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arXiv:1105.1051

Bound Molecules in an Interacting Quantum Walk

André Ahlbrecht, Andrea Alberti, Dieter Meschede, Volkher B. Scholz, Albert H. Werner, Reinhard F. Werner

Published May 5, 2011• 15 citations
arXivHTMLPDF

Abstract

We investigate a system of two atoms in an optical lattice, performing a quantum walk by state-dependent shift operations and a coin operation acting on the internal states. The atoms interact, e.g., by cold collisions, whenever they are in the same potential well of the lattice. Under such conditions they typically develop a bound state, so that the two atoms effectively perform a quantum walk together, rarely moving further from each other than a few lattice sites. The theoretical analysis is based on a theory of quantum walks with a point defect, applied to the difference variable. We also discuss the feasibility of an experimental realization in existing quantum walk experiments.

DOI
10.48550/arxiv.1105.1051

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We investigate a system of two atoms in an optical lattice, performing a quantum walk by state-dependent shift operations and a coin operation acting on the internal states. The atoms interact, e.g., by cold collisions, whenever they are in the same potential well of the lattice. Under such conditions they typically develop a bound state, so that the two atoms effectively perform a quantum walk together, rarely moving further from each other than a few lattice sites. The theoretical analysis is based on a theory of quantum walks with a point defect, applied to the difference variable. We also discuss the feasibility of an experimental realization in existing quantum walk experiments.
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We study hybrid atom-molecule quantum walks in one-dimensional optical lattices with two interacting bosonic atoms which may be converted into a molecule. The hybrid atom-molecule energy bands include a continuum band and two isolated bands, which respectively correspond to scattering states and dressed bound states (DBSs). Because of the atom-molecule coupling, the DBSs may appear even in the absence of atom-atom interaction. From an initial state of two atoms occupying the same site, in addition to independent quantum walks which correspond to scattering states, correlated quantum walks appear as a signature of DBSs. Even if the atom-atom interaction and the atom-molecule coupling are much stronger than the tunneling strengths, independent quantum walks may still appear under certain resonant conditions. The correlated quantum walks show two light cones with different propagation velocities, which can be analytically explained by the effective tunneling strengths of the two different DBSs. Furthermore, the effective nearest-neighbor tunneling of DBSs can be suppressed to zero, which can be explained by the destructive interference between the atomic pair and the molecule.
We show that the presence of an interaction in the quantum walk of two atoms leads to the formation of a stable compound, a molecular state. The wave function of the molecule decays exponentially in the relative position of the two atoms; hence it constitutes a true bound state. Furthermore, for a certain class of interactions, we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right. We propose a setup for the experimental realization as well as sketch the possibility to observe quasi-particle effects in quantum many-body systems.
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Optical interferometers comprising birefringent-crystal beam displacers, wave plates, and phase shifters serve as stable devices for simulating quantum information processes such as heralded coined quantum walks. Quantum walks are important for quantum algorithms, universal quantum computing circuits, quantum transport in complex systems, and demonstrating intriguing nonlinear dynamical quantum phenomena. We introduce fully controllable polarization-independent phase shifters in optical pathes in order to realize site-dependent phase defects. The effectiveness of our interferometer is demonstrated through realizing single-photon quantum-walk dynamics in one dimension. By applying site-dependent phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in localization effect in a quantum walk architecture. The walk is realized for different site-dependent phase defects and coin settings, indicating the strength of localization signature depends on the level of phase due to site-dependent phase defects and coin settings and opening the way for the implementation of a quantum-walk-based algorithm.