Area distribution of two-dimensional random walks on a square lattice

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A particular case generalizes the q-binomial theorem to the case of three addends. The distribution fits the L\'evy probability distribution for Brownian curves with its first-order 1/N correction quite well, even for N rather small.Comment: 8 pages, LaTeX 2e. Reformulated in terms of q-commutator

Reduced volume and reflection for bright optical tweezers with radial Laguerre–Gauss beams

Spatially structured light has opened a wide range of opportunities for enhanced imaging as well as optical manipulation and particle confinement. Here, we show that phase-coherent illumination with superpositions of radial Laguerre–Gauss (LG) beams provides improved localization for bright optical tweezer traps, with narrowed radial and axial intensity distributions. Further, the Gouy phase shifts for sums of tightly focused radial LG fields can be exploited for phase-contrast strategies at the wavelength scale. One example developed here is the suppression of interference fringes from reflection near nanodielectric surfaces, with the promise of improved cold-atom delivery and manipulation

Reduced volume and reflection for bright optical tweezers with radial Laguerre–Gauss beams

Spatially structured light has opened a wide range of opportunities for enhanced imaging as well as optical manipulation and particle confinement. Here, we show that phase-coherent illumination with superpositions of radial Laguerre–Gauss (LG) beams provides improved localization for bright optical tweezer traps, with narrowed radial and axial intensity distributions. Further, the Gouy phase shifts for sums of tightly focused radial LG fields can be exploited for phase-contrast strategies at the wavelength scale. One example developed here is the suppression of interference fringes from reflection near nanodielectric surfaces, with the promise of improved cold-atom delivery and manipulation

An advanced apparatus for the integration of nanophotonics and cold atoms

We combine nanophotonics and cold atom research in a new apparatus enabling the delivery of single-atom tweezer arrays in the vicinity of photonic crystal waveguides

The integration of photonic crystal waveguides with atom arrays in optical tweezers

Integrating nanophotonics and cold atoms has drawn increasing interest in recent years due to diverse applications in quantum information science and the exploration of quantum many-body physics. For example, dispersion-engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of ultracold neutral atoms via interactions with guided-mode light, but also the possibility to explore the physics of strong, photon-mediated interactions between atoms, as well as atom-mediated interactions between photons. While diverse theoretical opportunities involving atoms and photons in 1-D and 2-D nanophotonic lattices have been analyzed, a grand challenge remains the experimental integration of PCWs with ultracold atoms. Here we describe an advanced apparatus that overcomes several significant barriers to current experimental progress with the goal of achieving strong quantum interactions of light and matter by way of single-atom tweezer arrays strongly coupled to photons in 1-D and 2-D PCWs. Principal technical advances relate to efficient free-space coupling of light to and from guided modes of PCWs, silicate bonding of silicon chips within small glass vacuum cells, and deterministic, mechanical delivery of single-atom tweezer arrays to the near fields of photonic crystal waveguides

Selective κ Opioid Antagonists nor-BNI, GNTI and JDTic Have Low Affinities for Non-Opioid Receptors and Transporters

Background: Nor-BNI, GNTI and JDTic induce selective κ opioid antagonism that is delayed and extremely prolonged, but some other effects are of rapid onset and brief duration. The transient effects of these compounds differ, suggesting that some of them may be mediated by other targets. Results: In binding assays, the three antagonists showed no detectable affinity (Ki≥10 µM) for most non-opioid receptors and transporters (26 of 43 tested). There was no non-opioid target for which all three compounds shared detectable affinity, or for which any two shared sub-micromolar affinity. All three compounds showed low nanomolar affinity for κ opioid receptors, with moderate selectivity over μ and δ (3 to 44-fold). Nor-BNI bound weakly to the α2C-adrenoceptor (Ki = 630 nM). GNTI enhanced calcium mobilization by noradrenaline at the α1A-adrenoceptor (EC50 = 41 nM), but did not activate the receptor, displace radioligands, or enhance PI hydrolysis. This suggests that it is a functionally-selective allosteric enhancer. GNTI was also a weak M1 receptor antagonist (KB = 3.7 µM). JDTic bound to the noradrenaline transporter (Ki = 54 nM), but only weakly inhibited transport (IC50 = 1.1 µM). JDTic also bound to the opioid-like receptor NOP (Ki = 12 nM), but gave little antagonism even at 30 µM. All three compounds exhibited rapid permeation and active efflux across Caco-2 cell monolayers. Conclusions: Across 43 non-opioid CNS targets, only GNTI exhibited a potent functional effect (allosteric enhancement of α1A-adrenoceptors). This may contribute to GNTI's severe transient effects. Plasma concentrations of nor-BNI and GNTI may be high enough to affect some peripheral non-opioid targets. Nonetheless, κ opioid antagonism persists for weeks or months after these transient effects dissipate. With an adequate pre-administration interval, our results therefore strengthen the evidence that nor-BNI, GNTI and JDTic are highly selective κ opioid antagonists