Synchronization of weakly perturbed Markov chain oscillators

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained, symbolic dynamics. In contrast to limit cycle oscillators which are weakly perturbed by noise, the stochasticity in such systems may be strong and more complicated system topologies than the circle can be considered. Here we employ second order, time dependent perturbation theory to derive expressions for the mean frequency and phase diffusion constant of discrete state oscillators coupled or driven through weakly time dependent transition rates. We also describe a method of global control to optimize the response of the mean frequency in complex transition networks.Comment: 16 pages, 7 figure

Creating Artificial Ice States Using Vortices in Nanostructured Superconductors

We demonstrate that it is possible to realize vortex ice states that are analogous to square and kagome ice. With numerical simulations, we show that the system can be brought into a state that obeys either global or local ice rules by applying an external current according to an annealing protocol. We explore the breakdown of the ice rules due to disorder in the nanostructure array and show that in square ice, topological defects appear along grain boundaries, while in kagome ice, individual defects appear. We argue that the vortex system offers significant advantages over other artificial ice systems.Comment: 4 pages, 4 postscript figures; version to appear in Phys. Rev. Let

From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking

The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. In this paper, we make the following contributions by exploiting a connection between uncertainty relations and low-distortion embeddings of L2 into L1. We introduce the notion of metric uncertainty relations and connect it to low-distortion embeddings of L2 into L1. A metric uncertainty relation also implies an entropic uncertainty relation. We prove that random bases satisfy uncertainty relations with a stronger definition and better parameters than previously known. Our proof is also considerably simpler than earlier proofs. We apply this result to show the existence of locking schemes with key size independent of the message length. We give efficient constructions of metric uncertainty relations. The bases defining these metric uncertainty relations are computable by quantum circuits of almost linear size. This leads to the first explicit construction of a strong information locking scheme. Moreover, we present a locking scheme that is close to being implementable with current technology. We apply our metric uncertainty relations to exhibit communication protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio

Transcranial Electric Stimulation Entrains Cortical Neuronal Populations in Rats

Low intensity electric fields have been suggested to affect the ongoing neuronal activity in vitro and in human studies. However, the physiological mechanism of how weak electrical fields affect and interact with intact brain activity is not well understood. We performed in vivo extracellular and intracellular recordings from the neocortex and hippocampus of anesthetized rats and extracellular recordings in behaving rats. Electric fields were generated by sinusoid patterns at slow frequency (0.8, 1.25 or 1.7 Hz) via electrodes placed on the surface of the skull or the dura. Transcranial electric stimulation (TES) reliably entrained neurons in widespread cortical areas, including the hippocampus. The percentage of TES phase-locked neurons increased with stimulus intensity and depended on the behavioral state of the animal. TES-induced voltage gradient, as low as 1 mV/mm at the recording sites, was sufficient to phase-bias neuronal spiking. Intracellular recordings showed that both spiking and subthreshold activity were under the combined influence of TES forced fields and network activity. We suggest that TES in chronic preparations may be used for experimental and therapeutic control of brain activity

Real-Time Source Independent Quantum Random Number Generator with Squeezed States

Random numbers are a fundamental ingredient for many applications including simulation, modelling and cryptography. Sound random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. We demonstrate a real-time self-testing source independent quantum random number generator (QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source; only the detection device is trusted. We use a homodyne detection to alternatively measure the Q and P conjugate quadratures of our source. Using the entropic uncertainty relation, measurements on P allow us to estimate a bound on the min-entropy of Q conditioned on any classical or quantum side information that a malicious eavesdropper may detain. This bound gives the minimum number of secure bits we can extract from the Q measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed state and we compare its performance with a QRNG using thermal states. The real-time bit rate was 8.2 kb/s when using the squeezed source and between 5.2-7.2 kb/s when the thermal state source was used.Comment: 11 pages, 9 figure

On the Classical Model for Microwave Induced Escape from a Josephson Washboard Potential

We revisit the interpretation of earlier low temperature experiments on Josephson junctions under the influence of applied microwaves. It was claimed that these experiments unambiguously established a quantum phenomenology with discrete levels in shallow wells of the washboard potential, and macroscopic quantum tunneling. We here apply the previously developed classical theory to a direct comparison with the original experimental observations, and we show that the experimental data can be accurately represented classically. Thus, our analysis questions the necessity of the earlier quantum mechanical interpretation.Comment: 4 pages, one table, three figures. Submitted for publication on December 14, 200

Threshold Dynamics of a Semiconductor Single Atom Maser

We demonstrate a single-atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high quality factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account

Alpha-band rhythms in visual task performance: phase-locking by rhythmic sensory stimulation

Oscillations are an important aspect of neuronal activity. Interestingly, oscillatory patterns are also observed in behaviour, such as in visual performance measures after the presentation of a brief sensory event in the visual or another modality. These oscillations in visual performance cycle at the typical frequencies of brain rhythms, suggesting that perception may be closely linked to brain oscillations. We here investigated this link for a prominent rhythm of the visual system (the alpha-rhythm, 8-12 Hz) by applying rhythmic visual stimulation at alpha-frequency (10.6 Hz), known to lead to a resonance response in visual areas, and testing its effects on subsequent visual target discrimination. Our data show that rhythmic visual stimulation at 10.6 Hz: 1) has specific behavioral consequences, relative to stimulation at control frequencies (3.9 Hz, 7.1 Hz, 14.2 Hz), and 2) leads to alpha-band oscillations in visual performance measures, that 3) correlate in precise frequency across individuals with resting alpha-rhythms recorded over parieto-occipital areas. The most parsimonious explanation for these three findings is entrainment (phase-locking) of ongoing perceptually relevant alpha-band brain oscillations by rhythmic sensory events. These findings are in line with occipital alpha-oscillations underlying periodicity in visual performance, and suggest that rhythmic stimulation at frequencies of intrinsic brain-rhythms can be used to reveal influences of these rhythms on task performance to study their functional roles

Single microwave-photon detector using an artificial Λ\Lambda-type three-level system

Single photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here, we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an "impedance-matched" artificial $\Lambda$ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. We attain a single-photon detection efficiency of $0.66 \pm 0.06$ with a reset time of $\sim 400$~ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.Comment: 5 pages (4 figures) + 4 pages (5 figures