ cluster and have provided a fundamental insight into ultrafast dynamics of metal nanoclusters in the size regime where “each atom counts.” The excited-state dynamics of Ag${}_8$ involves an isomerization process from the initial structure with $T_{\mathrm{d}}$ symmetry to the quadratic antiprism structure with $D_{4\mathrm{d}}$ symmetry which takes place on a time scale of $~$600 fs and is clearly identified in a time-resolved harmonic signal. Our theoretical approach is generally applicable for the prediction of time-resolved harmonic spectra in complex systems with many nuclear degrees freedom and should serve to stimulate new ultrafast experiments utilizing harmonic signals as a probe for nonadiabatic processes in molecular systems.

We investigate high-order-harmonic generation of isotropically distributed gas-phase ${\mathrm{H}}_2$O molecules exposed to an intense laser field. The induced dipole of each individual molecule by the laser field is first calculated using the recently developed quantitative rescattering theory. In a thin medium, harmonic spectra generated coherently from all the molecules are then calculated by solving Maxwell’s equation of propagation. By using accurate transition dipoles of ${\mathrm{H}}_2$O, we show that the harmonics in the lower plateau region are quite different from models that employ the simpler strong-field approximation. We also examine the magnitude and phase of the harmonics and their dependence on laser focusing conditions.

Tunneling ionization of molecules from multiple orbitals produces parent ions in different electronic states. The excited parent ion will relax to its ground state through emitting a photon of light. Therefore, the contributions of different lower-lying orbitals can be separated by measuring the corresponding fluorescence emission. Here we report the observation of ${\mathrm{CO}}_2^{+}(A^2{\Pi }_u\to X^2{\Pi }_g)$ and ${\mathrm{CO}}_2^{+}(B^2{\Sigma }_u\to X^2{\Pi }_g)$ fluorescence emission in the system of neutral CO${}_2$ molecules irradiated by intense femtosecond laser pulses. These observations provide direct evidence that multiple molecular orbitals are simultaneously involved in the process of tunneling ionization. Meanwhile, fluorescence spectroscopy is also demonstrated to be a feasible approach to selectively probe lower-lying orbitals involved in the tunneling ionization of molecules.

Photofragmentation of tetrahydrofuran molecules in the vacuum-ultraviolet region, producing excited atomic and molecular fragments, has been studied over the energy range 14–68 eV using photon-induced fluorescence spectroscopy. Excited hydrogen atoms H($n$), $n$ $=$ 3–11, have been detected by observation of the ${\mathrm{H}}_{\alpha }$ to ${\mathrm{H}}_{ı}$ lines of the Balmer series. The diatomic CH($A^2\Delta$), CH($B^2{\Sigma }^{-}$) and ${\mathrm{C}}_2(d^3{\Pi }_g)$ fragments, which are excited to low vibrational and high rotational levels are identified by their $A^2\Delta \to X^2{\Pi }_r$, $B^2{\Sigma }^{-}\to X^2{\Pi }_r$ and $d^3{\Pi }_g\to a^3{\Pi }_u$ emission bands, respectively. Dissociation efficiency curves for CH$(A^2\Delta )$ and H($n$), $n$ $=$ 3–7, have been obtained in the photon energy ranges from their appearance thresholds up to 68 eV. The appearance energies for CH$(A^2\Delta )$ and H($n$), $n$ $=$ 3–7, have been determined and are compared with estimated fragmentation energy limits in order to discuss the possible fragmentation processes. In the present studies, superexcited states of tetrahydrofuran are found, which dissociate into the above excited atomic and molecular fragments.

We study condensate statistics and thermodynamics of weakly interacting Bose gas with a fixed total number $N$ of particles in a cubic box. We find the exact recursion relation for the canonical ensemble partition function. Using this relation, we calculate the distribution function of condensate particles for $N=200$. We also calculate the distribution function based on multinomial expansion of the characteristic function. Similar to the ideal gas, both approaches give exact statistical moments for all temperatures in the framework of Bogoliubov model. We compare them with the results of unconstraint canonical ensemble quasiparticle formalism and the hybrid master equation approach. The present recursion relation can be used for any external potential and boundary conditions. We investigate the temperature dependence of the first few statistical moments of condensate fluctuations as well as thermodynamic potentials and heat capacity analytically and numerically in the whole temperature range.

The Monte Carlo method within the so-called classical field approximation is applied to one-dimensional, weakly interacting, repulsive Bose gas trapped in a harmonic potential. Equilibrium statistical properties of the condensate are calculated within a canonical ensemble. We also calculate experimentally relevant, low-order correlation functions of the whole gas.