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Bulletin of the American Physical Society

Adiabatic construction of d-wave resonating valence bond states of ultracold fermionic atoms in optical lattices

Simon Trebst, Matthias Troyer, P. Zoller, Ulrich Schollw ock

Published Mar 22, 2005• 0 citations
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d-wave resonating valence bond states of ultracold fermionic atoms in optical lattices

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arXiv:1509.07362•Physical review. B./Physical review. B•Feb 29, 2016•8 citations
We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.
The concept of valence-bond resonance plays a fundamental role in the theory of the chemical bond and is believed to lie at the heart of many-body quantum physical phenomena. Here we show direct experimental evidence of a time-resolved valence-bond quantum resonance with ultracold bosonic atoms in an optical lattice. By means of a superlattice structure we create a three-dimensional array of independent four-site plaquettes, which we can fully control and manipulate in parallel. Moreover, we show how small-scale plaquette resonating valence-bond (RVB) states with s- and d-wave symmetry can be created and characterized. We anticipate our findings to open the path towards the creation and analysis of many-body RVB states in ultracold atomic gases.
We investigate magnetic properties of strongly interacting four component spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one particle per site in an optical lattice with honeycomb symmetry. In this limit, atomic tunneling is virtual, and only the atomic spins can exchange. We find a competition between symmetry-breaking and liquidlike disordered phases. Particularly interesting are valence bond states with bond centered magnetizations, situated between the ferromagnetic and conventional valence bond phases. In the framework of a mean-field theory, we calculate the phase diagram and identify an experimentally relevant parameter region where a homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki--like valence bond state is present.