The superfluid-to-Anderson-insulator transition of a strongly repulsive Bose gas is studied in a one-dimensional incommensurate optical lattice. In the hard-core limit, the Bose-Fermi mapping allows us to deal with the system using the exact numerical method. Based on the Aubry-André model, we exploit the phase transition of the hard-core boson system from the superfluid phase with all single-particle states extended to the Bose-glass phase with all the single-particle states being Anderson localized as the strength of the incommensurate potential increases relative to the hopping amplitude. We evaluate the superfluid fraction, one-particle density matrices, momentum distributions, the natural orbitals, and their occupations. All of these quantities show that there exists a superfluid-to-insulator phase transition in the system.

In this work, we present a systematic derivation of the distribution of eigenfrequencies for oscillations of the ground state of a repulsive Bose-Einstein condensate in the semi-classical (Thomas-Fermi) limit. Our calculations are performed in one, two, and three-dimensional settings. Connections with the earlier work of Stringari, with numerical computations, and with theoretical expectations for invariant frequencies based on symmetry principles are also given.

We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schrödinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.

We propose a method that enables efficient conversion of the quantum information frequency between different regions of a spectrum of light based on recently demonstrated strong parametric coupling between two narrow-band single-photon pulses propagating in a slow-light atomic medium [N. Sisakyan and Yu. Malakyan, Phys. Rev. A, 75, 063831 (2007)]. We show that an input qubit at telecom wavelength is transformed into another at a visible domain in a lossless and shape-conserving manner while keeping the initial quantum coherence and entanglement. These transformations can be realized with a quantum efficiency close to its maximum value.

We investigate the localized nonlinear matter waves of the quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity in the harmonic potential. It is shown that all of the Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their properties are determined by the principal quantum number $n$ and secondary quantum number $l$: the parity of the matter wave functions and the corresponding energy levels depend only on $n$, and the numbers of density packets for each quantum state depend on both $n$ and $l$, which describe the topological properties of the atom packets. We also give an experimental protocol to observe these phenomena in future experiments.

We present a generic study of the unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space dimensions less than or equal to $5$, this leads to the complete optimal solution. We demonstrate our method with a physical example, namely, the unambiguous comparison of $n$ quantum states, and find the optimal success probability.

We demonstrate the control of the $\alpha$-proton nuclear spin, $I$ $=1/2$, coupled to the stable radical ⋅CH(COOH)${}_2$, $S$ $=1/2$, in a $\gamma$-irradiated malonic acid single crystal using only microwave pulses. We show that, depending on the state of the electron spin ($m_S=\pm 1/2$), the nuclear spin can be locked in a desired state or oscillate between $m_I=+1/2$ and $m_I=-1/2$ on the nanosecond time scale. This approach provides a fast way of controlling nuclear spin qubits and also enables the design of switchable spin-based quantum gates by addressing only the electron spin.

Cold deuterium atoms in a supersonic beam have been decelerated from an initial velocity of $475$ m/s to zero velocity in the laboratory frame using a $24$-stage Zeeman decelerator. The atoms have been loaded in a magnetic quadrupole trap at a temperature of $~100$ mK and an initial density of $~10$${}^6$ cm${}^{-3}$. Efficient deceleration was achieved by pulsing the magnetic fields in the decelerator solenoids using irregular sequences of phase angles. Trap loading was optimized by monitoring and suppressing the observed reflection of the atoms by the field gradient of the back solenoid of the trap.

Recently, a seminal stimulated Raman adiabatic passage (STIRAP) experiment allowed the creation of ${}^{40}\mathrm{K}$${}^{87}\mathrm{Rb}$ molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. To describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release from the trap, the momentum distribution becomes asymptotically isotropic, while the particle density becomes anisotropic.

We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.

We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as $1-(t/\tau ){}^2$ (i.e., quadratically in time, with a characteristic timescale $\tau$ that is inversely proportional to the boundary size of the subsystem, that is, as an area law). For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a one-dimensional spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.

We studied the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit, the lowest order correction to the geometric phase is derived analytically and the general case is calculated numerically. It was found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact on the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.

The collision of two atoms is an intrinsic multichannel (MC) problem, as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of the open channel, are often applied in calculations. In this work the complete MC problem is solved numerically for the magnetic Feshbach resonances (MFRs) in collisions between generic ultracold ${}^6\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$ atoms in the ground state and in the presence of a static magnetic field $B$. The obtained MC solutions are used to test various existing as well as presently developed SC approaches. It was found that many aspects even at short internuclear distances are qualitatively well reflected. This can be used to investigate molecular processes in the presence of an external trap or in many-body systems that can be feasibly treated only within the framework of the SC approximation. The applicability of various SC approximations is tested for a transition to the absolute vibrational ground state around an MFR. The conformance of the SC approaches is explained by the two-channel approximation for the MFR.

We report measured and calculated results for elastic scattering of low-energy electrons by ethyl vinyl ether (ethoxyethene), a prototype system for studying indirect dissociative attachment processes that may play a role in DNA damage. The integral cross section displays the expected ${\pi }^{*}$ shape resonance. The agreement between the calculated and measured cross sections is generally good.

We consider the collective oscillations of an ultracold atomic cloud by using a wave kinetic description which retains phonon recoil effects. We derive an exact quantum-wave dispersion relation for hybrid plasma-acoustic oscillations and the associated atomic Landau damping. The quasilinear kinetic theory is also extended into the quantum regime, leading to a Boltzmann type of equation for the atoms in a collective force field. Comparison with our previous quasiclassical results is considered. Diffusion in velocity space due to density fluctuations is discussed in detail. This will us allow to establish an additional temperature limit, different from the usual Doppler limit, below which the laser cooling process is prevented by the density fluctuations. This work could also be useful to describe low-frequency Doppler instabilities, as well as collective phonon laser processes.

Starting from a general theory of time-resolved x-ray scattering, we derive a convenient expression for the diffraction signal based on a careful analysis of the relevant inelastic scattering processes. We demonstrate that the resulting inelastic limit applies to a wider variety of experimental conditions than similar, previously derived formulas, and it directly allows the application of selection rules when interpreting diffraction signals. Furthermore, we present a simple extension to systems simultaneously illuminated by x rays and a laser beam.

We use periodically modulated magnetic fields to drive spin-1 Bose-Einstein condensates (BECs) and study the corresponding spin-mixing dynamics. Due to the time-dependent driving, this system permits chaotic dynamics depending on the drive parameters, which could not occur in previous studies. From the investigation of the Poincaré sections, we find there exist complex trajectories in the phase space, leading to very complicated structures of the phase space with mixed regular and chaotic regions. By calculating the quasienergy levels of the corresponding Floquet operators, the signatures of quantum chaos are also found in this system. The level spacing distribution is very close to the Poisson distribution or Wigner distribution when the corresponding classical dynamics is regular or chaotic.

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method, we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin $x=0$, and (ii) when the first component has a maximum of density and the second a minimum of density at $x=0$. In the noninteracting case, the density profiles are symmetric around $x=0$. We numerically study the breakdown of this symmetry due to interspecies and intraspecies interactions acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.

We present an atom interferometer that differs from common atom interferometers as it is not based on the spatial splitting of electronic wave functions, but on orienting atoms in space. As an example we present how an orientational atom interferometer based on highly charged hydrogen–like atoms is affected by gravitational waves. We show that a monochromatic gravitational wave will cause a frequency shift that scales with the binding energy of the system rather than with its physical dimension. For a gravitational wave amplitude of $h={10}^{-23}$ the frequency shift is of the order of $110\hspace{0.5em}\mu \mathrm{Hz}$ for an atom interferometer based on a $91$-fold charged uranium ion. A frequency difference of this size can be resolved by current atom interferometers in $1\hspace{0.5em}\mathrm{s}$.

This article presents a comparison of two finite-temperature BCS–Bose-Einstein condensation (BEC) crossover theories above the transition temperature: Nozieres–Schmitt-Rink (NSR) theory and finite-$T$ extended BCS-Leggett theory. The comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by (primarily) radio frequency (rf) experiments. Both theories include pair fluctuations and exhibit pseudogap effects, although the nature of this pseudogap is very different. The pseudogap in finite-$T$ extended BCS-Leggett theory is found to follow a BCS-like dispersion which, in turn, is associated with a broadened BCS-like self-energy, rather more similar to what is observed in high-temperature superconductors (albeit, for a $d$-wave case). The fermionic quasiparticle dispersion is different in NSR theory and the damping is considerably larger. We argue that the two theories are appropriate in different temperature regimes with the BCS-Leggett approach being more suitable nearer to condensation. There should, in effect, be little difference at higher $T$ as the pseudogap becomes weaker and where the simplifying approximations used in the BCS-Leggett approach break down. On the basis of momentum-integrated rf studies of unpolarized gases, it would be difficult to distinguish which theory is the better one. A full comparison for polarized gases is not possible since it is claimed that there are inconsistencies in the NSR approach (not found in the BCS-Leggett scheme). Future experiments along the lines of momentum-resolved experiments look to be very promising in distinguishing the two theories.