Abstract
We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice.From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic—instead of diffusive—expansion in position space is not a good indicator of the range of coherent delocalization.We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences.For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.
Highlights
Coherent superposition of quantum states constitutes the key element of every application of quantum, such as quantum metrology, quantum communication and quantum simulation
As a complement to this phenomenological analysis, we provide a thorough discussion of physical decoherence mechanisms occurring in quantum walk experiments that are based on neutral atoms in an optical lattice
A classification scheme that provides insight into decoherence of discrete-time quantum walks relies on two criteria, which distinguish: (i) spatial and spin decoherence, (ii) whether the decoherence mechanism is directly induced by the environment independently of the walk operations or if, instead, it modifies the behavior of the coin operation or the shift operation
Summary
Coherent superposition of quantum states constitutes the key element of every application of quantum, such as quantum metrology, quantum communication and quantum simulation. We use a phenomenological decoherence model to analyze the quantum walk of a single cesium atom moving along a one-dimensional optical lattice. By comparing this model with our experimental data, we retrieve information about the main physical mechanisms that are responsible for the loss of coherence (see section 4). An electro-optic modulator imprinted controllable phase fluctuations between vertical and horizontal polarizations, which are randomized at each position and step, causing a transition to diffusive motion These experiments did not distinguish decoherence mechanisms related to the coin and shift degrees of freedom in quantum walks
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