Two-point microrheology measurements from widely separated colloidal particles approach the bulk viscosity of the host medium more reliably than corresponding single-point measurements. In addition, active microrheology offers the advantage of enhanced signal to noise over passive techniques. Recently, we reported the observation of a motional resonance induced in a probe particle in dual-trap optical tweezers when the control particle was driven externally [Paul et al., Phys. Rev. E 96, 050102(R) (2017)2470-004510.1103/PhysRevE.96.050102]. We now demonstrate that the amplitude and phase characteristics of the motional resonance can be used as a sensitive tool for active two-point microrheology to measure the viscosity of a viscous fluid. Thus, we measure the viscosity of viscous liquids from both the amplitude and phase response of the resonance, and demonstrate that the zero crossing of the phase response of the probe particle with respect to the external drive is superior compared to the amplitude response in measuring viscosity at large particle separations. We compare our viscosity measurements with those using a commercial rheometer and obtain an agreement ∼1%. The method can be extended to viscoelastic material where the frequency dependence of the resonance may provide further accuracy for active microrheological measurements.

Anderson localization lasers exploit resonant cavities formed due to structural disorder. The inherent randomness in the structure of these cavities realizes a probability distribution in all cavity parameters such as quality factors, mode volumes, mode structures etc, implying resultant statistical fluctuations in the temporal behavior. Here, we provide the first, direct experimental measurements of temporal width distributions of Anderson localization lasing pulses in intrinsically and extrinsically disordered coupled-microresonator arrays. We first illustrate signature exponential decays in the spatial intensity distributions of the lasing modes that quantify their localized character, and then measure the temporal width distributions of the pulsed emission over several configurations. We observe a hitherto-unreported dependence of temporal widths on the disorder strength, wherein the widths show a single-peaked, left-skewed distribution in extrinsic disorder and a dual-peaked distribution in intrinsic disorder. We propose a model based on coupled rate equations for an emitter and an Anderson cavity with a random mode structure, which gives excellent quantitative and qualitative agreement with the experimental observations. The experimental and theoretical analyses bring to the fore the temporal complexity in Anderson localization based lasing systems.

By numerical simulation and variational analysis of the Gross–Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose–Einstein condensate (DBEC) of 52Cr atoms in a three-dimensional bichromatic optical lattice (OL) generated by two monochromatic OLs of incommensurate wavelengths along three orthogonal directions. For a fixed dipole–dipole interaction, a localized state of a small number of atoms (∼1000) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with a short-range interaction and dipole–dipole interaction is given.

We experimentally investigate spectral statistics in Anderson localization in two-dimensional amorphous disordered media. Intensity distributions captured over an ultrabroad wavelength range of ∼ 600 nm and averaged over numerous configurations provided the Ioffe-Regel parameter to be ∼ 2.5 over the investigated wavelength range. The spectra of the disordered structures provided access to several quasimodes, whose widths and separations allowed to directly estimate the optical Thouless conductance g T h , consistently observed to be below unity. The probability distribution of g T h was measured to be a log-normal. Despite being in the Anderson localization regime, the spacings of energy levels of the system was seen to follow a near Wigner-Dyson function. Theoretical calculations based on the tight-binding model, modified to include coupling to a bath, yielded results that were in excellent agreement with experiments. From the model, the level-spacing behavior was attributed to the degree of localization obtained in the optical disordered system.

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