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Dynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates
We investigate the influence of a Bose-Einstein condensate (BEC) on the
properties of immersed impurity atoms, which are trapped in an optical lattice.
Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum
master equation for the lattice system. In the special case of fixed impurities
with two internal states the atoms represent a quantum register and the quantum
master equation reproduces the exact evolution of the qubits. We characterise
the qubit dephasing which is caused by the interspecies coupling and show that
the effect of sub- and superdecoherence is observable for realistic
experimental parameters. Furthermore, the BEC phonons mediate an attractive
interaction between the impurities, which has an important impact on their
spatial distribution. If the lattice atoms are allowed to move, there occurs a
sharp transition with the impurities aggregating in a macroscopic cluster at
experimentally achievable temperatures. We also investigate the impact of the
BEC on the transport properties of the impurity atoms and show that a crossover
from coherent to diffusive behaviour occurs with increasing interaction
strength.Comment: 22 pages, 8 figures, some typos correcte
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