The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still bounded error, quantum polynomial time complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a universal quantum interface, a device which enables control of an arbitrary computation through the control of a fixed number of spins, and using it as a building block to entirely remove the need for control, except in the system initialization. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a Quantum-Merlin-Arthur-complete problem.

The physical significances and the pros and cons involved in the usage of different time-delay formalisms are discussed. The delay-time matrix introduced by Eisenbud, where only $s$ waves participate in a reaction, is in general related to the definition of an angular time delay which is shown not to be equivalent to the so-called phase time delay of Eisenbud and Wigner even for single channel scattering. Whereas the expression due to Smith which is derived from a time-delayed radial wave packet is consistent with a lifetime matrix which is Hermitian, this is not true for any Eisenbud-type lifetime matrix which violates time-reversal invariance. Extending the angular time delay of Nussenzveig to multiple channels, we show that if one performs an average over the directions and subtracts the forward angle contribution containing an interference of the incident and scattered waves, the multichannel angle-dependent average time delay reduces to the one given by Smith. The present work also rectifies a recently misinterpreted misnomer of the relation due to Smith.

We report on the creation and characterization of heteronuclear ${}^{40}\text{K}{}^{87}\text{R}\text{b}$ Feshbach molecules in an optical dipole trap. Starting from an ultracold gas mixture of ${}^{40}\text{K}$ and ${}^{87}\text{R}\text{b}$ atoms, we create as many as 25 000 molecules at 300 nK by rf association. Optimizing the association process, we achieve a conversion efficiency of 25%. We measure the temperature dependence of the rf association process and find good agreement with a phenomenological model that has previously been applied to Feshbach molecule creation by slow magnetic-field sweeps. We also present a measurement of the binding energy of the heteronuclear molecules in the vicinity of the Feshbach resonance and provide evidence for Feshbach molecules as deeply bound as 26 MHz.

Bright and dark nonlinear magneto-optical resonances associated with the ground state Hanle effect have been studied experimentally and theoretically for $D_1$ excitation of atomic cesium. This system offers the advantage that the separation between the different hyperfine levels exceeds the Doppler width, and hence transitions between individual levels can be studied separately. At the same time, the system retains the advantages offered by ordinary glass cells, including simplicity and subnatural width Hanle resonances. Experimental measurements for various laser power densities and transit relaxation times are compared with a model based on the optical Bloch equations, which averages over the Doppler contour of the absorption line and simultaneously takes into account all hyperfine levels, as well as mixing of magnetic sublevels in an external magnetic field. In contrast to previous studies, which could not resolve the hyperfine transitions because of Doppler broadening, in this study there is excellent agreement between experiment and theory regarding the sign (bright or dark), contrast and width of the resonance. The results support the traditional theoretical interpretation, according to which these effects are related to the relative strengths of transition probabilities between different magnetic sublevels in a given hyperfine transition.

Optically trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We show that the measured cloud profiles of both species determine the total energy of universal gases for any trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. A global proof of the virial theorem yields the total energy of the gas at all temperatures in the scale-invariant form $E=⟨ϵ\partial U/\partial ϵ⟩$, where $ϵ$ is an arbitrary energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in any trap by observing only the cloud profiles, and provides a consistency check for many-body calculations in the universal regime.

We study the birefringence of quantized polarized light in a magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach effect of light. To explain this engineered birefringence microscopically, we derive an effective Shrödinger equation for the spatial motion of two orthogonally polarized components, which behave as a spin with an effective magnetic moment leading to a Stern-Gerlach split in a nonuniform magnetic field. We show that the electromagnetically-induced-transparency mechanism can enhance the magneto-optical Stern-Gerlach effect of light in the presence of a control field with a transverse spatial profile and a nonuniform magnetic field.

We investigate experimentally and theoretically nondegenerate four-wave mixing in rubidium vapor using a diamond configuration ($5S_{1/2}$, $5P_{1/2}$, $5P_{3/2}$, and $6S_{1/2}$ levels). We model this process of three classical fields interacting with a four-level atomic system with the Schrödinger equation. The experimental results are in good agreement with theoretical predictions for the generated light as a function of detuning.

We present an electromagnetic model describing liquid-core liquid-cladding optical fibers sustained by light radiation pressure that encompass the contribution of all the allowed propagating modes. Various sequences of unstable and stable equilibrium liquid column diameters are found above a threshold power. The nontrivial relationship between a single-valued or multivalued column diameter with a mono- or multimodal structure of the electromagnetic field is analyzed, and the influence of the light-matter interaction geometry is estimated. Moreover, we propose a geometrical interpretation based on a ray optics approach that brings an intuitive understanding of the role played by the higher-order propagation mode in the occurrence of a multistable liquid-core behavior.

In a recent paper by [Schlosshauer et al., Phys. Rev. A 77, 022111 (2008)] a model of a harmonic oscillator coupled to a spin bath was studied using the Born-Markov master equation. We show that the bath correlation function forbids application of the Born-Markov approximation, which renders this master equation incorrect and the conclusions following from its solution physically irrelevant.

Contrary to the assertion by Mogilevtsev and Shatokhin [preceding paper, Phys. Rev. A 78, 016101 (2008)], we show that the applicability of the Born-Markov master-equation approach in our treatment of the oscillator-spin model depends on the physical situation under study. Heating effects do occur although they may not be accurately captured by second-order perturbation theory inherent in the Born-Markov scheme.

The zero-point electromagnetic (Casimir) energy of an infinitely long cylindrical layer of finite thickness is calculated. The dielectric and magnetic properties of the layer and those of the surrounding medium are assumed to be described by real constant dielectric permittivities and magnetic permeabilities satisfying the relationship of constant speed of light across the interfaces. We use the mode summation technique together with the Riemann $\zeta$-function regularization procedure to remove the occurring divergences from the Casimir energy. We present analytical expressions and numerical calculations for various limiting cases in terms of the radial dimension, curvature, and material composition of the cylindrical layer.

Via a multidimensional complementarity relation we derive an operational entanglement measure for any discrete quantum system, i.e., for any multidimensional and multipartite system. This measure admits a separation into different classes of entanglement obtained by using a flip operator $2,3,\dots ,n$ times, defining a $m$-flip concurrence. This operator sum has the practical feature to allow one to calculate for mixed states bounds on this $m$-flip concurrence. Moreover, the information content of an $n$-partite multidimensional system admits a simple and intuitive interpretation in terms of single particle obtainable information, entanglement, and information due to lack of classical knowledge of the quantum state under investigation. Explicitly, the three qubit system is analyzed and, e.g., the physical difference in entanglement of the W state, the Greenberger-Horne-Zeilinger (GHZ) state, or a biseparable state is revealed.

State-to-state, summed charge transfer and stopping cross sections in collisions of protons and neutral hydrogen atoms with lithium atoms have been studied at collision energies ranging from $10\text{to}25\mathrm{keV}$. Cross sections were calculated using electron-nuclear dynamics (END), which is a nonadiabatic, time-dependent, direct approach for the study of ion-atom-molecule interaction processes. Our results show good agreement when compared to available theoretical and experimental data. We find that the charge transfer cross section for protons shows a bump and a maximum as a function of the projectile energy, both of them as a result of the large probability for capture into the projectile $2p$ orbital. The bump corresponds to a projectile energy of approximately $E_p\sim 0.7\mathrm{keV}$, and results from the electron capture probability in the low impact parameter region of approximately $b\sim 2.0\mathrm{a.u.}$ The maximum occurs at $E_p\sim 5\mathrm{keV}$ as a result of the larger capture probability in the intermediate impact parameter region near $b\sim 8\mathrm{a.u.}$ A similar behavior is found for the electron loss cross section for hydrogen projectiles. We find that the beam charge fraction, for all the energies considered, is nearly neutral. We also find that the largest contribution to the stopping cross section is for impact parameters around $b\sim 5\mathrm{a.u.}$ Finally, we report the total, electronic, and nuclear stopping cross sections to be within a factor of 2 of the reported values in the SRIM 06 code (SRIM stands for stopping and range of ions in matter) and other available experimental data. The largest discrepancy is due to the charge transfer process as well as to a transient $\mathrm{Li}{\mathrm{H}}^{+}$ molecular ion formed in the low projectile energy region.

Charge transfer and electronic excitation in collisions of ${\mathrm{H}}^{+}$ ions with $\mathrm{C}{\mathrm{H}}_3$ from a few tens of eV up to $10\mathrm{keV}$ are theoretically investigated. The adiabatic potential energy curves and corresponding wave functions are calculated by using the multireference single- and double-excitation configuration interaction method, and the scattering dynamics is studied based on the semiclassical impact parameter molecular-orbital close-coupling approach. Charge-transfer cross sections are found to be large and rather energy-dependent over the entire energy region studied. Electronic excitation is also energy-dependent with a sharp increase from below ${10}^{-17}\text{to}{10}^{-16}{\mathrm{cm}}^2$. Most of the molecular products produced through charge transfer or excitation are known to be unstable and undergo fragmentation producing various hydrocarbon radical species. Hence, identification of fragmented species and their production mechanism are important for spectroscopic analysis.

We obtain the exact time evolution for the one-dimensional integrable fermionic $1/r$ Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mott-insulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.

In this paper we develop a theoretical description of the correlations between ultracold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far-field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, mean-field decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.

We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find the anomalous enhancement of the quasiparticle current $J_{\mathrm{q}}$ carried by Bogoliubov phonons near a potential barrier, due to the supply of the excess current from the condensate. This effect leads to the increase of quasiparticle transmission probability in the low energy region found by Kovrizhin et al. We also show that the quasiparticle current twists the phase of the condensate wave function across the barrier, leading to a finite Josephson supercurrent $J_{\mathrm{s}}$ through the barrier. This induced supercurrent flows in the opposite direction to the quasiparticle current so as to cancel out the enhancement of $J_{\mathrm{q}}$ and conserve the total current $J=J_{\mathrm{q}}+J_{\mathrm{s}}$.

We study the ground states of one-dimensional Bose-Bose mixtures under harmonic confinement. As we vary the interspecies coupling strength up to the limit of infinite repulsion, we observe a generalized, composite-fermionization crossover. The initially coexisting phases demix as a whole for weak intraspecies interactions, whereas the atoms localize individually for strong intraspecies repulsion. By symmetry, the two components end up with strongly overlapping profiles, albeit sensitive to symmetry-breaking perturbations. Different pathways emerge if the two components have different atom numbers, different intraspecies interactions, or different masses and/or trap frequencies.

We study the dynamics of the quantum optical spring, i.e., a spring whose spring constant undergoes discrete jumps depending on the quantum state of another system. We show the existence of revivals and fractional revivals in the quantum dynamics reminiscent of similar dynamical features in cavity QED. We recover in the semiclassical limit the results for an oscillator whose frequency undergoes a sudden change. The quantum optical spring is conceivable, for example, by a micromirror under the influence of radiation pressure by a field which is strictly quantum mechanical. Our work suggests that driven systems would in general exhibit a very different dynamics if the drive is replaced by a quantum source.

The propagation and interaction of two solitary waves with angular momentum in bulk nematic liquid crystals, termed nematicons, have been studied in the nonlocal limit. These two spinning solitary waves are based on two different wavelengths of light and so are referred to as two-color nematicons. Under suitable boundary conditions, the two nematicons can form a bound state in which they spin about each other. This bound state is found to be stable to the emission of diffractive radiation as the nematicons evolve. In addition this bound state shows walk-off due to dispersion. Using an approximate method based on the use of suitable trial functions in an averaged Lagrangian of the two-color nematicon equations, modulation equations for the evolution of the individual nematicons are derived. These modulation equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found between solutions of the modulation equations and full numerical solutions of the nematicon equations. The shed diffractive radiation is found to play a much lesser role in the nonlocal limit than in the local limit.