Traction force microscopy on soft elastic substrates: a guide to recent computational advances

The measurement of cellular traction forces on soft elastic substrates has become a standard tool for many labs working on mechanobiology. Here we review the basic principles and different variants of this approach. In general, the extraction of the substrate displacement field from image data and the reconstruction procedure for the forces are closely linked to each other and limited by the presence of experimental noise. We discuss different strategies to reconstruct cellular forces as they follow from the foundations of elasticity theory, including two- versus three-dimensional, inverse versus direct and linear versus non-linear approaches. We also discuss how biophysical models can improve force reconstruction and comment on practical issues like substrate preparation, image processing and the availability of software for traction force microscopy.Comment: Revtex, 29 pages, 3 PDF figures, 2 tables. BBA - Molecular Cell Research, online since 27 May 2015, special issue on mechanobiolog

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs

Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which explode anisotropically. The viscosity of the fireball matter determines its ability to convert the initial spatial deformation into momentum anisotropies that can be measured in the final hadron spectra. A quantitatively precise empirical extraction of the QGP viscosity thus requires a good understanding of the initial fireball deformation. This deformation fluctuates from event to event, and so does the finally observed momentum anisotropy. We present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity. The final harmonic flow coefficients are found to depend non-linearly on the initial harmonic eccentricity coefficients. We show that, on average, initial density fluctuations suppress the buildup of elliptic flow relative to what one obtains from a smooth initial profile of the same eccentricity, and discuss implications for the phenomenological extraction of the QGP shear viscosity from experimental elliptic flow data.Comment: 22 pages, 17 figures. Relative to [v2], minor changes in text. Fig. 9 redrawn. This version accepted by Phys. Rev.

Indistinguishable photons from the resonance fluorescence of a single quantum dot in a microcavity

We demonstrate purely resonant continuous-wave optical laser excitation to coherently prepare an excitonic state of a single semiconductor quantum dot (QDs) inside a high quality pillar microcavity. As a direct proof of QD resonance fluorescence, the evolution from a single emission line to the characteristic Mollow triplet10 is observed under increasing pump power. By controlled utilization of weak coupling between the emitter and the fundamental cavity mode through Purcell-enhancement of the radiative decay, a strong suppression of pure dephasing is achieved, which reflects in close to Fourier transform-limited and highly indistinguishable photons with a visibility contrast of 90%. Our experiments reveal the model-like character of the coupled QD-microcavity system as a promising source for the generation of ideal photons at the quantum limit. From a technological perspective, the vertical cavity symmetry -- with optional dynamic tunability -- provides strongly directed light emission which appears very desirable for future integrated emitter devices.Comment: 24 pages, 6 figure

Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates

We theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.Comment: 4 pages, 5 figures, minor revision

Large variations in the hole spin splitting of quantum-wire subband edges

We study Zeeman splitting of zone-center subband edges in a cylindrical hole wire subject to a magnetic field parallel to its axis. The g-factor turns out to fluctuate strongly as a function of wire-subband index, assuming values that differ substantially from those found in higher-dimensional systems. We analyze the spin properties of hole-wire states using invariants of the spin-3/2 density matrix and find a strong correlation between g-factor value and the profile of hole-spin polarization density. Our results suggest possibilities for confinement engineering of hole spin splittings.Comment: 4 pages, 3 figures, RevTex4, to appear in PR