Probing the quantum commutation rules through cavity QED

Journals published by the American Physical Society can be found at http://publish.aps.org/We propose a cavity QED-based scheme to observe the noncommutativity between the creation and annihilation operators. By conditional measurement after the atom-field interaction in a cavity, it is possible to achieve a photon-added-then-subtracted state and a photon-subtracted-then-added state, which have different statistical properties. This scheme has the advantages of simple analytical results and much higher generation probabilities. We show that the ideal results of one-cycle photon addition and subtraction are approached in the short time limit. We also discuss the possible implementation scheme