We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique develops tools from many-body physics—based on finitely correlated or projected entangled pair states—to go beyond the cluster-state based one-way computer. We identify resource states radically different from the cluster state, in that they exhibit nonvanishing correlations, can be prepared using nonmaximally entangling gates, or have very different local entanglement properties. In the computational models, randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. We comment on the possibility of tailoring computational models to specific physical systems.

In equilibrium systems, time and ensemble averages of physical quantities are equivalent due to ergodic exploration of phase space. In driven systems, it is unknown if a similar equivalence of time and ensemble averages exists. We explore effective limits of such convergence in a sheared bubble raft using averages of the bubble velocities. In independent experiments, averaging over time leads to well-converged velocity profiles. However, the time averages from independent experiments result in distinct velocity averages. Ensemble averages are approximated by randomly selecting bubble velocities from independent experiments. Increasingly better approximations of ensemble averages converge toward a unique velocity profile. Therefore, the experiments establish that in practical realizations of nonequilibrium systems, temporal averaging and ensemble averaging can yield convergent (stationary) but distinct distributions.

The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement in its pure ground state. Here we establish scaling laws for this entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means. We consider the setting of $D$-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic—where an area law is proven to hold—or fermionic where we determine a logarithmic correction to the area law, which depends on the topology of the Fermi surface. We find Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.

We report, for the first time, laser spectroscopy of the clock transition in . A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminum’s electronic state to the beryllium’s hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency . They are also used to measure the lifetime of the metastable clock state , the ground state factor , and the excited state factor , in units of the Bohr magneton.

We propose a novel method to measure time-dependent linear susceptibilities in molecular simulations, which does not require the use of nonequilibrium simulations, subtraction techniques, or fluctuation-dissipation theorems. The main idea is an exact reformulation of linearly perturbed quantities in terms of observables accessible in a single unperturbed trajectory. We apply these ideas to supercooled liquids in a nonequilibrium aging regime. We show that previous work had underestimated deviations from fluctuation-dissipation relations in the case of a Lennard-Jones system, while our results for silica are in qualitative disagreement with earlier results.

We demonstrate the first guiding of atoms through a hollow-core photonic band-gap fiber. Rb atoms from a thermal oven source travel through 6.1 and 4.0 cm long fibers with a guiding potential $1/e^2$ radius of $3.0\mu \mathrm{m}$. When the photon scattering rate is small, the observed guiding efficiency is greater than 70%. An unexpected low-speed cutoff is attributed to inefficient optical coupling.

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.

Thermal noise generated by a hot resistor (resistance $R$) can, under proper conditions, catalyze heat removal from a cold normal metal ($N$) in contact with a superconductor ($S$) via a tunnel barrier ($I$). Such a NIS junction is reminiscent of Maxwell’s demon, rectifying the heat flow. Upon reversal of the temperature gradient between the resistor and the junction, the heat fluxes are reversed: this presents a regime which is not accessible in an ordinary voltage-biased NIS structure. We obtain analytical results for the cooling performance in an idealized high impedance environment and perform numerical calculations for general $R$. We conclude by assessing the experimental feasibility of the proposed effect.

Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density $J(\omega )\propto {\omega }^s$. We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, $s\ll 1$, weakly damped coherent oscillations on short time scales are possible even in the localized phase—this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.

We theoretically study the observable response of edge currents in two-dimensional cold atom optical lattices. As an example, we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of the Chern number using edge currents of a topologically ordered optical lattice insulator.

Sequences of residence times (RTs) associated with the escape from metastable states are observed in many fields. Here we study analytically and numerically the correlations among RTs for a bistable stochastic system driven by dichotomous noise. Our theory predicts an oscillatory behavior of the correlations with respect to the lag between RTs. Correlations vanish at all lags if the switching rate matches the hopping rate of the unperturbed system. It is also shown that RT correlations may reveal features of the driving which are not present in the single-RT statistics.

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length ${\sigma }_R$. For speckle potentials the Fourier transform of the correlation function vanishes for momenta $k>2/{\sigma }_R$ so that the Lyapunov exponent vanishes in the Born approximation for $k>1/{\sigma }_R$. Then, for the initial healing length of the condensate ${\xi }_{\mathrm{in}}>{\sigma }_R$ the localization is exponential, and for ${\xi }_{\mathrm{in}}<{\sigma }_R$ it changes to algebraic.

We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic and dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples.

The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the nonequilibrium regime which involves an integral over measurable velocity correlation functions.

We report on a study of the dynamics of decoherence of a matter-wave interferometer, consisting of a pair of low-dimensional cold atom condensates at finite temperature. We identify two distinct regimes in the time dependence of the coherence factor of the interferometer: quantum and classical. Explicit analytical results are obtained in both regimes. In particular, in the two-dimensional case in the classical (long time) regime, we find that the dynamics of decoherence is universal, exhibiting a power-law decay with an exponent, proportional to the ratio of the temperature to the Kosterlitz-Thouless temperature of a single 2D condensate. In the one-dimensional case in the classical regime we find a universal nonanalytic time dependence of decoherence, which is a consequence of the nonhydrodynamic nature of damping in 1D liquids.

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state.

We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the renormalization group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction term, we analyze the effect of quadrupole interactions in the self-consistent Hartree approximation. We show that in the case of a repulsive quadrupole interaction, there is a first-order phase transition to a stripe phase in agreement with the well-known Brazovskii result. However, in the case of attractive quadrupole interactions there is an isotropic-nematic second-order transition with higher critical temperature.

We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a ${}^{87}\mathrm{Rb}$ spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of $8.3\mathrm{pT}/{\mathrm{Hz}}^{1/2}$ over a measurement area of $120\mu {\mathrm{m}}^2$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as $0.15\mathrm{pT}/{\mathrm{Hz}}^{1/2}$ for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.

Controlled decoherence of free electrons due to Coulomb interaction with a truly macroscopic environment, the electron (and phonon) gas inside a semiconducting plate, is studied experimentally. The quantitative results are compared with different theoretical models. The experiment confirms the main features of the theory of decoherence and can be interpreted in terms of which-path information. In contrast to previous model experiments on decoherence, the obtained interferograms directly visualize the transition from quantum to classical.

We have produced and detected molecules using a $p$-wave Feshbach resonance between ${}^{40}\mathrm{K}$ atoms. We have measured the binding energy and lifetime for these molecules and we find that the binding energy scales approximately linearly with the magnetic field near the resonance. The lifetime of bound $p$-wave molecules is measured to be $1.0\pm 0.1\mathrm{ms}$ and $2.3\pm 0.2\mathrm{ms}$ for the $m_l=\pm 1$ and $m_l=0$ angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasibound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier.