In order to clarify factors determining the interface dipole, we have studied the electronic structures of pentacene adsorbed on Cu͑111͒, Ag͑111͒, and Au͑111͒ by using first-principles density functional theoretical calculations. In the structural optimization, a semiempirical van der Waals ͑vdW͒ approach ͓S. Grimme, J. Comput. Chem. 27, 1787 ͑2006͔͒ is employed to include long-range vdW interactions and is shown to reproduce pentacene-metal distances quite accurately. The pentacene-metal distances for Cu, Ag, and Au are evaluated to be 0.24, 0.29, and 0.32 nm, respectively, and work function changes calculated by using the theoretically optimized adsorption geometries are in good agreement with the experimental values, indicating the validity of the present approach in the prediction of the interface dipole at metal/organic interfaces. We examined systematically how the geometric factors, especially the pentacene-substrate distance ͑Z C ͒, and the electronic properties of the metal substrates contribute to the interface dipole. We found that at Z C Ն 0.35 nm, the work function changes ͑⌬'s͒ do not depend on the substrate work function ͑ m ͒, indicating that the interface level alignment is nearly in the Schottky limit, whereas at Z C Յ 0.25 nm, ⌬'s vary nearly linearly with m , and the interface level alignment is in the Bardeen limit. Our results indicate the importance of both the geometric and the electronic factors in predicting the interface dipoles. The calculated electronic structure shows that on Au, the long-range vdW interaction dominates the pentacene-substrate interaction, whereas on Cu and Ag, the chemical hybridization contributes to the interaction.
The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong-Ou-Mandel effect. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose-Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong-Ou-Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right, and could have implications for the quantum simulation of bosonic particles and analogue quantum computation via boson sampling.
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