Figure 4: Experimental results after addition-then-subtraction and subtraction-then-addition.

Only the real part of experimentally measured density matrices is shown (a) for an initial coherent state , (b) single-phonon added-then-subtracted state and (c) single-phonon subtracted-then-added state. (b) The state after addition-then-subtraction is basically identical to the original state. The fidelity of the state to the original state is 0.97(0.01) and the purity is 0.96(0.01). (c) The state after subtraction-then-addition is not the same as the original state, because the vacuum component is thrown away during the projective measurement. The small population in zero component mainly comes from the imperfection of the fluorescence detection and heating of the system, which is in good agreement with numerical simulation.