Hierarchies of Frequentist Bounds for Quantum Metrology: From Cram\'er-Rao to Barankin

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cram\'er-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.Comment: 6+7 pages, 1+1 figure

Three-dimensional Models of Core-collapse Supernovae From Low-mass Progenitors With Implications for Crab

We present 3D full-sphere supernova simulations of non-rotating low-mass (~9 Msun) progenitors, covering the entire evolution from core collapse through bounce and shock revival, through shock breakout from the stellar surface, until fallback is completed several days later. We obtain low-energy explosions [~(0.5-1.0)x 10^{50} erg] of iron-core progenitors at the low-mass end of the core-collapse supernova (LMCCSN) domain and compare to a super-AGB (sAGB) progenitor with an oxygen-neon-magnesium core that collapses and explodes as electron-capture supernova (ECSN). The onset of the explosion in the LMCCSN models is modelled self-consistently using the Vertex-Prometheus code, whereas the ECSN explosion is modelled using parametric neutrino transport in the Prometheus-HOTB code, choosing different explosion energies in the range of previous self-consistent models. The sAGB and LMCCSN progenitors that share structural similarities have almost spherical explosions with little metal mixing into the hydrogen envelope. A LMCCSN with less 2nd dredge-up results in a highly asymmetric explosion. It shows efficient mixing and dramatic shock deceleration in the extended hydrogen envelope. Both properties allow fast nickel plumes to catch up with the shock, leading to extreme shock deformation and aspherical shock breakout. Fallback masses of <~5x10^{-3} Msun have no significant effects on the neutron star (NS) masses and kicks. The anisotropic fallback carries considerable angular momentum, however, and determines the spin of the newly-born NS. The LMCCSNe model with less 2nd dredge-up results in a hydrodynamic and neutrino-induced NS kick of >40 km/s and a NS spin period of ~30 ms, both not largely different from those of the Crab pulsar at birth.Comment: 47 pages, 27 figures, 6 tables; minor revisions, accepted by MNRA

Local Detection of Quantum Correlations with a Single Trapped Ion

As one of the most striking features of quantum mechanics, quantum correlations are at the heart of quantum information science. Detection of correlations usually requires access to all the correlated subsystems. However, in many realistic scenarios this is not feasible since only some of the subsystems can be controlled and measured. Such cases can be treated as open quantum systems interacting with an inaccessible environment. Initial system-environment correlations play a fundamental role for the dynamics of open quantum systems. Following a recent proposal, we exploit the impact of the correlations on the open-system dynamics to detect system-environment quantum correlations without accessing the environment. We use two degrees of freedom of a trapped ion to model an open system and its environment. The present method does not require any assumptions about the environment, the interaction or the initial state and therefore provides a versatile tool for the study of quantum systems.Comment: 6 Pages, 5 Figures + 6 Pages, 1 Figure of Supplementary Materia

Nonlinear Spectroscopy of Controllable Many-Body Quantum Systems

We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional spectra in a chain of trapped ions with single-site addressability enables us, e.g., to distinguish coherent from incoherent transport processes, to quantify potential anharmonicities, and to identify decoherence-free subspaces.Comment: 12 pages, 3 figure

Betatron radiation diagnostics for AWAKE Run 2

AWAKE Run 2 aims to preserve the transverse normalised emittance of an externally injected electron beam throughout acceleration, requiring a new diagnostic to measure the beam emittance after the accelerating plasma stage. Spectroscopy of the betatron emission from the electron beam could be suitable for this case. The method of trace-space reconstruction from a measured betatron spectrum is described via a simplified analytical model in order to assess its suitability the AWAKE experiment. The expected betatron emission from witness electrons at AWAKE is characterised using 3D quasi-static PIC simulations, revealing a measurable quantity of UV to soft x-ray emission. Practical challenges for the measurement are discussed

Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate

A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here, we generate and measure geometric phases in a Bose-Einstein condensate of $^{87}$Rb using a combination of dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.Comment: 4+3 pages, 4+3 figure

Analize naprezanja i pomaka suvremenog postolja tokarilice metodom konačnih elemenata (MKE)

The Finite element method (FEM) was used in this study for the analysis of the strain and stress of a turning machine body. The final design decisions were made on the basis of stress and displacement field analysis of various design versions related to the structure of the considered machine tool. The results presented in this paper will be helpful for practical static and dynamic strength evaluation as well as for the appropriate design of machine tools using the FEM.Metoda konačnih elemenata (MKE) je primjenjena za analizu deformacija i naprezanja postolja stroja. Konačna odluka o oblikovanju je donešena na osnovi analize polja pomaka za različite varijante oblikovovanja elemenata razmatranih strojeva. Rezultati predstavljeni u ovom radu će biti korisni za procjenu statičke i dinamičke čvrstoće kao i za odgovarajuće oblikovanje strojnih alata korištenjem MKE