Quantum Speed Limit and Optimal Control of Many-Boson Dynamics

We extend the concept of quantum speed limit -- the minimal time needed to perform a driven evolution -- to complex interacting many-body systems. We investigate a prototypical many-body system, a bosonic Josephson junction, at increasing levels of complexity: (a) within the two-mode approximation {corresponding to} a nonlinear two-level system, (b) at the mean-field level by solving the nonlinear Gross-Pitaevskii equation in a double well potential, and (c) at an exact many-body level by solving the time-dependent many-body Schr\"odinger equation. We propose a control protocol to transfer atoms from the ground state of a well to the ground state of the neighbouring well. Furthermore, we show that the detrimental effects of the inter-particle repulsion can be eliminated by means of a compensating control pulse, yielding, quite surprisingly, an enhancement of the transfer speed because of the particle interaction -- in contrast to the self-trapping scenario. Finally, we perform numerical optimisations of both the nonlinear and the (exact) many-body quantum dynamics in order to further enhance the transfer efficiency close to the quantum speed limit.Comment: 5 pages, 3 figures, and supplemental material (4 pages 1 figure

Imaging of Optically Active Defects with Nanometer Resolution.

Point defects significantly influence the optical and electrical properties of solid-state materials due to their interactions with charge carriers, which reduce the band-to-band optical transition energy. There has been a demand for developing direct optical imaging methods that would allow in situ characterization of individual defects with nanometer resolution. Here, we demonstrate the localization and quantitative counting of individual optically active defects in monolayer hexagonal boron nitride using single molecule localization microscopy. By exploiting the blinking behavior of defect emitters to temporally isolate multiple emitters within one diffraction limited region, we could resolve two defect emitters with a point-to-point distance down to ten nanometers. The results and conclusion presented in this work add unprecedented dimensions toward future applications of defects in quantum information processing and biological imaging

High-fidelity quantum driving

The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize these quantum manipulations in the shortest possible time in order to minimize decoherence, and with a large stability against fluctuations of the control parameters. While optimizing a protocol for speed leads to a natural lower bound in the form of the quantum speed limit rooted in the Heisenberg uncertainty principle, stability against parameter variations typically requires adiabatic following of the system. The ultimate goal in quantum control is to prepare a desired state with 100% fidelity. Here we experimentally implement optimal control schemes that achieve nearly perfect fidelity for a two-level quantum system realized with Bose-Einstein condensates in optical lattices. By suitably tailoring the time-dependence of the system's parameters, we transform an initial quantum state into a desired final state through a short-cut protocol reaching the maximum speed compatible with the laws of quantum mechanics. In the opposite limit we implement the recently proposed transitionless superadiabatic protocols, in which the system perfectly follows the instantaneous adiabatic ground state. We demonstrate that superadiabatic protocols are extremely robust against parameter variations, making them useful for practical applications.Comment: 17 pages, 4 figure

Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators

We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums respectively, we derive analytic expressions for the asymptotic behaviour of one and two point correlators. We discuss quenches within the ordered and disordered phases as well as quenches between the phases and to the quantum critical point. We give detailed account of both methods.Comment: 65 pages, 21 figures, some typos correcte

Quench Dynamics in Two-Dimensional Integrable SUSY Models

We analyse quench processes in two dimensional quantum field theories with infinite number of conservation laws which also include fermionic charges that close a N=1 supersymmetric algebra. While in general the quench protocol induces a breaking of supersymmetry, we show that there are particular initial states which ensure the persistence of supersymmetry also for the dynamics out of equilibrium. We discuss the conditions that identify such states and, as application, we present the significant cases of the Tricritical Ising Model and the Sine-Gordon model at its supersymmetric point. We also address the issue of the Generalized Gibbs Ensemble in the presence of fermionic conserved charges

Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench in the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g. by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder

Entanglement entropy in a periodically driven Ising chain

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period \u3c4. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value \u3c4-periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a generalized Gibbs ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state

Detection of bridge emission above 50 GeV from the Crab pulsar with the MAGIC telescopes

The Crab pulsar is the only astronomical pulsed source detected at very high energy (VHE, E>100GeV) gamma-rays. The emission mechanism of VHE pulsation is not yet fully understood, although several theoretical models have been proposed. In order to test the new models, we measured the light curve and the spectra of the Crab pulsar with high precision by means of deep observations. We analyzed 135 hours of selected MAGIC data taken between 2009 and 2013 in stereoscopic mode. In order to discuss the spectral shape in connection with lower energies, 4.6 years of {\it Fermi}-LAT data were also analyzed. The known two pulses per period were detected with a significance of $8.0 \sigma$ and $12.6 \sigma$. In addition, significant emission was found between the two pulses with $6.2 \sigma$. We discovered the bridge emission above 50 GeV between the two main pulses. This emission can not be explained with the existing theories. These data can be used for testing new theoretical models.Comment: 5 pages, 4 figure

Measurement of the Crab Nebula spectrum over three decades in energy with the MAGIC telescopes

The MAGIC stereoscopic system collected 69 hours of Crab Nebula data between October 2009 and April 2011. Analysis of this data sample using the latest improvements in the MAGIC stereoscopic software provided an unprecedented precision of spectral and night-by-night light curve determination at gamma rays. We derived a differential spectrum with a single instrument from 50 GeV up to almost 30 TeV with 5 bins per energy decade. At low energies, MAGIC results, combined with Fermi-LAT data, show a flat and broad Inverse Compton peak. The overall fit to the data between 1 GeV and 30 TeV is not well described by a log-parabola function. We find that a modified log-parabola function with an exponent of 2.5 instead of 2 provides a good description of the data ($\chi^2=35/26$). Using systematic uncertainties of red the MAGIC and Fermi-LAT measurements we determine the position of the Inverse Compton peak to be at (53 $\pm$ 3stat + 31syst -13syst) GeV, which is the most precise estimation up to date and is dominated by the systematic effects. There is no hint of the integral flux variability on daily scales at energies above 300 GeV when systematic uncertainties are included in the flux measurement. We consider three state- of-the-art theoretical models to describe the overall spectral energy distribution of the Crab Nebula. The constant B-field model cannot satisfactorily reproduce the VHE spectral measurements presented in this work, having particular difficulty reproducing the broadness of the observed IC peak. Most probably this implies that the assumption of the homogeneity of the magnetic field inside the nebula is incorrect. On the other hand, the time-dependent 1D spectral model provides a good fit of the new VHE results when considering a 80 {\mu}G magnetic field. However, it fails to match the data when including the morphology of the nebula at lower wavelengths.Comment: accepted by JHEAp, 9 pages, 6 figure

The major upgrade of the MAGIC telescopes, Part II: A performance study using observations of the Crab Nebula

MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes located in the Canary island of La Palma, Spain. During summer 2011 and 2012 it underwent a series of upgrades, involving the exchange of the MAGIC-I camera and its trigger system, as well as the upgrade of the readout system of both telescopes. We use observations of the Crab Nebula taken at low and medium zenith angles to assess the key performance parameters of the MAGIC stereo system. For low zenith angle observations, the standard trigger threshold of the MAGIC telescopes is ~50GeV. The integral sensitivity for point-like sources with Crab Nebula-like spectrum above 220GeV is (0.66+/-0.03)% of Crab Nebula flux in 50 h of observations. The angular resolution, defined as the sigma of a 2-dimensional Gaussian distribution, at those energies is < 0.07 degree, while the energy resolution is 16%. We also re-evaluate the effect of the systematic uncertainty on the data taken with the MAGIC telescopes after the upgrade. We estimate that the systematic uncertainties can be divided in the following components: < 15% in energy scale, 11-18% in flux normalization and +/-0.15 for the energy spectrum power-law slope.Comment: 21 pages, 25 figures, accepted for publication in Astroparticle Physic