### Dynamics of 3D Spin Systems with Non-Adiabatically Traversed Quantum Phase Transitions

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Mark Rudner, Massachusetts Institute of Technology
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When cooled to very low temperatures, bosonic atoms undergro a phase transition to the so-called Bose Einstein Condensate (BEC) phase. In this state, the entire macroscopic sample exists in a single quantum state, which allows for the observation and manipulation of quantum effects on a macroscopic scale. In the presence of a sufficiently strong optical lattice potential, the ordinarily superfluid BEC undergoes another phase transition after which the atoms are localized on the sites of the lattice. Such systems are a hot area of current experimental research, and offer exciting possibilities for quantum information processing.

If the BEC atoms have two internal states which can be effectively isolated from all other atomic states, then the atom on each site of the lattice can be used as quantum bit (qubit) for quantum information processing. The evolution of such a system is equivalent to the evolution of a collection of quantum mechanical spins (S = ½) on the same lattice. If the interactions between atoms on different sites can be controlled, then the quantum phase diagram of the system can be explored.

Whereas ordinary phase transitions are typically characterized by the vanishing of an order parameter as temperature is swept through some critical value indicating a qualitative change in the state of a system, quantum phase transitions occur when changes in the values of certain system parameters lead to a qualitative change in the ground state of the quantum system. Here, we explore the dynamics of a 3D spin system in which a quantum phase transition is traversed at a finite rate.

**Abstract Author(s): **Mark Rudner