Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin squeezed state. This evolution is analysed in detail by developing a Bogoliubov theory which describes the entanglement of the atoms. Our calculation is a consistent expansion in $1/\sqrt{N}$, where $N$ is the number of particles in the condensate, and our theory predict that it is possible to produce spin squeezing by at least a factor of $1/\sqrt{N}$. Within the Bogoliubov approximation this result is independent of temperature.Comment: 14 pages, including 5 figures, minor changes in the presentatio

Antiferromagnetic noise correlations in optical lattices

We analyze how noise correlations probed by time-of-flight (TOF) experiments reveal antiferromagnetic (AF) correlations of fermionic atoms in two-dimensional (2D) and three-dimensional (3D) optical lattices. Combining analytical and quantum Monte Carlo (QMC) calculations using experimentally realistic parameters, we show that AF correlations can be detected for temperatures above and below the critical temperature for AF ordering. It is demonstrated that spin-resolved noise correlations yield important information about the spin ordering. Finally, we show how to extract the spin correlation length and the related critical exponent of the AF transition from the noise.Comment: 4 pages, 4 figure

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.Comment: 96 page

Structure of boson systems beyond the mean-field

We investigate systems of identical bosons with the focus on two-body correlations. We use the hyperspherical adiabatic method and a decomposition of the wave function in two-body amplitudes. An analytic parametrization is used for the adiabatic effective radial potential. We discuss the structure of a condensate for arbitrary scattering length. Stability and time scales for various decay processes are estimated. The previously predicted Efimov-like states are found to be very narrow. We discuss the validity conditions and formal connections between the zero- and finite-range mean-field approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the present method. We compare numerical results from present work with mean-field calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with modified figures and discussion

Raptors are still affected by environmental pollutants:Greenlandic Peregrines will not have normal eggshell thickness until 2034

The DDT-induced effects, eggshell thinning and breeding failure in Peregrine Falcon (Falco peregrinus) populations were reverted with restrictions on the use of the compound from the 1970s, and in most studied populations, the eggshell thickness is back to normal. In Greenland, a previous study of eggshell thinning in Peregrines found that shells had not yet reached pre-DDT levels. In this study, we extend the time series and reinterpret shell thinning data for 196 clutches covering a 45-year time span (1972–2017). There was a significant (P<0.001) increase in the eggshell thickness of 0.23% per year. This corresponds to a change in eggshell thinning from 14.5% to 5.4% in 2017 compared to the pre-DDT mean. With the current rate of change, pre-DDT shell thickness is predicted to be reached around the year 2034. However, a few clutches are still below the critical limit. The relatively slower recovery of the shell thickness in the Greenland population is likely indicative of the slower phasing out of DDT in the Greenlandic Peregrines’ wintering grounds in Latin America. The shell thinning in the Greenlandic population probably never crossed the 17% threshold associated with population declines, contrary to the populations in many other parts of the world

Differential Measurement of Trident Production in Strong Electromagnetic Fields

In this paper, we present experimental results and numerical simulations of trident production, $e^-\rightarrow e^-e^+e^-$, in a strong electromagnetic field. The experiment was conducted at CERN for the purpose of probing the strong-field parameter $\chi$ up to 2.4, using a 200 GeV electron beam penetrating a 400 $\mu$m thick germanium crystal oriented along the $\langle 110\rangle$ axis. For the current experimental parameters we found that the trident process is primarily a two-step process, and show remarkable agreement between theoretical predictions and experimental data. This paper is an extension of the previously published paper (Phys. Rev. Lett. 130, 071601 (2023)) and features new analysis differential in the energy of the produced positron and electron in the trident process. Even for the more demanding differential analysis, we find good agreement between theoretical predictions and experimental data, while a slight discrepancy is found in the high energy tail of the trident spectrum. This discrepancy could be an indication of the direct process, but further investigation is needed due to the large uncertainties in this part of the spectrum. Finally we present a suggestion for a future experiment, aiming to probe the direct process using thin crystals

Local Simulation Algorithms for Coulombic Interactions

We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.Comment: Proceedings Statphys22 10 page