This project involves a series of experiments with interacting cold atoms in far-off-resonance optical lattices. Arrays of coupled and independent one-dimensional gases of bosons will be prepared and studied to help resolve some outstanding mysteries of quantum statistical mechanics and quantum phase transitions. Prior experiments by this group have explored the physics of Bose-gases in one dimension, demonstrating that these gases never thermalize. New experiments will relax the one-dimensional confinement of atoms in several ways and explore the crossover between one-dimensional and three-dimensional behavior. These experiments will address a long open theoretical question of the existence of a threshold for chaos in a many-body quantum system, as there is in classical mechanics. This project may clarify how irreversibility of macroscopic behavior arises from the reversible behavior of individual atoms. Additionally the research will involve studies of arrays of coupled one-dimensional gases, an analog of Josephson junction arrays. Various phase transitions and dimensional crossovers will be studied with a high degree of control, allowing them to serve as models for a wide range of phenomena observed in more complicated systems.
The broader impacts of these experiments lie in the ability of cold-atom experiments to provide answers to long-open questions in nonlinear dynamics and mathematical physics. The research project will also improve the technology for creation and manipulation of Bose-Einstein Condensates with all-optical techniques. They will train undergraduate, graduate, and postdoctoral researchers in technologically important areas of physics.
A single assumption underlies statistical mechanics, that an isolated physical system in equilibrium will exist in a state of maximum entropy, i.e., it will be in one of a set of its most probable states. That assumption is violated for integrable many-body systems, because there are too many constraints in the problem, one per particle. It is an open question for quantum mechancial systems as to how far from an integrable point a system has to be for statistical mechanics to be valid. We are attacking this question experimentally, by taking 1D gases of ultra-cold atoms out of equilbrium, and trying to see what steady state they evolve to. The gases are confined in 1D by two-dimensional optical lattices. These gases have been shown to be very close to integrable, and therefore they are the only existing experimental system with which one can answer this question. We have previously demonstrated a surprising lack of thermalization, ie., approach to the state of maximum entropy. In this grant period we have tried to isolate the first onset of thermalization. The experimental difficulty has been to differentiate thermalization from the evolution of the system due to unavoidable heating processes. Therefore, along with observing these gases in great detail, we have worked to minimize heating, and to model the effects of heating in as much detail as possible. We have found that the more accurately we account for heating, the more the heating explains the observed evolution of the gases. It is still a work in progress. As we continue it, we are experimentally studying ways to purposely lift the system's integrability, for instance by modifying the atom trap.
