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Controlled hole burning for a cavity field with a single atom

We present a simple method of realizing controlled hole burning for a cavity mode in Fock space by using a single two-level atom. In the scheme, the atom is driven by a classical field and dispersively interacts with the cavity mode. Due to the photon number-dependent atomic transition frequency shift, the atom is excited only for a specific Fock state. As a result, the detection of the atom remaining in the ground state projects the cavity to the state with a desired hole in Fock space. An important feature of the scheme is that multiple holes can be burnt at the same time with a single atom driven by a pulse composed of multiple frequency components.