We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin-changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.

We demonstrate nanoscale resolved infrared imaging of single nanoparticles employing near-field coupling in the nanoscopic gap between the metal tip of a scattering-type near-field optical microscope and the substrate supporting the particles. Experimental and theoretical evidence is provided that highly reflecting or polariton-resonant substrates strongly enhance the near-field optical particle contrast. Using Si substrates we succeeded in detecting Au particles as small as 8 nm ($<\lambda /1000$) at midinfrared wavelengths of about $\lambda =10\mu \mathrm{m}$. Our results open the door to infrared spectroscopy of individual nanoparticles, nanocrystals, or macromolecules.

We report on the observation of Bloch oscillations on the unprecedented time scale of several seconds. The experiment is carried out with ultracold bosonic ${}^{88}\mathrm{Sr}$ atoms loaded into a vertical optical standing wave. The negligible atom-atom elastic cross section and zero angular momentum in the ground state makes ${}^{88}\mathrm{Sr}$ an almost ideal Bose gas, insensitive to typical mechanisms of decoherence due to thermalization and external stray fields. The small size of the system enables precision measurements of forces at micrometer scale. This is a challenge in physics for studies of surfaces, Casimir effects, and searches for deviations from Newtonian gravity predicted by theories beyond the standard model.

We introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries.

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of $S$-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over $ϵ=4-d$, where $d$ is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be $\mu /{\epsilon }_F=\frac{1}{2}{ϵ}^{3/2}+\frac{1}{16}{ϵ}^{5/2}\ln ϵ-0.0246{ϵ}^{5/2}+\cdots$ and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be $\Delta /\mu =2{ϵ}^{-1}-0.691+\cdots$. The minimum of the fermion dispersion curve is located at $|\mathit{p}|=(2m{\epsilon }_0{)}^{1/2}$, where ${\epsilon }_0/\mu =2+O(ϵ)$. Extrapolation to $d=3$ gives results consistent with Monte Carlo simulations.

The entanglement entropy of a pure quantum state of a bipartite system $A\cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of $z=2$ conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal “area law” contribution linear in the size of the $AB$ boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound $ϵ$. Making such simulations robust to decoherence using fault tolerance requires an additional factor of $\sim 1/ϵ$ gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system.

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring $N$ quantum systems with two dichotomic observables per site.

We introduce a new design concept for superconducting phase quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single-shot measurements.

We introduce driven exclusion processes with internal states that serve as generic transport models in various contexts, ranging from molecular or vehicular traffic on parallel lanes to spintronics. The ensuing nonequilibrium steady states are controllable by boundary as well as bulk rates. A striking polarization phenomenon accompanied by domain wall motion and delocalization is discovered within a mesoscopic scaling. We quantify this observation within an analytic description providing exact phase diagrams. Our results are confirmed by stochastic simulations.

We show that, for any composite system with an arbitrary number of finite-dimensional subsystems, it is possible to directly measure the multipartite concurrence of pure states by detecting only one single factorizable observable, provided that two copies of the composite state are available. This result can be immediately put into practice in trapped-ion and entangled-photon experiments.

A simulation method is presented that achieves a flat energy distribution by updating the statistical temperature instead of the density of states in Wang-Landau sampling. A novel molecular dynamics algorithm (STMD) applicable to complex systems and a Monte Carlo algorithm are developed from this point of view. Accelerated convergence for large energy bins, essential for large systems, is demonstrated in tests on the Ising model, the Lennard-Jones fluid, and bead models of proteins. STMD shows a superior ability to find local minima in proteins and new global minima are found for the 55 bead $AB$ model in two and three dimensions. Calculations of the occupation probabilities of individual protein inherent structures provide new insights into folding and misfolding.

Using fluorescence spectroscopy we directly measure entropy production of a single two-level system realized experimentally as an optically driven defect center in diamond. We exploit a recent suggestion to define entropy on the level of a single stochastic trajectory [Seifert, Phys. Rev. Lett. 95, 040602 (2005)]. Entropy production can then be split into one of the system itself and one of the surrounding medium. We demonstrate that the total entropy production obeys various exact relations for finite time trajectories.

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.

We present a nonperturbative analysis of a new experimental technique for probing ultracold bosons in an optical lattice by periodic lattice depth modulations. This is done using the time-dependent density-matrix renormalization group method. We find that sharp energy absorption peaks are not unique to the Mott insulating phase at commensurate filling but also exist for superfluids at incommensurate filling. For strong interactions, the peak structure provides an experimental measure of the interaction strength. Moreover, the peak height of the peaks at $\hslash \omega \gtrsim 2U$ can be employed as a measure of the incommensurability of the system.

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms’ momentum distribution around a vortex.

Phase-controllable transport in laser-irradiated spatially symmetric systems is shown to arise both quantum mechanically and classically from a common field-driven interference mechanism. Specifically, the quantum-to-classical transition for symmetry breaking in a quartic oscillator driven by an $\omega +2\omega$ field is studied. For this, a double perturbation theory in the oscillator anharmonicity and external field strength, that admits an analytic classical limit, is carried out in the Heisenberg picture. The interferences responsible for the symmetry breaking are shown to survive in the classical limit and are the origins of classical control. Differences between reflection symmetry that plays a key role in the analysis, and parity that does not, are discussed.

We demonstrate ultrafast coherent excitation of an atomic qubit stored in the hyperfine levels of a single trapped cadmium ion. Such ultrafast excitation is crucial for entangling networks of remotely located trapped ions through the interference of photon frequency qubits, and is also a key component for realizing ultrafast quantum gates between Coulomb-coupled ions.