We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an ad hoc manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case, subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.

We present a first-principles method for the determination of the van der Waals interactions for a collection of finite-sized macroscopic bodies. The method is based on fluctuational electrodynamics and a rigorous multiple-scattering method for the electromagnetic field. As such, the method takes fully into account retardation, many-body, multipolar, and near-fields effects. By application of the method to the case of two metallic nanoparticles, we demonstrate the breakdown of the standard $1/r^2$ distance law as the van der Waals force decays exponentially with distance when the nanoparticles are too close or too far apart.

In most studies of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent investigations of the effect of memory or correlations in error have led to speculation that nonanalytic behavior may occur in the capacity. Motivated by these observations, we connect the study of channels with correlated error to the study of many-body systems. This enables us to use many-body theory to solve some interesting models of correlated error. These models can display nonanalyticities analogous to quantum phase transitions.

We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.

We show that by raising the lattice “adiabatically” as in many current optical lattice experiments on bosons, even though the temperature may decrease initially, it will eventually rise linearly with lattice height, taking the system farther away from quantum degeneracy. This increase has nothing to do with the entropy of the bulk Mott phase and is caused by the adiabatic compression of the mobile atoms between Mott layers. Our studies show that one can reverse the temperature rise to reach quantum degeneracy by adiabatic expansion, which can be achieved by a variety of methods.

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where Mott insulator features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression.

We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method—which we call the tensor renormalization group method—by computing the magnetization of the triangular lattice Ising model.

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value $T_c=0.23(2){\epsilon }_F$ in the bulk, as predicted by the present authors in their Monte Carlo calculations.

By use of the Larmor equivalence between uniform rotation and a magnetic field, we consider in the strong-interaction Thomas-Fermi regime the single centered vortex as the first Zeeman-like excited state of the axisymmetric rotating Bose-Einstein condensate. This yields a resonant-drive nucleation mechanism whose threshold is in quite good agreement with ENS, MIT, and JILA experimental results.

Motivated by a recent experiment, we study nonequilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and we establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.

We demonstrate two key components for optical quantum information processing: a bright source of heralded single photons; and a bright source of entangled photon pairs. A pair of pump photons produces a correlated pair of photons at widely spaced wavelengths (583 nm and 900 nm), via a ${\chi }^{(3)}$ four-wave mixing process. We demonstrate nonclassical interference between heralded photons from independent sources with a visibility of 95% (after correction for background), and an entangled photon pair source, with a fidelity of 89% with a Bell state.

Using two trapped ion species ( and ) as primary and ancillary quantum systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94% measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spectroscopy of an optical clock transition.

We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover’s search algorithm and high-fidelity two-qubit quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.

We examine the stability of a trapped dipolar condensate mixed with a single-component fermion gas at $T=0$. Whereas pure dipolar condensates with a small $s$-wave interaction are unstable even at small dipole-dipole interaction strength, we find that the admixture of fermions can significantly stabilize them, depending on the strength of the boson-fermion interaction. Within the stable regime we find a region where a ground state is characterized by a density wave along the soft trap direction.

We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.

The contribution to the eighth-order anomalous magnetic moment ($g-2$) of the electron from a set of diagrams without closed lepton loops is recalculated using a new FORTRAN code generated by an automatic code generator. Comparing the contributions of individual diagrams of old and new calculations, we find an inconsistency in the old treatment of IR subtraction terms in two diagrams. Correcting this error leads to the revised value $-1.9144(35)(\alpha /\pi {)}^4$ for the eighth-order term. This theoretical change induces the shift of the inverse of the fine structure constant by $-6.41180(73)\times {10}^{-7}$.

We demonstrate an unconditional high-fidelity teleporter capable of preserving the broadband entanglement in an optical squeezed state. In particular, we teleport a squeezed state of light and observe $-0.8\pm 0.2\mathrm{dB}$ of squeezing in the teleported (output) state. We show that the squeezing criterion translates directly into a sufficient criterion for entanglement of the upper and lower sidebands of the optical field. Thus, this result demonstrates the first unconditional teleportation of broadband entanglement. Our teleporter achieves sufficiently high fidelity to allow the teleportation to be cascaded, enabling, in principle, the construction of deterministic non-Gaussian operations.

We analyze the possibility of a ferroelectric transition in heteronuclear molecules consisting of Bose-Bose, Bose-Fermi, or Fermi-Fermi atom pairs. This transition is characterized by the appearance of a spontaneous electric polarization below a critical temperature. We discuss the existence of a ferroelectric Fermi liquid phase for Fermi molecules and the existence of a ferroelectric superfluid phase for Bose molecules characterized by the coexistence of ferroelectric and superfluid orders. Lastly, we propose an experiment to detect ferroelectric correlations through the observation of coherent dipole radiation pulses.

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.