Identifying dynamical systems with bifurcations from noisy partial observation

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically integrate information in noisy time-series data from partial observations. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations, and the learned systems are shown to robustly inherit the bifurcation structure.Comment: 16 pages, 6 figure

Many-body localization and thermalization in the full probability distribution function of observables

We investigate the relation between thermalization following a quantum quench and many-body localization in quasiparticle space in terms of the long-time full distribution function of physical observables. In particular, expanding on our recent work [E. Canovi {\em et al.}, Phys. Rev. B {\bf 83}, 094431 (2011)], we focus on the long-time behavior of an integrable XXZ chain subject to an integrability-breaking perturbation. After a characterization of the breaking of integrability and the associated localization/delocalization transition using the level spacing statistics and the properties of the eigenstates, we study the effect of integrability-breaking on the asymptotic state after a quantum quench of the anisotropy parameter, looking at the behavior of the full probability distribution of the transverse and longitudinal magnetization of a subsystem. We compare the resulting distributions with those obtained in equilibrium at an effective temperature set by the initial energy. We find that, while the long time distribution functions appear to always agree {\it qualitatively} with the equilibrium ones, {\it quantitative} agreement is obtained only when integrability is fully broken and the relevant eigenstates are diffusive in quasi-particle space.Comment: 18 pages, 11 figure

A quantum beam splitter for atoms

An interferometric method is proposed to controllably split an atomic condensate in two spatial components with strongly reduced population fluctuations. All steps in our proposal are in current use in cold atom laboratories, and we show with a theoretical calculation that our proposal is very robust against imperfections of the interferometer.Comment: 6 pages, 3 figures, revtex

Nonclassical correlations of phase noise and photon number in quantum nondemolition measurements

The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime, quantization appears as a weak modulation of measurement probability. In this regime, the measurement result is strongly correlated with the amount of phase decoherence introduced by the measurement interaction. In particular, the accidental observation of half integer photon numbers preserves phase coherence in the light field, while the accidental observation of quantized values increases decoherence. The quantum mechanical nature of this correlation is discussed and the implications for the general interpretation of quantization are considered.Comment: 16 pages, 5 figures, final version to be published in Phys. Rev. A, Clarifications of the nature of the measurement result and the noise added in section I

Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice

Strong correlations can dramatically modify the thermodynamics of a quantum many-particle system. Especially intriguing behaviour can appear when the system adiabatically enters a strongly correlated regime, for the interplay between entropy and strong interactions can lead to counterintuitive effects. A well known example is the so-called Pomeranchuk effect, occurring when liquid 3He is adiabatically compressed towards its crystalline phase. Here, we report on a novel anomalous, isentropic effect in a spin mixture of attractively interacting fermionic atoms in an optical lattice. As we adiabatically increase the attraction between the atoms we observe that the gas, instead of contracting, anomalously expands. This expansion results from the combination of two effects induced by pair formation in a lattice potential: the suppression of quantum fluctuations as the attraction increases, which leads to a dominant role of entropy, and the progressive loss of the spin degree of freedom, which forces the gas to excite additional orbital degrees of freedom and expand to outer regions of the trap in order to maintain the entropy. The unexpected thermodynamics we observe reveal fundamentally distinctive features of pairing in the fermionic Hubbard model.Comment: 6 pages (plus appendix), 6 figure

Local asymptotic normality for qubit states

We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations T_{n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian set-up is also optimal within the pointwise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.Comment: 16 pages, 3 figures, published versio

The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise

Quantum noise correlations have been employed in several areas in physics including condensed matter, quantum optics and ultracold atom to reveal non-classical states of the systems. So far, such analysis mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool to characterize and study the non-equilibrium dynamics of one dimensional system. We consider the Ramsey sequence of one dimensional, two-component bosons, and obtain simple, analytical expressions of time evolutions of the full distribution functions for this strongly-correlated, many-body system. The analysis can also be directly applied to the evolution of interference patterns between two one dimensional quasi-condensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that one dimensional dynamics in these systems exhibits the phenomenon known as "prethermalization", where the observables of {\it non-equilibrium}, long-time transient states become indistinguishable from those of thermal {\it equilibrium} states.Comment: 22 pages, 11 figures+appendi

Antiferromagnetism of SrFe2As2 studied by Single-Crystal 75As-NMR

We report results of 75As nuclear magnetic resonance (NMR) experiments on a self-flux grown high-quality single crystal of SrFe2As2. The NMR spectra clearly show sharp first-order antiferromagnetic (AF) and structural transitions occurring simultaneously. The behavior in the vicinity of the transition is compared with our previous study on BaFe2As2. No significant difference was observed in the temperature dependence of the static quantities such as the AF splitting and electric quadrupole splitting. However, the results of the NMR relaxation rate revealed difference in the dynamical spin fluctuations. The stripe-type AF fluctuations in the paramagnetic state appear to be more anisotropic in BaFe2As2 than in SrFe2As2.Comment: 4 pages, 5 figures; discussion revised; accepted for publication in J. Phys. Soc. Jp

Paramagnetic Phase of a Heavy-Fermion Compound, CeFePO, Probed by 57Fe M\"{o}ssbauer Spectroscopy

57Fe M\"{o}ssbauer spectroscopy was applied to an iron-based layered compound CeFePO. At temperatures from 9.4 to 293 K, no magnetic splitting was observed in the M\"ossbauer spectra of CeFePO indicating a paramagnetic phase of the Fe magnetic sublattice. All the spectra were fitted with a small quadrupole splitting, and the Debye temperature of CeFePO was found to be \sim448 K. The isomer shift at room temperature, 0.32 mm/s, was almost equal to those of LnFeAsO (Ln = La, Ce, Sm). Comparing s-electron density using the isomer shifts and unit cell volumes, it was found that the Fe of CeFePO has a similar valence state to other layered iron-based quaternary oxypnictides except LaFePO

Understanding the dynamics of triple helix interactions. The case of English Higher Education Institutions

This paper examines the evolution of the dynamics of the triple helix interactions exemplified by the case of Higher Education Institutions (HEIs) in England. Results highlight the persisting heterogeneity between HEIs in their combination, geography and evolution of triple helix interactions, particularly between research oriented universities and newer universities with strong teaching orientations