We present a simple renormalization-group method of investigating ground-state properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large systems. It is conceptually simple and easy to implement, and allows investigation of properties unavailable through mean-field approximations, such as one- and two-particle reduced density matrices of the ground state. As an example, we model a weakly interacting one-dimensional Bose gas in a harmonic trap. Compared to the mean-field Gross-Pitaevskii approximation, our method provides a more accurate description of the ground-state one-particle density matrix. We have also obtained the Hall-Post lower bounds for the ground-state energy of the gas. All results have been obtained by straightforward numerical diagonalization of the Hamiltonian matrix.

We propose two experiments on the measurement of the Casimir force acting between a gold coated sphere and semiconductor plates with markedly different charge carrier densities. In the first of these experiments a patterned Si plate is used which consists of two sections of different dopant densities and oscillates in the horizontal direction below a sphere. The measurement scheme in this experiment is differential, i.e., it allows the direct high-precision measurement of the difference of the Casimir forces between the sphere and sections of the patterned plate or the difference of the equivalent pressures between Au and patterned parallel plates with static and dynamic techniques, respectively. The second experiment proposes to measure the Casimir force between the same sphere and a $\mathrm{V}{\mathrm{O}}_2$ film which undergoes the insulator-metal phase transition with the increase of temperature. We report the present status of the interferometer based variable temperature apparatus developed to perform both experiments and present the first results on the calibration and sensitivity. The magnitudes of the Casimir forces and pressures in the experimental configurations are calculated using different theoretical approaches to the description of optical and conductivity properties of semiconductors at low frequencies proposed in the literature. It is shown that the suggested experiments will aid in the resolution of theoretical problems arising in the application of the Lifshitz theory at nonzero temperature to real materials. They will also open new opportunities in nanotechnology.

A photon-number-resolving detector with single-photon resolution is described and demonstrated. It has $10\mathrm{bits}$ of resolution, does not require cryogenic cooling, and is sensitive to near ir wavelengths. This performance is achieved by flood illuminating a $32\times 32$ element ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{AsP}$ Geiger-mode avalanche photodiode array that has an integrated counter and digital readout circuit behind each pixel.

Quantum computers based on pulsed microwave operations are inherently sensitive to the pulse amplitude and detuning between the quantum bit and the microwave frequency. Designing techniques that can compensate both errors simultaneously have been challenging. Here we present a technique that achieves this goal by extending known numerical optimization schemes to obtain amplitude modulated microwave pulses robust against a large detuning range, and combining them with composite pulse techniques that are insensitive to amplitude errors.

The scalability of solid-state quantum computation relies on the ability of connecting the qubits to the macroscopic world. Quantum chains can be used as quantum wires to keep regions of external control at a distance. However, even in the absence of external noise their transfer fidelity is too low to assure reliable connections. We propose a method of optimizing the fidelity by minimal usage of the available resources, consisting of applying a suitable sequence of two-qubit gates at the end of the chain. Our scheme also allows the preparation of states in the first excitation sector as well as cooling.

We analyze a recent protocol for the transmission of quantum states via a dual spin chain [Burgarth and Bose, Phys. Rev. A 71, 052315 (2005)] under the constraint that the receiver’s measurement strength is finite. That is, we consider the channel where the ideal, instantaneous, and complete von Neumann measurements are replaced with a more realistic continuous measurement. We show that for optimal performance the measurement strength must be “tuned” to the channel spin-spin coupling, and once this is done, one is able to achieve a similar transmission rate to that obtained with ideal measurements. The spin chain protocol thus remains effective under measurement constraints.

The Breit-Pauli $R$-matrix method with 31 fine-structure levels is used to calculate elastic- and inelastic-scattering amplitudes between magnetic sublevels for He-like Cu ions by electron impact for x-ray polarization spectroscopy of ultrahigh-intensity laser-produced plasma. The collision strengths for inelastic scattering that produce aligned states are obtained for transitions from the ground state to the fine-structure levels of all the excited states of the $1s2l$ $(l=0,1)$ and $1s3l$ $(l=0,1,2)$ configurations. The collision strengths for elastic scattering that destroy the alignment of excited states are also obtained for transitions between magnetic sublevels of the $1s2p{}^{1}P_1$ states. The collision strengths including resonance structures are used for population alignment analysis. We find that resonances in the elastic scattering are significant for representing the relaxation effects of the alignment of excited states for the population alignment analysis.

A proof-of-principle electron electric-dipole-moment $\left(e\text{−}\mathrm{EDM}\right)$ experiment using slow cesium atoms, nulled magnetic fields, and electric-field quantization has been performed. With the ambient magnetic fields seen by the atoms reduced to less than $200\mathrm{pT}$, an electric field of $6\mathrm{MV}∕\mathrm{m}$ lifts the degeneracy between states of unequal $\mid m_F\mid$ and, along with the low $(\approx 3\mathrm{m}∕\mathrm{s})$ velocity, suppresses the systematic effect from the motional magnetic field. The low velocity and small residual magnetic field have made it possible to induce transitions between states and to perform state preparation, analysis, and detection in regions free of applied static magnetic and electric fields. This experiment demonstrates techniques that may be used to improve the $e\text{−}\mathrm{EDM}$ limit by two orders of magnitude, but it is not in itself a sensitive $e\text{−}\mathrm{EDM}$ search, mostly due to limitations of the laser system.

In this paper, we study the laser-pulse control of vibrational excitation for small molecules by employing an algebraic model. The analytical expression for the vibrational transition probability is obtained by using an algebraic approach. Selective vibrational excitation of diatomic and linear triatomic molecules are achieved. The influence of laser pulse frequencies and shapes on the control are studied.

We present experimental results in which single ${\mathrm{Ca}}^{+}$ ions in a chain of laser cooled ${\mathrm{Ca}}^{+}$ ions are further ionized by means of an intense short pulse laser. The ions are trapped in a linear Paul trap, which is instantaneously loaded by ions from a laser-produced ablation plasma. Due to sympathetic cooling the doubly charged ions are held in place. We study and characterize linear few-ion crystals with mixed charges by applying a radio frequency field, which excites the center of mass (c.m.) and breathing modes of different configurations. From the position shift of laser cooled ions initiated through the higher charge state we can deduce the charge of the nonfluorescing ion. This information might be used as an intensity probe for high intensity lasers.

We consider a two-dimensional (2D) nonlinear Schrödinger equation with self-focusing nonlinearity and a quasi-1D double-channel potential, i.e., a straightforward 2D extension of the well-known double-well potential. The model may be realized in terms of nonlinear optics and Bose-Einstein condensates. The variational approximation (VA) predicts a bifurcation breaking the symmetry of 2D solitons trapped in the double channel, the bifurcation being of the subcritical type. The predictions of the VA are confirmed by numerical simulations. The work presents an original example of the spontaneous symmetry breaking of 2D solitons in dual-core systems.

Recent experiments on strongly interacting bosons in optical lattices have revealed the coexistence of spatially separated Mott-insulating and number-fluctuating phases. We explore the condensate properties of the number fluctuating phase trapped between the Mott-insulating regions and derive the associated collective-mode structure. We discuss the crossover of the interlayer properties between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition from the normal to superfluid state.

We investigate the quantum dynamics of Raman-coupled Bose-Einstein condensates driven by laser beams that carry orbital angular momentum. By adiabatically eliminating the excited atomic state we obtain an effective two-state Hamiltonian for the coupled condensates, and quantization of the matter-wave fields results in collapse and revivals in the quantum dynamics. We show that the revival period depends on whether the initial nonrotating condensate displays broken $\mathrm{U}\left(1\right)$ symmetry or not, and that the difference may be detected by measuring the motion of quantized vortices that are nested in the density profile of the Raman-coupled condensates. We further study the steady-state population transfer using a linear sweep of the two-photon detuning, by which the atomic population is coherently transferred from an initial nonrotating state to the final vortex state.

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Lévy) distributed fluctuations depending on external control parameters. In the Lévy regime, the output pulse is highly irregular leading to huge deviations from a mean-field description. Monte Carlo simulations of a simplified model which includes the population of the medium demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.

We propose a simple unconventional geometric scenario to achieve a kind of nontrivial multiqubit operation with superconducting charge qubits placed in a microwave cavity. The proposed quantum operations are insensitive not only to the thermal state of the cavity mode but also to certain random operation errors, and thus may lead to high-fidelity quantum-information processing. By executing the designated quantum operations, a class of highly entangled cluster states may be generated efficiently in the present scalable solid-state system, enabling one to achieve one-way quantum computation.

Operator quantum error correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error correction, and provides a unified framework for topics such as quantum error correction, decoherence-free subspaces, and noiseless subsystems. This paper develops (a) easily applied algebraic and information-theoretic conditions that characterize when operator quantum error correction is feasible; (b) a representation theorem for a class of noise processes that can be corrected using operator quantum error correction; and (c) generalizations of the coherent information and quantum data processing inequality to the setting of operator quantum error correction.

We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the $\mathrm{H}+{\mathrm{D}}_2$ chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.

We discuss the equations for the bound one-active electron states based on analytic solutions of the Schrödinger and Pauli equations for a uniform magnetic field and a single attractive $\delta \left(\mathbf{r}\right)$ potential. It is very important that the electron ground states in a magnetic field differ essentially from the analogous state of spin-0 particles, whose binding energy was intensively studied more than forty years ago. We show that the binding-energy equations for spin-$1∕2$ particles can be obtained without using the language of boundary conditions in the $\delta$-potential model developed in the pioneering works. We use the obtained equations to calculate the energy level displacements analytically and to demonstrate nonlinear dependences on the field intensity. We show that the magnetic field indeed plays a stabilizing role in the considered systems in the case of weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions.