Our top 5 most popular images of the year

As 2016 draws to a close, we take a look at the top 5 most popular images from the JPhys+ image of the week series, and the research behind them.

1. Overlapping Rydberg atoms

Charge density ρ for wave function ${{rm{Psi }}}_{{M}}$ in equation (2) with nA = 20, lA = 2, ${m}_{A}=-1$ and nB = 15, lB = 1, mB = 1. The dashed sphere with radius RA (RB) denotes the classical outer turning point of the electron of atom A (B).

Charge density ρ for wave function of two Rydberg atoms in different electronic states. The dashed sphere with radius  denotes the classical outer turning point of the electron of atoms. Adapted from Martin Kiffner et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49 204004 © 2016 IOP Publishing Ltd

In JPhysB’s Special Issue on Addressing Quantum Many-body Problems with Cold Atoms and Molecules,  Martin Kiffner et al perform calculations of autoionization rates for two rubidium Rydberg atoms with overlapping electron clouds.  They find that, independent of the initial state of the atoms, the autoionization rates increase exponentially with the amount of charge overlap.

2. Hofstadter butterfly in the Falicov–Kimball model

image-of-the-week-07_11

The Hofstadter butterfly: single particle energy spectrum as a function of magnetic flux per plaquette alpha = p/q in an infinite square lattice. Taken from J. Phys. Cond. Mat. 28 505502 © 2016 IOP Publishing Ltd.

This fantastic work comes from a recent Journal of Physics: Condensed Matter paper from Subhasree Pradhan. She used exact diagonalisation and Monte Carlo methods to compare spinless, interacting electrons on finite size triangular and square lattices, highlighting interplay between the applied magnetic field and electronic correlation.

3. Patterson Patterns

Patterson function contours in the (x,y)-plane for a Skyrme crystal.

Patterson function contours in the (x,y)-plane for a Skyrme crystal. Taken from J. Phys. G: Nucl. Part. Phys. 43 055104 © IOP Publishing, All Rights Reserved.

Probing the nucleon with the electron scattering technique is one of the best ways to understand nuclear structure.

Authors M Karliner, C King and N S Manton from Tel Aviv University and the University of Cambridge have used the Patterson function for calculating the electron scattering intensity off randomly oriented Skyrmions. The above image is actually a periodic approximation which can be used to obtain the Patterson function for a B = 108 Skyrmion. The Patterson function is typically used in crystallography; however the application here as part of an averaging technique can be considered analogous to an x-ray powder diffraction experiment due to the random, uncorrelated nature of the nuclei.

There are a host of excellent graphical representations in this paper, so check it out!

4. Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice

Diagram of final state of each atom in the lattice. Each site contains one atom in state |±> with angular momentum ≈ ±ħ

Diagram of final state of each atom in the lattice. Each site contains one atom in state |±> with angular momentum ≈ ±ħ, taken from Anthony Kiely et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49 215003, © IOP Publishing Ltd, 2016.

Optical lattices are very useful systems for quantum simulation and studying quantum many body systems.  In their excellently named manuscript: Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice, Kiely et al propose a method to produce higher orbital states of cold atoms in an optical lattice.  Their method involves ‘shaking’ the lattice (changing the positions of the minima in the trap).  The image below shows the target state of their method, with the atoms in an anti-ferromagnetic arrangment in the lattice.

5. A root diagram and Dynkin diagrams

(a) The root diagram of the su(4) algebra, (b) the Dynkin diagram of the the su(4) algebra, and (c) the four types of the unitary equivalence classes of the matrix representations of the su(2) subalgebras. In (c), the chosen simple roots and the omitted simple roots are indicated by the filled black circles and the open gray circles, respectively.

(a) The root diagram of the su(4) algebra, (b) the Dynkin diagram of the the su(4) algebra, and (c) the four types of the unitary equivalence classes of the matrix representations of the su(2) subalgebras. In (c), the chosen simple roots and the omitted simple roots are indicated by the filled black circles and the open gray circles, respectively.  Copyright IOP Publishing, All Rights Reserved.

I’m not a mathematician, but Emi Yukawa and Kae Nemoto from the National Institution of Informatics in Japan certainly are. Their recent work in JPhysA studies squeezing — not physical squeezing, but a mathematical treatment of squeezing in a collective SU(2J+1) system consisting of spin-particles (J > 1/2). Our image of the week comes from visualising the roots of SU4 algebra and the following Dynkin diagrams.

Find more fabulous images from JPhys+ here.

Find our top 5 most read stories of the year here.


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Categories: Journal of Physics A: Mathematical and Theoretical, Journal of Physics B: Atomic, Molecular and Optical Physics, Journal of Physics D: Applied Physics, Journal of Physics G: Nuclear and Particle Physics, Journal of Physics: Condensed Matter, JPhys+

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