A recently developed [Guan et al., Phys. Rev. A 76, 053411 (2007)] general ab initio and nonperturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom is applied to multiphoton ionization of argon atoms. The field-free Hamiltonian and the dipole matrices are generated using a flexible $B$-spline $R$-matrix method, which allows for the use of nonorthogonal sets of one-electron orbitals. The solution of the TDSE is propagated in time using the Arnoldi-Lanczos method. The effects of the pulse length and the laser intensity on the ionization rate for different photon energies are analyzed. In the long-pulse regime, good agreement with predictions from $R$-matrix Floquet calculations is achieved.

We present detailed measurements of the frequency and damping of three different collective modes in an ultracold trapped Fermi gas of ${}^6\mathrm{Li}$ atoms with resonantly tuned interactions. The measurements are carried out over a wide range of temperatures. We focus on the unitarity limit, where the scattering length is much greater than all other relevant length scales. The results are compared to theoretical calculations that take into account Pauli blocking and pair correlations in the normal state above the critical temperature for superfluidity. We show that these two effects nearly compensate each other and the behavior of the gas is close to that of a classical gas.

In a numerical experiment based on Gross-Pitaevskii formalism, we demonstrate unique topological quantum coherence in optically trapped Bose-Einstein condensates (BECs). Exploring the fact that vortices in a rotating BEC can be pinned by a geometric arrangement of laser beams, we show the parameter range in which vortex-antivortex molecules or multiquantum vortices are formed as a consequence of the optically imposed symmetry. Being low-energy states, we discuss the conditions for spontaneous nucleation of these unique molecules and their direct experimental observation, and provoke the potential use of the phase print of an antivortex or a multiquantum vortex when realized in unconventional circumstances.

The kinetics of the phase separation transition in boson-fermion cold-atom mixtures is investigated. We identify the parameters at which the transition is governed by a quantum nucleation mechanism, responsible for the formation of critical nuclei of a stable phase. We demonstrate that for low fermion-boson mass ratio the density dependence of the quantum nucleation transition rate is experimentally observable. The crossover to the macroscopic quantum tunneling regime is analyzed. Based on a microscopic description of interacting cold-atom boson-fermion mixtures, we derive an effective action for the critical droplet and obtain an asymptotic expression for the nucleation rate in the vicinity of the phase transition and near the spinodal instability of the mixed phase. We show that dissipation due to excitations in the fermion subsystem play a dominant role close to the transition point.

This paper presents observations and an interpretation of laser-induced excitation and fluorescence in a ladder $g\text{−}e\text{−}f$ of three molecular levels [$X{}^1\Sigma _g^{+}(v^{″}=0,J^{″}=7)$, $A{}^1\Sigma _u^{+}(v^{\prime }=10,J^{\prime }=8)$, and $5{}^1\Sigma _g^{+}(v=10,J=9)$, respectively] observed in a supersonic molecular beam of ${\mathrm{Na}}_2$. The $g\text{−}e$ coupling, by cw laser $P$, is strong. A weak cw laser $S$ couples levels $e$ and $f$. The basic observations are of level-$f$ fluorescence as a function of the detuning of the $S$ laser from resonance. The signal profile does not appear as the typical Autler-Townes doublet, but as a spectral structure, whose position, width, and shape depend upon several laser parameters. We interpret these results using a simple model of three nondegenerate quantum states coherently excited while undergoing population loss to states outside the three-level system. We invoke the mechanism of optical pumping and evolution along adiabatic states, together with Landau-Zener transition probabilities. We also present results from numerical studies, which include all quantum states, all radiative couplings, coherent and incoherent, as well as convolutions with the relevant distribution functions (velocities and Zeeman sublevels). Although no adjustable parameters are involved, excellent agreement with the experiment is found. Since successive avoided crossings of adiabatic eigenvalues occur, interference effects may be relevant. Such effects are not expected to be visible in the present experiment, for reasons that are discussed. However, we discuss conditions which would allow resolving the interference structure experimentally. We also suggest possible interesting applications of the interference to rapidly switch off Rydberg state population or to control its spatial distribution.

We study numerically the dynamics of the Rabi Hamiltonian, which describes the interaction of a single cavity mode and a two-level atom without the rotating wave approximation. We analyze this system subjected to damping and dephasing reservoirs, included via the usual Lindblad superoperators in the master equation. We show that the combination of the antirotating term and the atomic dephasing leads to linear asymptotic photon generation from the vacuum. We reveal the origins of the phenomenon and estimate its importance in realistic situations.

We study the coherent scattering process of a single photon confined in an one-dimensional (1D) coupled cavity-array, where a $\Lambda$-type three-level atom is placed inside one of the cavities in the array and behaves as a functional quantum node (FQN). We show that, through the electromagnetically-induced-transparency mechanism, the $\Lambda$-type FQN bears complete control over the reflection and transmission of the incident photon along the cavity array. We also demonstrate the emergence of a quasibound state of the single photon inside a secondary cavity constructed by two distant FQN’s as two end mirrors, from which we are motivated to design an all-optical single photon storage device of quantum coherence.

Self-similar propagation of optical beams inside a one-dimensional nonlinear graded-index waveguide amplifier is studied. By employing the lens-type and Husimi transformations, movable exact quasisoliton similaritons are obtained. Under certain conditions, these similaritons are well described by bright, Gaussian, and dark solitons on a compact parabolic background. Approximate but highly accurate analytical methods are developed to describe the interaction dynamics of exact quasisoliton similaritons.

We consider the effect of induced transparency in an ensemble of $\Lambda$ atoms controlled by high-power radiation. We study the case of an optically dense medium where nonlinear interaction between probe radiation and a Stokes satellite of the drive wave is important. It is shown that the probe radiation and the Stokes satellite form normal biharmonic modes. Each normal mode is characterized by a fixed ratio between the amplitudes of different-frequency partial components and that both partial waves have a common absorption coefficient and a common group velocity. Transparency of an optically dense medium is ensured in the regime of amplification of one of the normal modes. An exact solution (without considering inhomogeneous broadening) is constructed for an arbitrary nonuniform distribution of $\Lambda$ atoms along the probe radiation path and uniform drive-wave intensity. A geometric-optical approach is developed for the case of a spatially varied intensity of the drive field. The obtained solution contains both new results and a generalization of the results of the previous papers.

The fragmentation dynamics of $\mathrm{C}{\mathrm{O}}_2$ molecules subsequent to $K$-shell photoexcitation and ionization was studied using a multicoincidence ion momentum imaging technique. The detailed analysis via fragment momentum correlation plots (Newton diagrams) clearly reveals concurrent fragmentation mechanisms for the three-body dissociation of $\mathrm{C}\mathrm{O}_2{}^{2+}$ into ${\mathrm{C}}^{+}+{\mathrm{O}}^{+}+\mathrm{O}$, for both linear and bent geometry states of $\mathrm{C}\mathrm{O}_2{}^{2+}$. The experimental results are supported by a classical trajectory simulation based on a Coulomb explosion model, which elucidates energy and angular correlations between fragments for different fragmentation processes.

When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-$1∕2$ particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace that grows quadratically with the number of spins. We also derive explicit formulas for expressing arbitrary, identical, local decoherence in terms of these states. We then investigate the open system dynamics of experimentally relevant nonclassical collective atomic states, including superposition and spin squeezed states, subject to various symmetric but local decoherence models.

The contribution of quantum electromagnetic field fluctuations to the free energy of a system of mesoscopic bodies determines Casimir forces between such bodies. Casimir forces are conventionally computed to one-photon-loop order in quantum electrodynamic theory. An instability in the Casimir free energy may be the signature for the onset of a phase transition from an unstable phase to a stable phase. The full computation of the stable phase will then involve higher-order photon loops. These observations are applied to the case of ferroelectric phase transitions.

We present an analysis of squeezed single photon states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent state teleportation and entanglement swapping. We include an analysis of the squeezed vacuum as a simpler approximation to small-amplitude cat states. We also investigate the effects of imperfect sources and inefficient detection on the proposed experiments.

We study the entangling power and perfect entangler nature of ${\mathrm{SWAP}}^{1∕m}$ for $m⩾1$ and controlled-unitary (CU) gates. It is shown that ${\mathrm{SWAP}}^{1∕2}$ is the only perfect entangler in the ${\mathrm{SWAP}}^{1∕m}$ family. On the other hand, a subset of CU gates which is locally equivalent to controlled-NOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.

The separability problem is approached from the perspective of ellipsoidal classification. A density operator of dimension $N$ can be represented as a vector in a real vector space of dimension $N^2-1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the minimum volume covering ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite density operator to this ellipsoid. If the vectorized density operator falls inside the ellipsoid, it is regarded as separable, otherwise it will be taken as entangled. Our method is scalable and can be implemented straightforwardly in any desired dimension. Moreover, we show that it allows for detection of bound entangled states.

The form of a local Clifford [LC, also called local Gaussian (LG)] operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which cannot be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.

We have theoretically studied vortex waves of Bose-Einstein condensates in elongated harmonic traps. Our focus is on the axisymmetric varicose waves and helical Kelvin waves of singly quantized vortex lines. Growth and decay dynamics of both types of vortex waves are discussed. We propose a method to experimentally create these vortex waves on demand.

We apply an analytical model for anisotropic, colliding Bose-Einstein condensates in a spontaneous four-wave-mixing geometry to evaluate the second-order correlation function of the field of scattered atoms. Our approach uses quantized scattering modes and the equivalent of a classical, undepleted pump approximation. Results to lowest order in perturbation theory are compared with a recent experiment and with other theoretical approaches.

A set of universal relations between various properties of any few-body or many-body system consisting of fermions with two spin states and a large but finite scattering length have been derived by Shina Tan. We derive generalizations of the Tan relations for a two-channel model for fermions near a Feshbach resonance that includes a molecular state whose detuning energy controls the scattering length. We use quantum field theory methods, including renormalization and the operator product expansion, to derive these relations. They reduce to the Tan relations as the scattering length is made increasingly large.

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-type oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wave function.