Abstract
The fifth lesson was devoted to the description of electrodynamic circuit experiments that enabled John Martinis' team to synthesize arbitrary states of a radio-frequency resonator and intricate states of two resonators. We began by describing the deterministic preparation of Fock states, which involves repeatedly coupling the radio-frequency resonator to a qubit exchanging a quantum of energy with it, before being reset to its excited state. One by one, photons are injected into the oscillator until the desired state is generated. This state is then detected by observing the Rabi oscillation of the qubit, at a pure frequency proportional to the square root of the photon number. We then show how the method has been generalized to the synthesis of arbitrary states of the radio-frequency resonator, defined by their development on the basis of Fock states. Following the procedure established by Law and Eberly and already used in trapped-ion physics, we begin by determining the sequence of operations enabling us, starting from the target state we seek to generate, to arrive at the vacuum by deleting the quanta one by one in the resonator. All that remains is to apply these operations in reverse to generate the target state from the vacuum. The operations we combine are individual qubit rotations and phase shifts, as well as Rabi oscillation pulses transferring energy between the qubit and the oscillator. Once the state has been generated, it is reconstructed by quantum tomography, either as a density operator in the Fock basis of states, or as a Wigner function. Various coherent superpositions of Fock states have been produced and reconstructed.
