The favorite model systems of quantum mechanics, the two-level system and the harmonic oscillator, can be implemented in various experimental systems, but only become useful when their quantum states can be sufficiently well controlled. This is case for two level systems where any desired quantum state can be prepared with high accuracy, allowing them to be used as qubits. Harmonic oscillators, however, have only been prepared in certain types of quantum states. Number states, for example, have remained elusive.

I will demonstrate the generation of number states [1] and arbitrary superpositions of them [2] in a microwave oscillator. We use the precise control over a superconducting phase qubit to transfer microwave photons into the resonator, one at a time [3]. This protocol allows us to create arbitrary quantum states of the photon field, up to approximately 10 photons, limited by decoherence. We analyze the prepared states by mapping out their Wigner function, a full description of the quantum state of a resonator in phase space, equivalent to its density matrix. The figure shows the Wigner function of the state |0> + i|3> + |6>.

[1] Max Hofheinz et al. Nature 454, 310-314 (2008)
[2] Max Hofheinz et al. Nature 459, 546-549 (2009)
[3] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055-1058 (1996)