We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case, the accumulated distance traveled by the particles, $x$, scales with the time, $t$, as $x\sim t^{1/z}$, with a dynamical exponent $z>0$. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method, we exactly calculate $z_{\mathrm{P}\mathrm{W}}$ for particlewise disorder, which is argued to be related as $z_{\mathrm{S}\mathrm{W}}=z_{\mathrm{P}\mathrm{W}}/2$ for sitewise disorder. In the symmetric case with zero mean drift, the particle diffusion is ultraslow, logarithmic in time.

The phase dynamics of a semiconductor laser with optical feedback is studied by construction of the Hilbert phase from its experimentally measured intensity time series. The Hurst exponent is evaluated for the phase fluctuations and grows from 0.5 to $\sim 0.7$ (indicating fractional Brownian motion) as the feedback strength is increased. A comparison with numerical computations based on a delay-differential equation model shows excellent agreement and reveals the relative roles of spontaneous emission noise and deterministic dynamics for different feedback strengths.

We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable states are found from an instanton calculation, leading to an effective two-state system on a long time scale. In the bistable current range, the telegraph noise dominates the distribution, whose logarithm is found to be universally described by a tilted ellipse.

For a quantum gas, being subject to continuous feedback of a macroscopic observable, the single-particle dynamics is studied. Despite feedback-induced particle correlations, it is shown that analytic solutions are obtained by formally extending the single-particle Hilbert space by an auxiliary degree of freedom. The particle’s motion is then fed by colored noise, which effectively maps quantum-statistical correlations onto the single particle. Thus, the single particle in the continuously controlled gas follows a non-Markovian trajectory in phase space.

A suitable sequence of sharp pulses applied to a spin coupled to a bosonic bath can cool its state, i.e., increase its polarization or ground state occupation probability. Starting from an unpolarized state of the spin in equilibrium with the bath, one can reach very low temperatures or sizable polarizations within a time shorter than the decoherence time. Both the bath and external fields are necessary for the effect, which comes from the backreaction of the spin on the bath. This method can be applied to cool at once a disordered ensemble of spins.

For quantum critical spin chains without disorder, it is known that the entanglement of a segment of $N\gg 1$ spins with the remainder is logarithmic in $N$ with a prefactor fixed by the central charge of the associated conformal field theory. We show that for a class of strongly random quantum spin chains, the same logarithmic scaling holds for mean entanglement at criticality and defines a critical entropy equivalent to central charge in the pure case. This effective central charge is obtained for Heisenberg, $XX$, and quantum Ising chains using an analytic real-space renormalization-group approach believed to be asymptotically exact. For these random chains, the effective universal central charge is characteristic of a universality class and is consistent with a $c$-theorem.

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the environment and its coupling with the system yields a unique geometric phase distribution that applies even for mixed states, nonunitary dynamics, and noncyclic evolutions.

We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of Regal et al. [Nature (London) 427, 47 (2003)] as well as Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003)] without adjustable parameters.

We prove a powerful theorem for tripartite remote entanglement distribution protocols that establishes an upper bound on the amount of entanglement of formation that can be created between two single-qubit nodes of a quantum network. Our theorem also provides an operational interpretation of concurrence as a type of entanglement capacity.

We describe a quantum scheme to “color code” a set of objects in order to record which one is which. In the classical case, $N$ distinct colors are required to color code $N$ objects. We show that, in the quantum case, only $\frac{N}{e}$ distinct “colors” are required, where $e\approx 2.71828$ is Euler’s constant. If the number of colors is less than optimal, the objects may still be correctly distinguished with some success probability less than 1. We show that the success probability of the quantum scheme is better than the corresponding classical one and is information-theoretically optimal.

We report on fluorescence fluctuations of nanoparticles diffusing through a laser focus. Subject to an intensity threshold the fluorescence signal is transformed into time traces of on and off periods. The distribution functions of the experimental on and off times follow power laws $t^{-\alpha }$ over several orders of magnitude with exponents $\alpha \simeq 1.5-2$. At long times the distribution functions cross over to exponential decays. For the interpretation of the experimental data a diffusion-reaction equation is proposed which covers both, the diffusion controlled recurrence and the photon statistics as the relevant processes.

We evaluate thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with the direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency-reference cavity of order $1\mathrm{H}\mathrm{z}/\sqrt{\mathrm{H}\mathrm{z}}$ ($0.01\mathrm{H}\mathrm{z}/\sqrt{\mathrm{H}\mathrm{z}}$) at 10 mHz (100 Hz) at room temperature. This level coincides with the world-highest level stabilization results.

A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and one in the other are connected by a domain wall of the relative phase, constituting a “vortex molecule,” which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.

By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with a few other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary measuring apparatus, by using it in combination with a tomographer in a correlation setup with an input bipartite system. The method is robust to imperfections of the tomographer, and works for practically any input state of the bipartite system.

We consider a system of $N$ nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for $N$ large, but below some critical value, the properties of the $N$-boson bound state are universal. In particular, the ratio of the binding energies of $(N+1)$- and $N$-boson systems, $B_{N+1}/B_N$, approaches a finite limit, approximately 8.567, at large $N$. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state $B_3^{(0)}=16.522688(1)B_2$ and for the excited state $B_3^{(1)}=1.2704091(1)B_2$.

We study the Feshbach resonance assisted stimulated adiabatic passage of an effective coupling field for creating stable molecules from an atomic Bose condensate. By exploring the properties of the coherent population trapping state, we show that, contrary to the previous belief, mean-field shifts need not limit the conversion efficiency as long as one chooses an adiabatic passage route that compensates the collision mean-field phase shifts and avoids the dynamical unstable regime.

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of $d$-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers, etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations, and the string-order parameter.

We show how to construct a near deterministic CNOT gate using several single photons sources, linear optics, photon number resolving quantum nondemolition detectors, and feed forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate is nondemolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.