Rotated multifractal network generator

The recently introduced multifractal network generator (MFNG), has been shown to provide a simple and flexible tool for creating random graphs with very diverse features. The MFNG is based on multifractal measures embedded in 2d, leading also to isolated nodes, whose number is relatively low for realistic cases, but may become dominant in the limiting case of infinitely large network sizes. Here we discuss the relation between this effect and the information dimension for the 1d projection of the link probability measure (LPM), and argue that the node isolation can be avoided by a simple transformation of the LPM based on rotation.Comment: Accepted for publication in JSTA

High-resolution vibronic spectroscopy of a single molecule embedded in a crystal

Vibrational levels of the electronic ground states in dye molecules have not been previously explored at high resolution in solid matrices. We present new spectroscopic measurements on single polycyclic aromatic molecules of dibenzoter- rylene embedded in an organic crystal made of para-dichlorobenzene. To do this, we use narrow-band continuous-wave lasers and combine spectroscopy methods based on fluorescence excitation and stimulated emission depletion (STED) to select individual vibronic transitions at a resolution of ∼30 MHz dictated by the linewidth of the electronic ex- cited state. In this fashion, we identify several exceptionally narrow vibronic levels in the electronic ground state with linewidths down to values around 2 GHz. Additionally, we sample the distribution of vibronic wavenumbers, relax- ation rates, and Franck-Condon factors, both in the electronic ground and excited states for a handful of individual molecules. We discuss various noteworthy experimental findings and compare them with the outcome of DFT cal- culations. The highly detailed vibronic spectra obtained in our work pave the way for studying the nanoscopic local environment of single molecules. The approach also provides an improved understanding of the vibrational relaxation mechanisms in the electronic ground state, which may help to create long-lived vibrational states for applications in quantum technology

Quantum Optomechanics in a Liquid

53 pages, 15 figures, 1 table (including supplementary information)International audienceOptomechanical systems provide a means for studying and controlling quantum effects in the motion of macroscopic objects. To date, quantum optomechanical effects have been studied in objects made from solids and gases. Here we describe measurements of quantum behavior in the vibrations of a liquid body. Specifically, we monitor the fluctuations of an individual acoustic standing wave in superfluid liquid helium, and find that it displays the characteristic signatures of zero-point motion and measurement back-action. This opens the possibility of exploiting the properties of liquids in general (and superfluid helium in particular) to access qualitatively new regimes of quantum optomechanics

Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime

We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator's mean phonon number n is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 +- 0.22 (corresponding to a mode temperature T = 28 +- 7 microK). We also infer n from the calibrated area of each of the two sidebands, and from the oscillator's total damping. The values of n inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator's temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator.Comment: 12 pages, 3 figure