Traditional two-photon excitation suffers from two difficulties that prevent complete population transfer: dynamic Stark shifts and multiphoton ionization. We describe a technique for overcoming these limitations by using a second field to control dynamic Stark shifts via Stark-chirped rapid adiabatic passage (SCRAP) and simultaneously suppress undesired photoionization via laser-induced continuum structure (LICS). We illustrate this proposed procedure by numerical simulations of two-photon excitation of the metastable $2s$ state of hydrogen, showing that efficient excitation can be expected when the two laser pulses are properly crafted.

We discuss an approach to the problem of creating a photon-number-resolving detector using the giant Kerr nonlinearities available in electromagnetically induced transparency. Our scheme can implement a photon-number quantum-nondemolition measurement with high efficiency $(\sim 99\%)$ using fewer than 1600 atoms embedded in a dielectric waveguide.

An event-ready (or deterministic) source of entangled states is of interest in the practical implementation of schemes of quantum computation and cryptography as well as in the experiments aimed to elucidate the foundations of quantum mechanics. I study the phase matching geometry and detection conditions for the process of three-photon frequency down-conversion, which is a possible source of that kind. It is apparently free of some limitations of the schemes based on two-photon frequency down-conversion. The goal of the proposed setup is not the generation of an entangled state of three photons (in a GHZ-state sense), but of an entangled state of two photons with a “trigger” signal. As an example, I estimate the values of the trios’ flux and trigger’s reliability for the particular case of crystal calcite illuminated by the fourth harmonic of a $\mathrm{Nd}:\mathrm{YAG}$ mode-locked laser.

We consider generic $(m\times n)$-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as $(m+n)$-mode Gaussian states invariant under local mode permutations on the $m$-mode and $n$-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n-2$ uncorrelated single-mode states. The entanglement between the $m$-mode and the $n$-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of $(m+n)$-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.

We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for Greenberger-Horne-Zeilinger (GHZ) -type superposition states decreases with the size of the system, while for a class of other states—namely, all graph states with constant degree—the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles to independent environments, described by some quantum optical master equation of Lindblad form. For GHZ states, we derive analytic expressions for the lifetime of distillable entanglement and determine when the state becomes fully separable. For all graph states, we derive lower and upper bounds on the lifetime of entanglement. The lower bound is based on a specific distillation protocol, while upper bounds are obtained by showing that states resulting from decoherence in general become nondistillable or even separable after a finite time. This is done using different methods, namely, (i) the map describing the decoherence process (e.g., the action of a thermal bath on the system) becomes entanglement breaking, (ii) the resulting state becomes separable, and (iii) the partial transposition with respect to certain partitions becomes positive. To this aim, we establish a method to calculate the spectrum of the partial transposition for all mixed states which are diagonal in a graph-state basis. We also consider entanglement between different groups of particles and determine the corresponding lifetimes as well as the change of the kind of entanglement with time. This enables us to investigate the behavior of entanglement under rescaling and in the limit of large number of particles $N\to \mathrm{\infty }$. Finally we investigate the lifetime of encoded quantum superposition states and show that one can define an effective time in the encoded system which can be orders of magnitude smaller than the physical time. This provides an alternative view on quantum error correction and examples of states whose lifetime of entanglement (between groups of particles) in fact increases with the size of the system.

As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this paper we explore the extension of this approach to nonuniform systems, and we discuss its potential for density functional theory. For the spherically- and system-averaged pair density of two-electron atoms we obtain very accurate short-range properties, including, for nuclear charge $Z⩾2$, “on-top” values (zero electron-electron distance) essentially indistinguishable from those coming from precise variational wave functions. By means of a nonlinear adiabatic connection that separates long- and short-range effects, we also obtain Kohn-Sham correlation energies whose error is less than $4\mathrm{mhartree}$, again for $Z⩾2$, and short-range-only correlation energies whose accuracy is one order of magnitude better.

A closed-form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one interparticle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result is suited for high-precision calculations of relativistic effects in lithium and light lithiumlike ions.

A relatively uncomplicated mathematical prescription based on the theory of ordinary differential equations together with certain properties of higher transcendental functions is used to obtain a useful analytical expression for the $s$-wave Coulomb off-shell Jost solution.

We have developed a potential-energy surface for spin-polarized $\mathrm{K}\left({}^{2}S\right)+{\mathrm{K}}_2\left({}^3\Sigma _u^{+}\right)$ collisions and carried out quantum dynamical calculations of vibrational quenching at low and ultralow collision energies for both bosons ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$ and fermions ${}^{40}\mathrm{K}$. At collision energies above about $0.1\mathrm{mK}$ the quenching rates are well described by a classical Langevin model, but at lower energies a fully quantal treatment is essential. We find that for the low initial vibrational state considered here $(v=1)$, the ultracold quenching rates are not substantially suppressed for fermionic atoms. For both bosons and fermions, vibrational quenching is much faster than elastic scattering in the ultralow-temperature regime. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.

We compute the dipole polarizability for ${\mathrm{Si}}_n$ clusters across the prolate to compact shape transition region, $n=20–28$, and also for a prolate and compact isomer at $n=50$. We find a clear shape dependence in the calculated values, with prolate structures having systematically larger polarizabilities, and very different trends in per atom polarizabilities with cluster size. The shape dependence is not due to highest unoccupied molecular orbital (HOMO)-lowest unoccupied molecular orbital gap differences or to differences in the binding of the HOMO electron. Instead, charge density analyses show a metalliclike response of the clusters to an external field. In addition, the size trends for the calculated polarizabilities for the compact and prolate clusters are reproduced by the predictions of jellium models for spheres and cylinders, respectively, further suggesting that these small clusters exhibit metallic character.

We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime. This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wavelength. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.

We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to two can be transformed into an orthogonal state using only linear optics. According to a recently suggested definition of polarization degree, this implies that all such states are fully polarized. This is also found to be true for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2) orbit. Complete two- and three-photon bases whose basis states are related by only phase shifts or geometrical rotations are also derived.

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement between the coin and the position degrees of freedom from the algorithm, and the results match those obtained with a quantum coin toss instruction.

Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a realistic multilevel atomic transition. Based on the concept of an effective Hamiltonian and on the Heisenberg formalism, we discuss the coupled dynamics of the quantum fluctuations of the polarization Stokes components of propagating light and of the collective spin fluctuations of the scattering atoms. We show that in the process of coherent forward scattering, this dynamics can be described in terms of a polariton-type spin wave created in the atomic sample. Our work presents a general example of an entangling process in the system of collective quantum states of light and atomic angular momenta, previously considered only for the case of spin-$\frac{1}{2}$ atoms. We use the developed general formalism to test the applicability of the spin-$\frac{1}{2}$ approximation for modeling the quantum nondemolishing measurement of atoms with a higher angular momentum.

We demonstrate that $V^{N-M}$ approximation is a good starting point for the configuration interaction calculations for many-electron atoms and ions. $N$ is the total number of electrons in the neutral atom, $M$ is the number of valence electrons. $V^{N-M}$ is the self-consistent Hartree-Fock potential for a closed-shell ion with all valence electrons removed. Using of the $V^{N-M}$ approximation considerably simplifies the many-body perturbation theory for the core-valence correlations. It makes it easier to include higher-order correlations which often significantly improves the accuracy of the calculations. Calculations for krypton and barium and their positive ions are presented for illustration.

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wave packets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wave-function dynamics.

We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground-state concurrence appears in the absence of a quantum phase transition. It is opposed to the popular belief that the nonanalyticity property of ground-state concurrence can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground-state concurrence in general can be more intricate than that of the ground-state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the nonanalyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, cannot reveal quantum phase transitions in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed.

The impact of the operator-valued commutator on the nonclassical properties of continuous polarization variables is discussed. The definition of polarization squeezing is clarified to exclude those squeezed states which do not contain any new physics beyond quadrature squeezing. We present a consistent derivation of the general nonseparability criterion for the continuous variables with the operator-valued commutator and apply it to the polarization variables.

Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid-state nuclear magnetic resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results obtained give us an insight to the quantum control required when simulating quantum systems with NMR techniques. The simulation of other physical systems, with different particle statistics, is also discussed.