Experimental creation and analysis of displaced number states

We create displaced number states, which are non-classical generalizations of coherent states, of a vibrational mode of a single trapped ion. The creation of these states is accomplished by a combination of optical and electrical manipulation of the ion. A number state is first prepared by laser-driven climbing of the Jaynes–Cummings ladder, followed by displacement created by a sudden shift of the electrostatic trapping potential. Number states n = 0, 1 and 2 are prepared, and displacement amplitudes of up to α ≈ 2.8 are reached. The states are analysed by the experimental reconstruction of the number state distribution, and we find good agreement with the theoretically expected results for displaced number states. Quantum features elucidating the concept of interference in phase space are clearly demonstrated experimentally.