We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity with the two sides coupled dispersively. This system is characterized by the cavity-induced nonlinearity; after integrating out the fast degree of freedom of the cavity mode, the potential felt by the condensate depends on the condensate itself. Adopting a discrete-mode approximation for the condensate, we map out the steady configurations of the system. It is found that due to the nonlinearity of the system, the nonlinear levels of the system may fold up in some parameter regimes. That will lead to the breakdown of adiabatic evolution of the system. Analysis of the dynamical stability of the steady states indicates that the same level structure also results in optical bistability.

Quantum fluctuations in time-dependent, harmonically trapped Bose-Einstein condensates are studied within Bogoliubov theory. An eigenmode expansion of the linear field operators permits the diagonalization of the Bogoliubov–de Gennes equation for a stationary condensate. When trap frequency or interaction strength is varied, the inhomogeneity of the background gives rise to off-diagonal coupling terms between different modes. This coupling is negligible for low energies, i.e., in the hydrodynamic regime, and an effective space-time metric can be introduced. The influence of the intermode coupling will be demonstrated in an example, where I calculate the quasiparticle number for a quasi-one-dimensional Bose-Einstein condensate subject to an exponential sweep of interaction strength and trap frequency.

We examine and explain the spatial emission patterns of ultracold excited fermions in highly anisotropic trapping potentials in the presence of a spin-polarized Fermi sea of ground-state atoms. Due to the Pauli principle, the Fermi sea modifies the available phase space for the recoiling atom. This leads to the well-known modification of the atomic decay rate, but also to a spatial modulation in the probability of the emitted photon’s direction. In this work we carry out the first detailed investigation into these spatial anisotropies and show that they are due to an intricate interplay between Fermi energies and degeneracy values of specific energy levels. We identify different regimes and show that the emission can be engineered to become highly directional. As the latter is usually only possible in cavity settings, our results describe an alternative idea for a directional photon source.

We demonstrate a robust fiber-optics-based fluorescence detector, fully integrated on an atom chip, which detects single atoms propagating in a guide with 66% efficiency. We characterize the detector performance and the atom flux by analyzing the photon statistics. Near-perfect photon antibunching proves that single atoms are detected, and allows us to study the second-order intensity correlation function of the fluorescence over three orders of magnitude in atomic density.

We experimentally examine the nonclassical character of a class of non-Gaussian states known as phase-diffused squeezed states. These states may show no squeezing effect at all and therefore provide an interesting example to test nonclassicality criteria. The characteristic function of the Glauber-Sudarshan representation ($P$ function) proves to be a powerful tool to detect nonclassicality. Using this criterion we find that phase-diffused squeezed states are always nonclassical, even if the squeezing effect vanishes. Testing other criteria of nonclassicality based on higher-order squeezing and the positive semidefiniteness of special matrices of normally ordered moments, it is found that these criteria fail to reveal the nonclassicality for some of the prepared phase-diffused squeezed states.

We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes, which correspond, respectively, to deterministic and stochastic master equation dynamics. For the quantum feedback control scheme with continuous nondemolition observations, we exploit the separation theorem of filtering and control aspects for quantum stochastic dynamics to derive a generalized Hamilton-Jacobi-Bellman equation. If the control is restricted to only Hamiltonian terms this is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term. In this work, we consider, in particular, the case when control is restricted only to observation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure state from a mixed state of a quantum two-level system.

Relativistic many-body perturbation theory is applied to studying the properties of singly ionized ytterbium, ${\text{Yb}}^{+}$. Specifically, energies of the $\left[\text{Xe}\right]4f^{14}n{s}_{1/2}$, $\left[\text{Xe}\right]4f^{14}n{p}_j$, and $\left[\text{Xe}\right]4f^{14}n{d}_j$ $\left(n\le 9\right)$ are calculated through third order. Reduced matrix elements, oscillator strengths, and transition rates are determined for electric-dipole transitions including the $6s$, $7s$, $8s$, $6p$, $7p$, $5d$, and $6d$ states. Lifetime values are determined for the $6p$ states. Electric-dipole $\left(6s_{1/2}-n{p}_j,n=6–12\right)$ matrix elements are calculated to obtain the ground-state E1 polarizability. The hyperfine $A$ values are determined for the low-lying levels up to $n=7$ of ${}^{171}\text{Y}\text{b}$ II. The quadratic Stark effect on hyperfine structure levels of ${}^{171}\text{Y}\text{b}$ II ground state is investigated. The calculated shift for the $\left(F=1,M=0\right)\leftrightarrow \left(F=0,M=0\right)$ transition is $-0.1796\text{Hz}/{\left(\text{kV}/\text{cm}\right)}^2$, in agreement with the previous theoretical result $-0.171\pm 0.009$. These calculations provide a theoretical benchmark for comparison with experiment and theory.

We consider resonant dynamics in a dilute atomic gas falling under gravity through a periodically pulsed standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and we show that quantum resonances are highly sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. For particular values of the atomic acceleration, we observe fractional resonances. We investigate the effect of the initial atomic momentum width on the fractional resonances and quantify the sensitivity of fractional resonances to thermal effects.

We analyze the performance of a protocol to prepare an atomic ensemble in a superposition of two macroscopically distinguishable states. The protocol relies on conditional measurements performed on a light field, which interacts with the atoms inside an optical cavity prior to detection, and we investigate cavity enhanced probing with continuous beams of both coherent and squeezed light. The stochastic master equations used in the analysis are expressed in terms of the Hamiltonian of the probed system and the interaction between the probed system and the probe field and are thus quite generally applicable.

Recently Kim et al. [Phys. Rev. A 78, 020101(R) (2008)] performed electrostatic calibrations for a plane plate above a centimeter-size spherical lens at separations down to 20–30 nm and observed “anomalous behavior.” It was found that the gradient of the electrostatic force does not depend on separation as predicted on the basis of a pure Coulomb contribution. Some hypotheses which could potentially explain the deviation from the expected behavior were considered, and qualitative arguments in favor of the influence of patch surface potentials were presented. We demonstrate that for the large lenses at separations of a few tens of nanometers from the plate, the electrostatic force law used by the authors is not applicable due to possible deviations of the mechanically polished and ground lens surface from a perfect spherical shape. A model is proposed which provides a possible explanation for the observed anomalous behavior using the standard Coulomb force.

In a recent Comment, Decca et al. [Phys. Rev. A 79, 026101 (2009)] discussed the origin of the anomalies recently reported by us in Phys. Rev. A 78, 036102(R) (2008). Here we restate our view corroborated by their considerations that quantitative geometrical and electrostatic characterizations of the conducting surfaces (a topic not discussed explicitly in the literature until very recently) are critical for the assessment of precision and accuracy of the demonstration of the Casimir force and for deriving meaningful limits on the existence of Yukawian components possibly superimposed to the Newtonian gravitational interaction.

Quantum control requires full knowledge of the system many-body Hamiltonian. In many cases this information is not directly available due to restricted access to the system. Here we show how to indirectly estimate all the coupling strengths in a spin chain by measuring one spin at the end of the chain. We also discuss the efficiency of this “quantum inverse problem” and give a numerical example.

When a quantum many-body system undergoes a quench, the time-averaged density matrix $\overline{\rho }$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $\overline{\rho }$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to nonperturbative quenches in the nonintegrable Bose-Hubbard model: in finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, show that $\overline{\rho }$ bears a memory of the initial state.

We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast this formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through nonuniform gravitational fields and find that the alternative formulation predicts decorrelation of the optical entanglement under experimentally realistic conditions.

To evaluate the radiative electron capture for the collisions of ${\text{U}}^{89+}$ ion with ${\text{N}}_2$, radiative recombination cross sections and the corresponding emitted photon energies are calculated from the ground state $1s^{2}2s$ to $1s^{2}2sn{l}_j\left(2\le n\le 9,0\le l\le 6\right)$ using the newly developed relativistic radiative recombination program RERR06 based on the multiconfiguration Dirac-Fock method. The x-ray spectra for radiative electron capture in the collision have been obtained by convolving the radiative recombination cross sections and the Compton profile of ${\text{N}}_2$. Good agreement is found between the calculated and experimental spectra. In addition, the transition energy levels and probabilities among the 147 levels from the captured $1s^{2}2sn{l}_j$ have been calculated. From the calculated results, radiative decay cascade processes followed by the radiative electron capture have also been studied with the help of multistep model and coupled rate equations, respectively. The present results not only make us understand the details of the radiative electron captures and the radiative decay cascade spectra in the experiment but also show a more efficient way to obtain the cascade spectra. Finally, the equivalence between the multistep model and coupled rate equations has been shown under a proper condition and the latter can hopefully be extended to investigate other cascade processes.

In this paper we report energy and angular distributions of electrons emitted in collisions of protons with $\text{neon-}\left({\text{F}}^{-},{\text{Ne}}^0,{\text{Na}}^{+}\right)$, $\text{argon-}\left({\text{Cl}}^{-},{\text{Ar}}^0,{\text{K}}^{+}\right)$, $\text{krypton-}\left({\text{Br}}^{-},{\text{Kr}}^0,{\text{Rb}}^{+}\right)$, and $\text{xenon-}\left({\text{I}}^{-},{\text{Xe}}^0\right)$ isoelectronic series for high and intermediate impact energies. Calculations were performed within the continuum distorted wave-eikonal initial-state method using an angular expansion in spherical harmonics and a numerical evaluation of the radial functions corresponding to both: the initial (bound) and the final (continuum) states in the same central potential. The first Born approximation was calculated on equal footing. The shellwise local plasma approximation was also calculated when possible. A complete and exhaustive comparison with the available experimental data is carried out. We have spanned almost all the published experiments in our range of interest. Successes and failures of the different theoretical methods are pointed out. Possible signatures of many-electron effects are noticed.

We consider single ionization of helium by very fast highly charged ions. The ionization is treated as a three-body problem which involves the “active” target electron, the target core (consisting of the target nucleus and the “passive” target electron) and the projectile ion. In contrast to the previous studies of this process, in which the interaction between the projectile and the target core was treated as a purely Coulomb one, we describe this interaction using the same core potential which acts on the active electron and which has both Coulomb and short-range parts. According to our results the deviation of the interaction between the projectile and the target core from the purely Coulomb law has on overall a weak effect on the ionization dynamics. In particular, we show that the account of this deviation does not enable one to get any better agreement with experimental data on the fully differential cross section for the electron emission into the so-called perpendicular plane.