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We demonstrate, theoretically and experimentally, self-trapping of optical beams in nanoparticle suspensions by virtue of thermophoresis. We use light to control the local concentration of nanoparticles, and increase their density at the center of the optical beam, thereby increasing the effective refractive index in the beam vicinity, causing the beam to self-trap.

We use magnetic force microscopy (MFM) to characterize superconductivity across the superconducting dome in BaFe 2 (As 1-x P x ) 2 , a pnictide with a peak in the penetration depth ( ab λ )at optimal doping (x opt ), as shown in sample-wide measurements. Our local measurements show a peak at x opt and a C T vs.2 ab λ − dependence similar on both sides of x opt . Near the underdoped edge of the dome ab λ increases sharply suggesting that superconductivity competes with another phase. Indeed MFM vortex imaging shows correlated defects parallel to twin boundaries only in underdoped samples and not for x ≥ x opt .2The origin of superconductivity in the iron-based materials is still under debate although there is mounting evidence for the role of magnetic order and fluctuations [1][2][3][4]. For instance, it is well established that the parent compound for the pnictides is a metal with spin-density-wave (SDW) order and that doping by electrons, holes or isovalently gives rise to superconductivity and suppresses the magnetic order and an associated structural phase transition [5][6][7][8][9]. Moreover, the optimal doping for the superconducting transition temperature ( C T ) is only slightly higher than the maximum doping for which SDW order has been observed. Here we report magnetic force microscopy (MFM) measurements of the local absolute value of the in-plane penetration depth ( ab λ ) in BaFe 2 (As 1-x P x ) 2 . At the location where we measure ab λ we also measure the local C T in order to determine the relationship between these two fundamental superconducting properties. In addition we use MFM to map the location of superconducting vortices, which can become trapped by defects in the material. This allows us to learn about correlated defects that may arise as a result of structural and magnetic phase transitions.Our samples were high-quality single crystals grown by the self-flux method and annealed in affected by a region in the sample only up to a few micrometers in diameter and only a few hundred nanometers deep, on the order of ab λ , our results are less sensitive to inhomogeneity than measurements which average over the whole sample [28,29]. The locality also allows us to check homogeneity by comparing measurements from different areas in each sample.In our setup the magnetic MFM tip [30] is subjected to forces due to the Meissner response from the superconducting sample, the magnetic field from vortices and magnetic fields from other sources, if they are present. We minimize the electrostatic forces between the tip and the sample by compensating for the contact potential difference. We work with frequency modulated MFM in which the forces on the tip shift the resonant frequency of the cantilever holding it:is the cantilever's natural resonance frequency, 0 k is the spring constant, z is the direction normal to the sample surface and C is a constant offset) [31].For ab λ measurements we cool the sample in low magnetic field and find an area without vortices and visible defects. For this we scan...

We study, theoretically and experimentally, autoresonant dynamics of optical waves in a spatially chirped nonlinear directional coupler. We show that adiabatic passage through a linear resonance in a weakly coupled light-wave system yields a sharp threshold transition to nonlinear phase locking and amplification to predetermined amplitudes. This constitutes the first observation of autoresonance phenomena in optics.

We report drive-response experiments on individual superconducting vortices on a plane, a realization for a 1+1-dimensional directed polymer in random media. For this we use magnetic force microscopy (MFM) to image and manipulate individual vortices trapped on a twin boundary in YBCO near optimal doping. We find that when we drag a vortex with the magnetic tip it moves in a series of jumps. As theory suggests the jump-size distribution does not depend on the applied force and is consistent with power-law behavior. The measured power is much larger than widely accepted theoretical calculations.While the dynamics of driven systems in ordered media are well understood, disorder gives rise to much more elaborate behavior. Particularly interesting are phenomena arising from the interplay between disorder and elasticity [1, 2] such as the conformations of polyelectrolytes [3] (e.g. polypeptides and DNA [4]), kinetic roughening of driven interfaces (e.g. wetting in paper [5,6], magnetic and ferroelectric domain wall motion [7][8][9][10], the growth of bacterial colony edges [5]), non-equilibrium effects that occur in randomly stirred fluids [11] and more. Superconducting vortices, in materials in which they behave like elastic strings, are among the most important examples of such systems [12]. Despite a dearth of direct experimental proof, these quantized whirlpools of supercurrent are considered textbook examples of the theory of directed polymers in random media (DPRM) [13][14][15], a foundation model for systems where disorder and elasticity compete. This model, that yields many results that are considered generic and universal, provides the backdrop for our experiment.Here we concentrate on vortices that are trapped on a twin boundary (TB), a planar defect in YBa 2 Cu 3 O 7−δ (YBCO) [16]. We cool the sample through the superconducting transition temperature T c in the presence of an external magnetic field H = Hẑ, which directs the curve along which vortices cross the sample. Figure 1a depicts a vortex away from a TB (V in Fig. 1a) that is free to meander in the d ⊥ = 2 directions perpendicular to H. For a vortex trapped on a TB (TBV in Fig. 1a) the meandering is limited to a plane, i.e. d ⊥ = 1. We concentrate on TB-vortices both because the reduced dimensionality makes data analysis simpler and, more importantly, because, unlike DPRM in higher dimensions, 1 + 1-DPRM is a tractable model [17].The path of a vortex across a sample is determined by the competition between elasticity and disorder: while meandering allows a vortex to lower the energy of the system by locating its core near defects, the associated stretching is limited by finite line tension κ [12]. As a result the unavoidable random disorder in a sample can make the optimal path for an isolated vortex elaborate. Despite this, DPRM theory provides many predictions for disorder-averaged quantities [18]. For example, the thermal and disorder averaged offset distance from the field axisẑ (∆) scales like a power-law given by the wandering exponent ζ(