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The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph. Fluctuations are quantified by the number of traversals of the random walk across edges during a fixed time window, more precisely, by the corresponding counting statistics. The variance-to-mean ratio of the counting statistics is typically lowered if two end vertices of an edge belong to different clusters as defined by spectral clustering. In particular, we relate the fluctuations to the algebraic connectivity and the Fiedler vector of the graph. Building on these results we suggest a centrality score based on fluctuations of random walks. Our findings imply that local fluctuations of continuous-time Markov processes on discrete state space depend strongly on the global topology of the underlying graph in addition to the specific transition rates., Comment: 7 pages, 3 figures

A fundamental question in quantum transport is how quantum coherence influences charge transfer through nanostructures. We address this issue for linear triple quantum dots by comparison of a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics for coherent and sequential charge tunneling, respectively. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of large coupling to the drain reservoir, can be used to unambiguously evidence coherent processes involved in charge transport across triple quantum dots. Our analytical results are obtained by using the characteristic polynomial approach to full counting statistics.

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose performance is optimal when operating in the partially coherent regime, as opposed to the extremes of fully coherent or classical regimes. The algorithm builds on continuous-time quantum stochastic walks (QSWs) on graphs and the algorithmic performance is quantified by the distinguishing power (DIP) between non-isomorphic graphs. The QSW explores the entire graph and acquires information about the underlying structure, which is extracted by monitoring stochastic jumps across an auxiliary edge. The resulting counting statistics of stochastic jumps is used to identify the spectrum of the dynamical generator of the QSW, serving as a novel graph invariant, based on which non-isomorphic graphs are distinguished. We provide specific examples of non-isomorphic graphs that are only distinguishable by QSWs in the presence of decoherence., Comment: To appear in Physical Review A, 6 pages, 3 figures

Nitrogen-vacancy (NV) centers in diamond have emerged as valuable tools for sensing and polarizing spins. Motivated by potential applications in chemistry, biology, and medicine, we show that NV-based sensors are capable of detecting single spin targets even if they undergo diffusive motion in an ambient thermal environment. Focusing on experimentally relevant diffusion regimes, we derive an effective model for the NV-target interaction, where parameters entering the model are obtained from numerical simulations of the target motion. The practicality of our approach is demonstrated by analyzing two realistic experimental scenarios: (i) time-resolved sensing of a fluorine nuclear spin bound to an N-heterocyclic carbene-ruthenium (NHC-Ru) catalyst that is immobilized on the diamond surface and (ii) detection of an electron spin label by an NV center in a nanodiamond, both attached to a vibrating chemokine receptor in thermal motion. We find in particular that the detachment of a fluorine target from the NHC-Ru carrier molecule can be monitored with a time resolution of a few seconds., Comment: 14 pages, 8 figures, supplemental material

We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a double-well potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via density-density interactions with the bosons. The system is analogous to a two-level atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are selected in both energy and momentum by adjusting the impurity's potential. We show how to use the detector to observe coherent density waves and to measure temperatures of the Bose gas down to the nano-Kelvin regime. We analyze how our scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision from a single experimental run., Comment: 11+4 pages, 7 figures

Environmental noise usually hinders the efficiency of charge transport through coherent quantum systems; an exception is dephasing-assisted transport (DAT). We show that linear triple quantum dots in a transport configuration and subjected to pure dephasing exhibit DAT if the coupling to the drain reservoir exceeds a threshold. DAT occurs for arbitrarily weak dephasing and the enhancement can be directly controlled by the coupling to the drain. Moreover, for specific settings, the enhanced current is accompanied by a reduction in relative shot noise. We identify the quantum Zeno effect and long-distance tunnelling as underlying dynamical processes involved in dephasing-assisted and -suppressed transport. Our analytical results are obtained by using the density matrix formalism and the characteristic polynomial approach to full counting statistics., Comment: To appear in New Journal of Physics, 20 pages, 5 figures

We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the transition, parametrized by cumulants, is the only available information about the system. We present an analytical method for reconstructing generators of the time evolution of the system compatible with the observations. The practicality of the reconstruction method is demonstrated by the examples of a laser-driven atom and the kinetics of enzyme-catalyzed reactions. Moreover, we propose cumulant-based criteria for testing the non-classicality and non-Markovianity of the time evolution, and lower bounds for the system dimension. Our analytical results rely on the close connection between the cumulants of the counting statistics and the characteristic polynomial of the generator, which takes the role of the cumulant generating function., Comment: 18 pages, 2 figures

Measuring heat flow through nanoscale systems poses formidable practical difficulties as there is no `ampere meter' for heat. We propose to overcome this problem by realizing heat transport through a chain of trapped ions. Laser cooling the chain edges to different temperatures induces a current of local vibrations (vibrons). We show how to efficiently control and measure this current, including fluctuations, by coupling vibrons to internal ion states. This demonstrates that ion crystals provide a suitable platform for studying quantum transport, e.g., through thermal analogues of quantum wires and quantum dots. Notably, ion crystals may give access to measurements of the elusive large fluctuations of bosonic currents and the onset of Fourier's law. These results are supported by numerical simulations for a realistic implementation with specific ions and system parameters., Comment: closer to published version

We study transfer of a quantum state through XX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material., Comment: 7 pages, 3 figures + spinGUIn description and Matlab files iepsolve.m, spinGUIn.fig, spinGUIn.p

Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas., Comment: 7 pages, 3 figures

We study transport of fermions in a system composed of a short optical lattice connecting two finite atomic reservoirs at different filling levels. The average equilibration current through the optical lattice, for strong lattice-reservoir coupling and finite temperatures, is calculated within the Landauer formalism using a nonequilibrium Green's functions approach. We moreover determine quantum and thermal fluctuations in the transport and find significant shot-to-shot deviations from the average equilibration current. We show how to control the atomic current by engineering specific optical lattice potentials without requiring site-by-site manipulations and suggest the realization of a single level model. Based on this model we discuss the blocking effect on the atomic current resulting from weak interactions between the fermions., Comment: 8 pages, 5 figures

Using near-exact numerical simulations we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas which allows one to measure properties of the Bose gas non-destructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the cross-over of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas and the effects on the impurity in both of these strongly-interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas, giving an experimentally controllable example of noise-enhanced quantum transport., Comment: 11 pages, 7 figures

We present an analysis of Bose-Fermi mixtures in optical lattices for the case where the lattice potential of the fermions is tilted and the bosons (in the superfluid phase) are described by Bogoliubov phonons. It is shown that the Bogoliubov phonons enable hopping transitions between fermionic Wannier-Stark states; these transitions are accompanied by energy dissipation into the superfluid and result in a net atomic current along the lattice. We derive a general expression for the drift velocity of the fermions and find that the dependence of the atomic current on the lattice tilt exhibits negative differential conductance and phonon resonances. Numerical simulations of the full dynamics of the system based on the time-evolving block decimation algorithm reveal that the phonon resonances should be observable under the conditions of a realistic measuring procedure., Comment: 8 pages, 5 figures

We study the interaction-induced localization -- the so-called self-trapping -- of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -- unlike repulsive impurities -- attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value. Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself., Comment: 7 pages, 5 figures

We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter., Comment: 25 pages, 6 figures

We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise model we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e., expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five qubit linear cluster state and a Greenberger-Horne-Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained., Comment: 27 pages, 13 figures. To appear in New Journal of Physics

We consider the dephasing of two internal states |0> and |1> of a trapped impurity atom, a so-called atomic quantum dot (AQD), where only state |1> couples to a Bose-Einstein condensate (BEC). A direct relation between the dephasing of the internal states of the AQD and the temporal phase fluctuations of the BEC is established. Based on this relation we suggest a scheme to probe BEC phase fluctuations nondestructively via dephasing measurements of the AQD. In particular, the scheme allows to trace the dependence of the phase fluctuations on the trapping geometry of the BEC., Comment: 11 pages, 3 figures