Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms

We present a detailed analysis of the dynamical response of ultra-cold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stoferle et al [Phys. Rev. Lett. 92, 130403 (2004)] we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Omega. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator to the superfluid regime. Our results produce many of the features seen in the experiment, namely a broad response in the superfluid regime, and narrow discrete resonances in the Mott-insulator regime. We identify several signatures of the superfluid-Mott insulator transition that are manifested in the spectrum as it evolves from one limit to the other.Comment: 18 pages and 12 figures; Some improved results and additional references. To appear in a special issue of New J. Phy

The Optical Excitation of Zigzag Carbon Nanotubes with Photons Guided in Nanofibers

We consider the excitation of electrons in semiconducting carbon nanotubes by photons from the evanescent field created by a subwavelength-diameter optical fiber. The strongly changing evanescent field of such nanofibers requires dropping the dipole approximation. We show that this leads to novel effects, especially a high dependence of the photon absorption on the relative orientation and geometry of the nanotube-nanofiber setup in the optical and near infrared domain. In particular, we calculate photon absorption probabilities for a straight nanotube and nanofiber depending on their relative angle. Nanotubes orthogonal to the fiber are found to perform much better than parallel nanotubes when they are short. As the nanotube gets longer the absorption of parallel nanotubes is found to exceed the orthogonal nanotubes and approach 100% for extremely long nanotubes. In addition, we show that if the nanotube is wrapped around the fiber in an appropriate way the absorption is enhanced. We find that optical and near infrared photons could be converted to excitations with efficiencies that may exceed 90%. This may provide opportunities for future photodetectors and we discuss possible setups.Comment: 14 pages, 14 figure

Singlet Generation in Mixed State Quantum Networks

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of `quantum preprocessing' on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks.Comment: 17 pages, 21 figure

Long Distance Entanglement Generation in 2D Networks

We consider 2D networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank two states. By using this method and combining it with the concept of percolation we also show that the generation of long distance entanglement is possible with rank three states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application on networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol can not generate a singlet between any two nodes. On the other hand, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.Comment: 10 pages, 9 figures, 1 tabl

Probing microscopic models for system-bath interactions via parametric driving

We show that strong parametric driving of a quantum harmonic oscillator coupled to a thermal bath allows one to distinguish between different microscopic models for the oscillator-bath coupling. We consider a bath with an Ohmic spectral density and a model where the system-bath interaction can be tuned continuously between position and momentum coupling via the coupling angle $\alpha$. We derive a master equation for the reduced density operator of the oscillator in Born-Markov approximation and investigate its quasi-steady state as a function of the driving parameters, the temperature of the bath and the coupling angle $\alpha$. We find that the time-averaged variance of position and momentum exhibits a strong dependence on these parameters. In particular, we identify parameter regimes that maximise the $\alpha$-dependence and provide an intuitive explanation of our results.Comment: 13 pages, 8 figure

Entanglement consumption of instantaneous nonlocal quantum measurements

Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty an infinite amount of entanglement must be distributed initially and all this entanglement is necessarily consumed. In this work we sharpen the characterisation of instantaneous nonlocal measurements by explicitly devising schemes in which only a finite amount of the initially distributed entanglement is ever utilised. This enables us to determine an upper bound to the average consumption for the most general cases of nonlocal measurements. This includes the tasks of state verification, where the measurement verifies if the system is in a given state, and verification measurements of a general set of eigenstates of an observable. Despite its finiteness the growth of entanglement consumption is found to display an extremely unfavourable exponential of an exponential scaling with either the number of qubits needed to contain the Schmidt rank of the target state or total number of qubits in the system for an operator measurement. This scaling is seen to be a consequence of the combination of the generic exponential scaling of unitary decompositions combined with the highly recursive structure of our scheme required to overcome the no-signalling constraint of relativistic causality.Comment: 32 pages and 14 figures. Updated to published versio

Efficient generation of graph states for quantum computation

We present an entanglement generation scheme which allows arbitrary graph states to be efficiently created in a linear quantum register via an auxiliary entangling bus. The dynamics of the entangling bus is described by an effective non-interacting fermionic system undergoing mirror-inversion in which qubits, encoded as local fermionic modes, become entangled purely by Fermi statistics. We discuss a possible implementation using two species of neutral atoms stored in an optical lattice and find that the scheme is realistic in its requirements even in the presence of noise.Comment: 4 pages, 3 figures, RevTex 4; v2 - Major changes and new result

What is a quantum simulator?

Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use of quantum simulators. Our answers address two important areas. First, the difference between an operation termed simulation and another termed computation. This distinction is related to the purpose of an operation, as well as our confidence in and expectation of its accuracy. Second, the threshold between quantum and classical simulations. Throughout, we provide a perspective on the achievements and directions of the field of quantum simulation.Comment: 13 pages, 2 figure

Optical control of the current-voltage relation in stacked superconductors

We simulate the current-voltage relation of short layered superconductors, which we model as stacks of capacitively coupled Josephson junctions. The system is driven by external laser fields, in order to optically control the voltage drop across the junction. We identify parameter regimes in which supercurrents can be stabilised against thermally induced phase slips, thus reducing the effective voltage across the superconductor. Furthermore, single driven Josephson junctions are known to exhibit phase-locked states, where the superconducting phase is locked to the driving field. We numerically observe their persistence in the presence of thermal fluctuations and capacitive coupling between adjacent Josephson junctions. Our results indicate how macroscopic material properties can be manipulated by exploiting the large optical nonlinearities of Josephson plasmons.Comment: 7 pages, 7 figure