2005 Abstracts

Making Schrödinger cats from Bose Einstein Condensates (BEC) with massively parallel processors

Mary Ann Leung, University of Washington

Superposition states are a curious result of quantum theory and have been the subject of intellectual curiosity and debate for several decades. Erwin Schrödinger proposed an example of a superposition state in a thought experiment highlighting some of the “strange” consequences of quantum theory, and thus was born the “Schrödinger cat”, a cat simultaneously alive and dead. While a cat that is both dead and alive seems a preposterous idea, superposition states have been created with photons, four ions, and recently with cold atoms in optical lattices. This implies a question: if we can make a “small cat” of a few atoms or photons, can we make a “large” cat of perhaps millions of atoms?

BECs are a new state of matter where dilute but strongly interacting gases behave like a single macroscopic quantum object. They provide a unique opportunity to study the peculiarities of quantum mechanics (such as Schrödinger cats), superfluidity, properties and interactions of cold atoms, as well as nonlinear matter wave optics. Originally predicted by Einstein and Bose in 1924, the first gaseous atomic BEC was made in the laboratory in 1995. BECs are now made routinely and contain approximately 10⁷ atoms, all governed by a single macroscopic wavefunction and phase. The macroscopic nature of the BEC makes it an ideal system for creation of Schrödinger cats.

We are currently studying the dynamics of two coupled double well BECs in a ring configuration with tunable couplings. We work with a time dependent control Hamiltonian, H(t), an N by N matrix, and numerically solve the dynamics by time propagating N-coupled ordinary differential equations, where N=(n+w-1)!/(n!(w-1)!) with n = total number of particles, w = number of wells = 4. In typical BEC experiments, n~10⁷, and thus, the problem size necessitates deployment on massively parallel processor systems. Our numerical studies focus on moderate-size systems from n=50-1,000, and so N may be as large as tens of thousands to hundreds of millions. From these results, we extrapolate to experimental regimes.

Abstract Author(s): Mary Ann Leung* and William P. Reinhardt**<br />Department of Chemistry, University of Washington, Seattle, WA 98195-1700<br />&nbsp;<br />* Department of Energy Computational Science Graduate Fellow<br /> ** work supported in part by NSF Physics