  We experimentally demonstrate a quantum walk on a line in phase space using
one and two trapped ion. A walk with up to 23 steps is realized by subjecting
an ion to state-dependent displacement operations interleaved with quantum coin
tossing operations. To analyze the ion's motional state after each step we
apply a technique that directly maps the probability density distribution onto
the ion's internal state. The measured probability distributions and the
position's second moment clearly show the non-classical character of the
quantum walk. To further highlight the difference between the classical
(random) and the quantum walk, we demonstrate the reversibility of the latter.
Finally, we extend the quantum walk by using two ions, giving the walker the
additional possibility to stay instead of taking a step.
