We provide a generalization of the normal mode decomposition for nonsymmetric or locality constrained situations. This allows, for instance, to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to elementary pairs into which all correlations are condensed. Similarly, it enables us to decouple the interaction parts of multimode channels into single-mode and pair interactions where the latter are shown to be a clear signature of squeezing between system and environment. In mathematical terms the result is a canonical matrix form with respect to real symplectic equivalence transformations.

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, $g$, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal ($g\to \infty$), an insulator ($g\to 0$), and the metal-insulator transition ($g\to g_c$) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions ($d\le 2$). Several examples are discussed in detail.

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.

A connection between the state estimation problem and the separability problem is noticed and exploited to find efficient numerical algorithms to solve the first one. Based on these ideas, we also derive a systematic method to obtain upper bounds on the maximum local fidelity when the states are distributed among several distant parties.

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent ${\alpha }_c=0.402\pm 0.002$ marks a transition to a nonmonotonic underdamped phase. The critical exponent ${\alpha }_R=0.441\dots$ marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.

We consider a boundary between a Mott insulator and a superfluid region of a Bose-Hubbard model at unit filling. Initially both regions are decoupled and cooled to their respective ground states. We show that, after switching on a small tunneling rate between both regions, all particles of the Mott region migrate to the superfluid area. This migration takes place whenever the difference between the chemical potentials of both regions is less than the maximal energy of any eigenmode of the superfluid. We verify our results numerically with density matrix renormalization group simulations and explain them analytically with a master equation approximation, finding good agreement between both approaches. Finally we carry out a feasibility study for the observation of the effect in coupled arrays of microcavities and optical lattices.

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid ($S$) core and a rigidly rotating normal ($N$) gas. The interface between the two phases is characterized by a density discontinuity $n_N/n_S=0.85$, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.

We consider a gas of noninteracting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the Středa formula.

We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does not realize the ideal functionality and, therefore, does not satisfy the demands for universally composable security. Moreover, through a comparison within a small restricted bias range, we show that an arbitrary QCF is distinguishable from a black-boxed coin flip unless it is unbiased on both sides of parties against insensitive cheating. We also point out the difficulty in developing cheat-sensitive quantum bit commitment in terms of the uncomposability of a QCF.

In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson’s “coupling from the past” approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the Markov chain Monte Carlo dynamics from parts of the configurations (patches) on increasing length scales, and it allows us to generate “exact samples” of the Boltzmann distribution, which are rigorously proven to be uncorrelated with the initial condition. We validate our approach in the two-dimensional Ising spin glass on lattices of size $64\times 64$.

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits—three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length $\mathcal{L}$. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as $1/{\mathcal{L}}^2$. For negative scattering length a condensate of size $\mathcal{L}$ may exist as a metastable state. These findings are generalized to anisotropic traps.

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of gray solitons, or density notches, which serve as an experimental signature of this phenomenon.

We present a scheme for linear optical quantum computation that is highly robust to imperfect single photon sources and inefficient detectors. In particular we show that if the product of the detector efficiency with the source efficiency is greater than $2/3$, then efficient linear optical quantum computation is possible. This high threshold is achieved within the cluster state paradigm for quantum computation.

We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is super-Ohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that performance better than classical is possible with a super-Ohmic environment, with no a priori knowledge of the energy spectrum.

Quantum chaotic maps can efficiently generate pseudorandom states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the system. We show that such multipartite entanglement is robust, in the sense that, when realistic noise is considered, distillable entanglement of bipartitions remains almost maximal up to a noise strength that drops only polynomially with the number of qubits.

We derive the collective low-energy excitations of the quantum phase model of interacting lattice bosons within the superfluid state using a dynamical variational approach. We recover the well-known sound (or Goldstone) mode and derive a gapped (Higgs-type) mode that was overlooked in previous studies of the quantum phase model. This mode is relevant to ultracold atoms in a strong optical lattice potential. We predict the signature of the gapped mode in lattice modulation experiments and show how it evolves with increasing interaction strength.

The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.

We present a new measurement of the Newtonian gravitational constant $G$ based on cold-atom interferometry. Freely falling samples of laser-cooled rubidium atoms are used in a gravity gradiometer to probe the field generated by nearby source masses. In addition to its potential sensitivity, this method is intriguing as gravity is explored by a quantum system. We report a value of $G=6.667\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$, estimating a statistical uncertainty of $\pm 0.011\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$ and a systematic uncertainty of $\pm 0.003\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement accuracy below the 100 ppm level.

Dense packings of freely jointed chains of tangent hard spheres are produced by a novel Monte Carlo method. Within statistical uncertainty, chains reach a maximally random jammed (MRJ) state at the same volume fraction as packings of single hard spheres. A structural analysis shows that as the MRJ state is approached (i) the radial distribution function for chains remains distinct from but approaches that of single hard sphere packings quite closely, (ii) chains undergo progressive collapse, and (iii) a small but increasing fraction of sites possess highly ordered first coordination shells.