A random walk is basically a mathematical formalisation of a trajectory that consists of taking successive random steps, and it is particularly used in physics and mathematics. Examples of random walks include the 'Galton board' which is used to show binomial distribution to students. Here, balls are dropped from the top and either bounce left or right in a random way as they hit pins that are stuck in the board. The 'Brownian motion' denotes the seemingly random movement of particles suspended in a fluid such as liquid or gas.
The researchers in this latest study used a hiker as an example. A hiker must determine the direction they want to take when they come to a junction. Lacking a map, they randomly decide on which path to follow. Whether they go through detours or not, they arrive at their destination finally.
The physicists used one and two trapped ions to show a quantum walk on a line in phase space (a space encompassing all possible states of a system). This study offers the physics world a first-time look at this quantum process using trapped ions.
IQOQI's Drs Christian Roos and Rainer Blatt, along with their colleagues, transferred this principle of random walk to quantum systems and stimulated an atom to 'take a quantum walk'.
'We trap a single atom in an electromagnetic ion trap and cool it to prepare it in the ground state,' Dr Roos explained. 'We then create a quantum mechanical superposition of two inner states and send the atom on a walk.'
According to the researchers, the two internal states correspond to the decision of the hiker to go left or right. The atom is distinct, however, in that it does not have to decide on a direction; the superposition of the two states allows the possibilities to be presented at the same time.
'Depending on the internal state, we shift the ion to the right or to the left,' Dr Roos pointed out. 'Thereby, the motional and internal states of the ion are entangled.'
The team modified the superposition of the inner states after each step. A laser pulse was used for the change. They then shifted the ion to the left or right. They successfully repeated this randomly controlled process up to 23 times and gathered data on the performance of quantum walks. The use of the second ion allowed the physicists to extend the experiment and enabled the walking ion to 'stay' rather than move left or right.
According to the scientists, by performing a statistical analysis of the 23 steps, they effectively confirmed that quantum walks are not the same as classical 'random' walks.