Collapse and revival oscillations as a probe for the tunneling amplitude in an ultra-cold Bose gas

We present a theoretical study of the quantum corrections to the revival time due to finite tunneling in the collapse and revival of matter wave interference after a quantum quench. We study hard-core bosons in a superlattice potential and the Bose-Hubbard model by means of exact numerical approaches and mean-field theory. We consider systems without and with a trapping potential present. We show that the quantum corrections to the revival time can be used to accurately determine the value of the hopping parameter in experiments with ultracold bosons in optical lattices.Comment: 10 pages, 12 figures, typos in section 3A correcte

A Strictly Single-Site DMRG Algorithm with Subspace Expansion

We introduce a strictly single-site DMRG algorithm based on the subspace expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS basis enrichment method is sufficient to avoid local minima during the optimisation, similarly to the density matrix perturbation method, but computationally cheaper. Each application of $\hat H$ to $|\Psi\rangle$ in the central eigensolver is reduced in cost for a speed-up of $\approx (d + 1)/2$, with $d$ the physical site dimension. Further speed-ups result from cheaper auxiliary calculations and an often greatly improved convergence behaviour. Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard model compared to the previous single-site method and by up to a factor of 3.9 compared to two-site DMRG. The method is compatible with real-space parallelisation and non-abelian symmetries.Comment: 9 pages, 6 figures; added comparison with two-site DMR

Spectral functions and time evolution from the Chebyshev recursion

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $\sim\frac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.Comment: 12 pages + 6 pages appendix, 11 figure

Exact real-time dynamics of the quantum Rabi model

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of and for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.Comment: 8 pages, 7 figures, published versio

Imaginary-time matrix product state impurity solver for dynamical mean-field theory

We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and less entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three band model in the single and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix product state based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.Comment: 8 pages + 4 pages appendix, 9 figure

Dynamical correlation functions and the quantum Rabi model

We study the quantum Rabi model within the framework of the analytical solution developed in Phys. Rev. Lett. 107,100401 (2011). In particular, through time-dependent correlation functions, we give a quantitative criterion for classifying two regions of the quantum Rabi model, involving the Jaynes-Cummings, the ultrastrong, and deep strong coupling regimes. In addition, we find a stationary qubit-field entangled basis that governs the whole dynamics as the coupling strength overcomes the mode frequency.Comment: 8 pages, 8 figures. Revised version, accepted for publication in Physical Review

Empirical-deterministic prediction of disease and losses caused by Cercospora leaf spots in sugar beets

Neben einer Negativ-Prognose des Epidemiebeginns, epidemieorientierten Bekämpfungsschwellen (BK) und einer wirtschaftlichen Schadensschwelle (WS) beinhaltet das Quaternäre IPS (Integriertes Pflanzenschutz)-Konzept zur Kontrolle des Cercospora-Befalls eine Verlustprognose. Die Verlustprognose erhält ihren praktischen Sinn dadurch, dass die epidemischen Stadien von BK und WS ein Intervall von 5–10 Wochen beinhalten. Die Befallsstärke (BS) zum Zeitpunkt von BK beträgt 0,01%, hingegen toleriert die Zuckerrübe 5% BS ohne wirtschaftlichen Schaden. Die Verlustprognose trifft daher Vorhersagen, ob der künftige Befallsverlauf die WS zum Erntezeitpunkt überschreiten wird und insofern, ob Bekämpfungsmaßnahmen benötigt werden. Das Modell ist als empirisch zu charakterisieren, nachdem die Herleitung der Verlustprognose auf 105 Feldstudien (Deutschland und Österreich) einer Epidemie von Cercospora beticola und ihren ertraglichen Konsequenzen beruht. Des Weiteren ist das Modell deterministisch, weil die Krankheitssituation zum gegenwärtigen Zeitpunkt die Prognose der zukünftigen Befallsentwicklung determiniert. In jeglicher Feldstudie implizierte der Epidemieverlauf eine Phase geringer Progression der BS, gefolgt von einem steilen Anstieg mit Tendenz zu einem Maximum des Befalls. Die Prognose des Befallsverlaufes in Submodul (i) basiert daher auf der sigmoiden Funktion „BS = BSmax/(1+exp(-(CW-a)/b))“. Demnach hängt die Kalkulation von BS von der Kalenderwoche (CW) und den Variablen BSmax, a und b ab. Letztere werden geschätzt mittels mathematischer Funktionen in Abhängigkeit vom Epidemiebeginn (CWBH5%), definiert als jene Kalenderwoche, zu der eine Befallshäufigkeit (BH) der Blätter von ≥5% eintritt. Die Verluste sind hierbei abhängig von der Fläche unter der Befallskurve (AUDPC). Für die Kalkulation der AUDPC-Werte finden die BS-Werte Verwendung, wie mit Submodul (i) geschätzt. Die Prognose von Verlusten an Rüben- und Bereinigtem Zuckerertrag geschieht auf Basis von Befalls-Verlust-Relationen (Submodul ii, iii). Die wirtschaftliche Schadensschwelle ist definiert als AUDPC=1, entsprechend einem Verlust an Bereinigtem Zuckerertrag von ≉1,5%. Folglich sind Fungizidapplikationen entbehrlich, sofern der Befall bis zur Ernte <AUDPC=1 verbleibt. Alle Berechnungen zur Modellentwicklung haben die Sorten-Anfälligkeiten „hoch“ und „gering“ berücksichtigt. Darüber hinaus benötigt die Verlustprognose Angaben über den zu erwartenden Ertrag und den voraussichtlichen Erntetermin. Diagnose und Erhebung des Befalls sind Voraussetzungen für die Anwendung des Modells, da die Einschätzung der zukünftigen Entwicklung auf einer Konkretisierung der gegenwärtigen Krankheitssituation gründet.Besides negative-prognosis of epidemic onset, epidemic spraying thresholds (ET) and economic damage threshold (DT), loss prediction is a part of the Quaternary IPM (Integrated Pest Management)-concept to control Cercospora leaf spots (CLS). The practical need of loss prediction originates from the fact, that disease levels of ET and DT implicate an interval of 5–10 weeks. Disease severity (DS) of ET for an initial treatment is 0.01, whereas the beet plant may tolerate 5% DS without economic losses. Therefore, in order to assess the necessity of control measures, the model is focused on to predict whether DS will exceed DT at harvest time. The model is empiric, because loss prediction was derived from epidemic and yield data of 105 field trials conducted in Germany and Austria (1993-2000). The model is also deterministic, because the disease incidence at present date and cultivar susceptibility determine the prediction of future disease progress. In every field study, course of DS involved a period of slight followed by a more or less steep increase tending to a maximum of DS. The incidence prediction in submodel (i), therefore, was based on the sigmoidal function “DS = DSmax/(1+exp(-(CW-a)/b))”, where the calculation of DS is depending on the actual calendar week (CW) and the variables DSmax, a and b. These variables are estimated through curve fittings depending on the epidemic onset (CWDIL5%), respectively the calendar week when disease incidence per leaf (DIL) increases to ≥5%. Losses are dependent on the area under disease progress curve (AUDPC). Creation of AUDPC-values is based on the DS-values as calculated by submodel (i). The prediction of losses is performed through disease-loss-relationships (submodel ii, iii). The economic damage threshold is defined as AUDPC=1, equal to a loss of ≉1.5% sugar. Therefore fungicide sprays may be avoided, if the AUDPC remains beneath 1 till scheduled harvest time. All calculations for model development involved two grades of cultivar susceptibility, either highly or low susceptible. Moreover, prediction of yield loss needs indications of expected yield and scheduled harvest time. Proper diagnosis and disease scoring is a precondition for error free functioning of the model, since future progress is estimated by an assessment of the actual incidence situation

Solving nonequilibrium dynamical mean-field theory using matrix product states

We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix product states (MPS). This allows us to treat much larger bath sizes and by that reach substantially longer times (factor $\sim$ 2 -- 3) than with exact diagonalization. We show that the star geometry of the underlying impurity problem can have substantially better entanglement properties than the previously favoured chain geometry. This has immense consequences for the efficiency of an MPS-based description of general impurity problems: in the case of equilibrium DMFT, it leads to an orders-of-magnitude speedup. We introduce an approximation for the two-time hybridization function that uses time-translational invariance, which can be observed after a certain relaxation time after a quench to a time-independent Hamiltonian.Comment: 11 pages + 3 pages appendix, 14 figure

Second Harmonic Generation from Phononic Epsilon-Near-Zero Berreman Modes in Ultrathin Polar Crystal Films

Immense optical field enhancement was predicted to occur for the Berreman mode in ultrathin films at frequencies in the vicinity of epsilon near zero (ENZ). Here, we report the first experimental proof of this prediction in the mid-infrared by probing the resonantly enhanced second harmonic generation (SHG) at the longitudinal optic phonon frequency from a deeply subwavelength-thin aluminum nitride (AlN) film. Employing a transfer matrix formalism, we show that the field enhancement is completely localized inside the AlN layer, revealing that the observed SHG signal of the Berreman mode is solely generated in the AlN film. Our results demonstrate that ENZ Berreman modes in intrinsically low-loss polar dielectric crystals constitute a promising platform for nonlinear nanophotonic applications