Abstract. We consider the tunnelling of phonon excitations across a potential barrier spatially separating two condensates with different macroscopic phases. We analyse the relation between the phase difference ϕ of the two condensates and the transmission coefficient T by solving the Bogoliubov equations. It is found that T strongly depends on ϕ, and that the perfect transmission of low-energy excitations disappears when the phase difference reaches the critical value which gives the maximum supercurrent of the condensate. We also discuss the feasibility of observing the phase differences in experiments.

Ways to characterize and control excited states at the single-molecule and atomic levels are needed to exploit excitation-triggered energy-conversion processes. Here, we present a single-molecule spectroscopic method with micro–electron volt energy and submolecular-spatial resolution using laser driving of nanocavity plasmons to induce molecular luminescence in scanning tunneling microscopy. This tunable and monochromatic nanoprobe allows state-selective characterization of the energy levels and linewidths of individual electronic and vibrational quantum states of a single molecule. Moreover, we demonstrate that the energy levels of the states can be finely tuned by using the Stark effect and plasmon-exciton coupling in the tunneling junction. Our technique and findings open a route to the creation of designed energy-converting functions by using tuned energy levels of molecular systems.

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS-Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green's function formalism developed by Côté and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair-breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.PACS numbers:where c jσ is the annihilation operator of a fermion on the jth site with pseudospin σ =↑, ↓.Here, J is the nearest-neighbor hopping energy, U is the on-site interaction energy, and µ is the chemical potential. We assume an attractive interaction between atoms (U < 0).In order to calculate the density response function, we introduce a fictitious timedependent external field P j (t) which is coupled with the density. The Hamiltonian with

Three-dimensional (3D) information of the optical response in the nanometre scale is important in the field of nanophotonics science. Using photoinduced force microscopy (PiFM), we can visualize the nano-scale optical field using the optical gradient force between the tip and sample. Here, we demonstrate 3D photoinduced force field visualization around a quantum dot in the single-nanometre spatial resolution with heterodyne frequency modulation technique, using which, the effect of the photothermal expansion of the tip and sample in the ultra-high vacuum condition can be avoided. The obtained 3D mapping shows the spatially localized photoinduced interaction potential and force field vectors in the single nano-scale for composite quantum dots with photocatalytic activity. Furthermore, the spatial resolution of PiFM imaging achieved is ~0.7 nm. The single-nanometer scale photoinduced field visualization is crucial for applications such as photo catalysts, optical functional devices, and optical manipulation.