Molecular binding in interacting quantum walks

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Andre Ahlbrecht, Andrea Alberti, Dieter Meschede, Volkher B Scholz, Albert H Werner and Reinhard F Werner


New Journal of Physics Volume 14 July 2012
Andre Ahlbrecht et al 2012 New J. Phys. 14 073050 doi:10.1088/1367-2630/14/7/073050

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.

Introduction and background. Quantum walks represent the quantum motion of a particle on a lattice with a strictly local dynamics, meaning that in a finite time the walker propagates over only a finite distance. This situation can be realized with spinor particles by applying an alternating sequence of spin-dependent shift operations and coherent spin manipulations. The fully discrete nature of such quantum systems—both in space and time—makes them highly attractive in a wide range of quantum applications, e.g., from their utilization as primitives for quantum information processing to the possibility of simulating complex quantum-mechanical systems. As a first step in this direction, we study here the problem of two interacting walkers forming molecular states.

Main results. We analytically predict that on-site interactions in a two-particle quantum walk give rise to a dynamically stable bound state. Proving that the distance between the two particles is exponentially bounded, we interpret these bound states as molecules and develop an effective theory that describes their dynamics as the quantum walk of a single compound particle (see the figure). We make an experimental proposal based on realistic conditions to test the prediction of molecules using individual atoms in optical lattices.

Wider implications. Our result is a first important step in a bottom-up approach towards the simulation of collective excitations of many particles, e.g., Cooper pairs or excitons. In addition, the discrete nature of our system could open new routes for controlling and studying decoherence and damping in simulated quantum systems.