Detecting noncommutative phase space by the Aharonov-Bohm effect

Noncommutative phase space plays an essential role in particle physics and quantum gravity at the Planck scale. However, direct experimental evidence or observation to demonstrate the existence of noncommutative phase space is still lacking. We study a quantum ring in noncommutative phase space based on the Seiberg-Witten map and give the effective magnetic potential and field coming from the noncommutative phase space, which induces the persistent current in the ring. We introduce two variables as two signatures to detect the noncommutative phase space and propose an experimental scheme to detect the noncommutative phase space as long as we measure the persistent current and the external magnetic flux.

Figure 1

The signatures of noncommutative phase space for odd-electron number rings vs the external magnetic flux. (a) $log\lambda \sim \varphi$ with $log\lambda \sim log\varphi$ in the inset of (a) as a standard of $-1/\varphi$ divergence. (b) $log\sigma \sim \varphi$ with $log\sigma \sim log\varphi$ in the inset of (b) as a standard of $1/\varphi$ divergence. The unit of the magnetic flux is the magnetic flux quantum ${\varphi }_0$.

Figure 2

The signatures of noncommutative phase space for even-electron number rings vs the external magnetic flux. (a) $log\lambda \sim \varphi$ and $log\sigma \sim \varphi$ with different electron numbers. (b) $log\lambda \sim log\varphi$ and $log\sigma \sim log\varphi$ as a standard of $1/\varphi$ behavior. The unit of the magnetic flux is the magnetic flux quantum ${\varphi }_0$.