Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate

Abstract

We propose a scheme to implement the simplest and best-studied version of quantum random walk, the discrete Hadamard walk, in one dimension using coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC). Implementation of quantum walk using BEC gives access to the familiar quantum phenomena on a macroscopic scale. This paper uses rf pulse to implement Hadamard operation (rotation) and stimulated Raman transition technique as unitary shift operator. The scheme suggests implementation of Hadamard operation and unitary shift operator while the BEC is trapped in long Rayleigh range optical dipole trap. The Hadamard rotation and a unitary shift operator on BEC prepared in one of the internal state followed by a bit flip operation, implements one step of the Hadamard walk. To realize a sizable number of steps, the process is iterated without resorting to intermediate measurement. With current dipole trap technology it should be possible to implement enough steps to experimentally highlight the discrete quantum random walk using a BEC leading to further exploration of quantum random walks and its applications.

7 pages, 3 figures

References in corpus (2)

• Spatial search by quantum walk
• Feshbach resonances in rubidium 87: Precision measurement and analysis

Cited by in corpus (8)

• Optimizing the discrete time quantum walk using a SU(2) coin
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Symmetries and noise in quantum walk
• Nonlinear optical Galton board
• Quantum phase transition using quantum walks in an optical lattice
• Symmetry-noise interplay in quantum walk on an n-cycle
• Quantum Walk-based Generation of Entanglement Between Two Walkers
• Generic quantum walk using a coin-embedded shift operator