The Intrinsic Difficulties of Constructing Strongly Correlated States of Lattice Quantum Gases by Connecting Up Pre-engineered Isolated Atomic Clusters

Abstract

Suppose one engineers an artificial antiferromagnet on an array of {\em isolated} wells, and then increases the tunneling between wells slowly, will the system finally become an {\em equilibrium} antiferromagnet? Here, we show that due to the intrinsic non-adiabaticity at the start of this process, and that the atoms in the initial state in different wells are completely uncorrelated, the final equilibrium state will have a temperature $T_f$ far above the Neel temperature. Constructing other strongly correlated states (with characteristic energy per particle $E^{\ast }$ comparable to the hopping or the virtual hopping scale) with the same method will suffer the same problem, i.e. $T_f>>E^{\ast }$.

4 pages

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