We propose experimental schemes to create and probe minimum forms of different topologically ordered states in a plaquette of an optical lattice: resonating valence bond, and Laughlin and string-net-condensed states. We show how to create anyonic excitations on top of these liquids and detect their fractional statistics. In addition, we propose a way to design a plaquette ring-exchange interaction, the building block Hamiltonian of a lattice topological theory. Our preparation and detection schemes combine different techniques already demonstrated in experiments with atoms in optical superlattices.

We show that one can cool a micromechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (self-cooling). From a theory based on Heisenberg-Langevin equations we find that optimal self-cooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations, thus reducing the mirror temperature by several orders of magnitude. We also present dynamical calculations which show how to access the mirror temperature from a homodyne measurement of the fluctuations of the reflected field.

A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite commutation relations between even and odd operators. The final FW Hamiltonian can be expanded into a power series in the Planck constant which characterizes the order of magnitude of quantum corrections. Exact expressions for low-order terms in the Planck constant can be derived. Finding these expressions allows one to perform a simple transition to the semiclassical approximation which defines a classical limit of the relativistic quantum mechanics. As an example, interactions of spin-1/2 and scalar particles with a strong electromagnetic field have been considered. Quantum and semiclassical equations of motion of particles and their spins have been deduced. Full agreement between quantum and classical theories has been established.

We consider the decay of quantum entanglement quantified by the concurrence of a pair of two-level systems, each of which is interacting with a reservoir at finite temperature $T$. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time, i.e., “entanglement sudden death” occurs. This class includes all states which previously had been found to have long-lived entanglement in zero-temperature reservoirs. Our general result is illustrated by an example.

Small anharmonicity, created along the axial direction of the trap, allows controlling the motional states of ions adiabatically using electric fields. In this paper several important aspects of this control scheme are explored theoretically. The pulses for various state transformations, including universal quantum gates, are derived using the optimal control theory. They exhibit simple shapes and other favorable properties, which indicate a promising route for practical implementation.

We consider a model of two driven and collectively damped atoms with different quantum feedbacks. We find that the steady entanglement depends on the initial condition in the case of symmetric feedback but is independent of the initial condition in the case of nonsymmetric feedback. We also find that in the process of the transition from the symmetric feedback to the nonsymmetric feedback, the entanglement between the two atoms is discontinuous. Without the feedback (symmetric case), in the symmetric subspace the steady entanglement between the two atoms will be very small; then we apply a feedback just to one of the atoms (nonsymmetric case), the steady entanglement will increase greatly, which can reach $C\approx 0.82$. It is very interesting that if we withdraw the feedback, the strong steady entanglement will remain, i.e., the whole process is irreversible, and reminds us of the hysteresis phenomena.

It was shown by J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz [Phys. Rev. Lett. 49, 1691 (1982)]; J. P. Perdew and M. Levy [Phys. Rev. Lett. 51, 1884 (1983)]; and L. J. Sham and M. Schlüter [Phys. Rev. Lett. 51, 1888 (1983)] that the exact Kohn-Sham exchange-correlation potential $v_{\text{xc}}\left(\vec{r}\right)$ of an open system may jump discontinuously as the particle number crosses an integer, with important physical consequences. The original derivations of the size and nature of the discontinuity rely on an implicit assumption that, when $N\to J$ from above and below, the effective potential of the interacting system with particle number $N$ becomes identical (modulo a constant) to the effective potential at an integer particle number $J$ so that the Kohn-Sham orbitals change continuously as $N$ passes through $J$ at fixed external potential. We prove under mild assumptions that the noninteracting kinetic energy of the interacting system is a continuous function of the particle number (as is the density itself), and hence argue that the original assumption is likely correct; if so, then all energy components are continuous. A rigorous proof of the existence and size of the $v_{\text{xc}}$ discontinuity is presented in the special case where the particle number crosses 1, by showing that, even when the Levy-Lieb constrained search for a minimum kinetic energy expectation value is taken to go over ensembles instead of wave functions, the noninteracting kinetic energy is still given by the von Weizsäcker functional for all densities with real particle number $N$ between 0 and 2 inclusive. We also prove that the von Weizsäcker functional is a lower bound on the ensemble-search noninteracting kinetic energy for all real $N>2$. To illustrate the $v_{\text{xc}}$ discontinuity and related results, we construct an analytic model density for the ${\text{H}}^{-}$ ion and plot the exchange-correlation potential as the particle number approaches 1 from above and below, and 2 from below. Finally, we discuss the behavior of the free-electron continuum as the particle number crosses an integer and the case where the particle number of a hydrogen or helium atom crosses $J=2$, the maximum number of electrons they can bind.

Differential (DCS), integral $\left(Q_{\mathrm{I}}\right)$, momentum transfer $\left(Q_{\mathrm{M}}\right)$, and viscosity $\left(Q_{\mathrm{V}}\right)$ cross sections are obtained both experimentally and theoretically for elastic electron scattering by lead atoms in the energy range from $10\text{to}100\mathrm{eV}$. The experiment is performed using an electron spectrometer with crossed electron and atom-beam arrangement. The relative DCS measurements are placed on an absolute scale using measured elastic-to-inelastic intensity ratios and the absolute DCS of the $6p7s$ ${}^{3}P_1$ state [S. Milisavljević, M. S. Rabasović, D. Šević, V. Pejčev, D. M. Filipović, L. Sharma, R. Srivastava, A. D. Stauffer, and B. P. Marinković, Phys. Rev. A 76, 022714 (2007)] at a scattering angle of 10° for incident energies of 40, 60, 80, and $100\mathrm{eV}$ and at 30° for 10 and $20\mathrm{eV}$. Corresponding theoretical results are obtained from a relativistic approach based on solving the Dirac equation using Hartree-Fock and Dirac-Fock wave functions to calculate cross sections at all the energies measured. Comparisons between the present experiment and theory, as well as comparisons with other available results, have been made.

We present a closed-form expression for the infinity of high-order partial waves and symmetry classes required to converge differential cross sections for vibrationally elastic or inelastic electron scattering from a linear molecule. This expression combines correction terms based on the first Born approximation with terms that contain $T$-matrix elements from accurate, non-Born scattering calculations such as those of body-frame fixed-nuclear-orientation theory. The equations for analytic Born completion reduce the convergence requirements for a differential cross section from several potentially infinite sums over angular-momentum quantum numbers to a single parameter that determines the partial-wave order at which the switch to the Born approximation occurs. We demonstrate the efficacy and accuracy of these equations for low-energy collisions of electrons with ${\text{H}}_2$ and ${\text{N}}_2$.

A parallelized three-dimensional Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for molecules with a single electron, assuming the motion of the nucleus is frozen, is presented in this paper. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternate times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using the domain decomposition method on distributed memory machines by applying a multilevel graph-partitioning technique. The solver is validated using a $\mathrm{H}_2{}^{+}$ molecule system, both by observing the total electron probability and total energy conservation without laser interaction, and by comparing the ionization rates with previous two-dimensional axisymmetric simulation results with an aligned incident laser pulse. The parallel efficiency of this TDSE solver is presented and discussed; the parallel efficiency can be as high as 75% using 128 processors. Finally, examples of the temporal evolution of the probability distribution of laser incidence onto a $\mathrm{H}_2{}^{+}$ molecule at inter-nuclear distance of $9\mathrm{a.u.}$ ($\chi =0°$ and 90°) and the spectral intensities of harmonic generation at internuclear distance of $2\mathrm{a.u.}$ ($\chi =0°$, 30°, 60°, and 90°) are presented to demonstrate the powerful capability of the current TDSE solver. Future possible extensions of the present method are also outlined at the end of this paper.

The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.

We study the coherent control of microwave photons propagating in a superconducting waveguide consisting of coupled transmission line resonators, each of which is connected to a tunable charge qubit. While these coupled line resonators form an artificial photonic crystal with an engineered photonic band structure, the charge qubits collectively behave as spin waves in the low excitation limit, which modify the band-gap structure to slow and stop the microwave propagation. The conceptual exploration here suggests an electromagnetically controlled quantum device based on the on-chip circuit QED for the coherent manipulation of photons, such as the dynamic creation of laserlike output from the waveguide by pumping the artificial atoms for population inversion.

We measured the ensemble-averaged spectral correlation functions and statistical distributions of spectral spacing and intensity for lasing modes in weakly scattering systems, and compared them to those of the amplified spontaneous-emission spikes. Their dramatic differences illustrate distinct physical mechanisms. Our numerical simulation revealed that even without reabsorption the number of potential lasing modes might be greatly reduced by local excitation of a weakly scattering system. The lasing modes can be drastically different from the quasimodes of the passive system, due to selective amplification of the feedback from the scatterers within the local gain region.

We demonstrate an all-optical switch that operates at ultra-low-light levels and exhibits several features necessary for use in optical switching networks. An input switching beam, wavelength $\lambda$, with an energy density of ${10}^{-2}$ photons per optical cross section $[\sigma ={\lambda }^2∕\left(2\pi \right)]$ changes the orientation of a two-spot pattern generated via parametric instability in warm rubidium vapor. The instability is induced with less than $1\mathrm{mW}$ of total pump power and generates several $\mu \mathrm{Ws}$ of output light. The switch is cascadable: the device output is capable of driving multiple inputs, and exhibits transistor-like signal-level restoration with both saturated and intermediate response regimes. Additionally, the system requires an input power proportional to the inverse of the response time, which suggests thermal dissipation does not necessarily limit the practicality of optical logic devices.

We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and linewidth (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index $n$ and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes $N$. The Petermann factor in the linewidth of the longest-living resonance also decreases for increasing $n$ and scales as $\sqrt{N}$, but is less sensitive to polarization. For resonances of intermediate lifetime, the Petermann factor scales linearly with $N$. These qualitative parametric dependencies are consistent with the random-matrix theory of resonators with small openings. However, for a small refractive index where the resonators are very open, the details of the statistics become nonuniversal. This is demonstrated by comparison with a particular dynamical model.

In this paper, we introduce a transformation operator expression to give a criterion for faithful teleportation of an arbitrary two-qubit state via a four-qubit entangled state. The general relation between the transformation operator and the SLOCC invariant of quantum channel is obtained and its applicability is illuminated by some known examples for the measurement in the Bell basis.

One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps, $\Delta ⪡J$. The critical point is found to be ${\left(J/U\right)}_c=0.05974\left(3\right)$, in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.

By using the variational approach, we find that two mutually incoherent beams with different widths and wavelengths can form a Manakov vector soliton due to nonlocal nonlinearity. For such solitons to exist, the total incident power must be equal to a critical value and the ratio of the square of the beamwidths must be inversely proportional to the ratio of the wave numbers. The periodic oscillations of such vector solitons are also studied extensively when the incident power does not satisfy the necessary condition for stability.

We present a remarkably accurate method for determining the wave field of an x-ray nanobeam. The intensity profile of a beam was directly measured over a range of three orders of magnitude while its phase distribution was successfully recovered using an iterative algorithm. The evolution of the wave field along the beam propagation direction was precisely simulated, and there was good agreement with the experimental results.

We show the possibility of generating gain-assisted superluminal optical solitons in a room-temperature three-state active Raman gain medium. We demonstrate both analytically and numerically that under appropriate conditions a signal field of very low intensity can evolve into a stable shape-preserving wave form that propagates with superluminal velocity. Shape recovery of superluminal solitons after collision is also demonstrated numerically.