Creating Electron Lattices with Sound Waves

Tapio Simula, Peter Engels, Ian R. Coddington +3 more

Repulsive laser potential pulses applied to vortex lattices of rapidly rotating Bose-Einstein condensates create propagating density waves which we have observed experimentally and modeled computationally to high accuracy. We have observed a rich variety of dynamical phenomena ranging from interference effects and shock-wave formation to anisotropic sound propagation.

David Blair

This chapter explores the patterns of electron probability waves around atoms, called orbitals, and the way they spread out to encompass groups of atoms to make molecules, and spread out even further to become the conduction bands in metals that allow electrons to flow freely. It shows standing waves, from optical standing waves created when laser light is reflected back on itself, to sound waves in metal plates, to probability waves for electrons in hydrogen, and one created when electrons reflect off atoms in a metal surface. The physics of atoms allows the reader to understand how the world works. The Pauli exclusion principle explains the structure of atoms and, astonishingly, also explains white dwarf stars and neutron stars. The world of atoms and solids is the world around the reader, but the tiny size of atoms and quantum rules that they obey is normally considered beyond the reach of school science.

Maksim Tomchenko

A new class of solutions for Bose crystals with a simple cubic lattice consisting of N atoms is found. The wave function (WF) of the ground state takes the form Ψ_0=e^{S_{w}^{l}+S_{b}}*\prod_j [\sin{k_{l_x}x_{j}}\sin{k_{l_y}y_{j}}\sin{k_{l_z}z_{j}}], where e^{S_{b}} is the ground-state WF of a fluid, and \textbf{k}_l=(π/a_l, π/a_l, π/a_l) (a_l is the lattice constant). The state with a single longitudinal acoustic phonon is described by the WF Ψ_k=[ρ_{-k}+corrections + 7 permutations]Ψ_0, where the permutations give the terms with different signs of components of vector k. The structure of Ψ_k is such that the excitation corresponds, in fact, to the replacement of \textbf{k}_l in some triple of sines from Ψ_0 by \textbf{k}. Such a structure of Ψ_0 and Ψ_k means that the crystal is created by sound: the ground state of a cubic crystal is formed by N identical three-dimensional standing waves similar to a longitudinal sound. It is also shown that the crystal in the ground state has a condensate of atoms with \textbf{k}=\textbf{k}_l. The nonclassical inertia moment observed in crystals He-4 can be related to the synchronous tunneling of condensate atoms.

Marco Giliberti, Luisa Lovisetti